Convert files to Unix EOL
Sébastien Villemot
parent
c079ace8c3
commit
02efbd31a8
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@ -1,53 +1,53 @@
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% computes the steady state of fs2000 analyticaly
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% largely inspired by the program of F. Schorfheide
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function [ys,check] = fs2000ns_steadystate(ys,exe)
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global M_
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alp = M_.params(1);
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bet = M_.params(2);
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gam = M_.params(3);
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mst = M_.params(4);
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rho = M_.params(5);
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psi = M_.params(6);
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del = M_.params(7);
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check = 0;
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dA = exp(gam);
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gst = 1/dA;
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m = mst;
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khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
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xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
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nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
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n = xist/(nust+xist);
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P = xist + nust;
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k = khst*n;
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l = psi*mst*n/( (1-psi)*(1-n) );
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c = mst/P;
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d = l - mst + 1;
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y = k^alp*n^(1-alp)*gst^alp;
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R = mst/bet;
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W = l/n;
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ist = y-c;
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q = 1 - d;
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e = 1;
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P_obs = 1;
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Y_obs = 1;
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ys =[
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m
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P
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c
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e
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W
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R
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k
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d
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n
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l
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Y_obs
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P_obs
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y
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% computes the steady state of fs2000 analyticaly
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% largely inspired by the program of F. Schorfheide
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function [ys,check] = fs2000ns_steadystate(ys,exe)
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global M_
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alp = M_.params(1);
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bet = M_.params(2);
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gam = M_.params(3);
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mst = M_.params(4);
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rho = M_.params(5);
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psi = M_.params(6);
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del = M_.params(7);
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check = 0;
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dA = exp(gam);
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gst = 1/dA;
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m = mst;
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khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
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xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
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nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
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n = xist/(nust+xist);
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P = xist + nust;
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k = khst*n;
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l = psi*mst*n/( (1-psi)*(1-n) );
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c = mst/P;
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d = l - mst + 1;
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y = k^alp*n^(1-alp)*gst^alp;
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R = mst/bet;
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W = l/n;
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ist = y-c;
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q = 1 - d;
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e = 1;
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P_obs = 1;
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Y_obs = 1;
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ys =[
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m
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P
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c
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e
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W
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R
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k
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d
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n
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l
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Y_obs
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P_obs
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y
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dA ];
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@ -1,210 +1,210 @@
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data_q = [
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18.02 1474.5 150.2
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17.94 1538.2 150.9
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18.01 1584.5 151.4
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18.42 1644.1 152
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18.73 1678.6 152.7
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19.46 1693.1 153.3
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19.55 1724 153.9
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19.56 1758.2 154.7
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19.79 1760.6 155.4
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19.77 1779.2 156
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19.82 1778.8 156.6
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20.03 1790.9 157.3
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20.12 1846 158
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20.1 1882.6 158.6
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20.14 1897.3 159.2
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20.22 1887.4 160
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20.27 1858.2 160.7
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20.34 1849.9 161.4
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20.39 1848.5 162
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20.42 1868.9 162.8
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20.47 1905.6 163.6
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20.56 1959.6 164.3
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20.62 1994.4 164.9
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20.78 2020.1 165.7
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21 2030.5 166.5
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21.2 2023.6 167.2
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21.33 2037.7 167.9
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21.62 2033.4 168.7
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21.71 2066.2 169.5
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22.01 2077.5 170.2
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22.15 2071.9 170.9
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22.27 2094 171.7
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22.29 2070.8 172.5
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22.56 2012.6 173.1
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22.64 2024.7 173.8
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22.77 2072.3 174.5
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22.88 2120.6 175.3
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22.92 2165 176.045
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22.91 2223.3 176.727
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22.94 2221.4 177.481
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23.03 2230.95 178.268
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23.13 2279.22 179.694
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23.22 2265.48 180.335
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23.32 2268.29 181.094
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23.4 2238.57 181.915
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23.45 2251.68 182.634
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23.51 2292.02 183.337
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23.56 2332.61 184.103
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23.63 2381.01 184.894
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23.75 2422.59 185.553
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23.81 2448.01 186.203
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23.87 2471.86 186.926
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23.94 2476.67 187.68
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24 2508.7 188.299
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24.07 2538.05 188.906
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24.12 2586.26 189.631
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24.29 2604.62 190.362
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24.35 2666.69 190.954
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24.41 2697.54 191.56
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24.52 2729.63 192.256
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24.64 2739.75 192.938
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24.77 2808.88 193.467
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24.88 2846.34 193.994
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25.01 2898.79 194.647
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25.17 2970.48 195.279
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25.32 3042.35 195.763
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25.53 3055.53 196.277
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25.79 3076.51 196.877
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26.02 3102.36 197.481
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26.14 3127.15 197.967
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26.31 3129.53 198.455
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26.6 3154.19 199.012
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26.9 3177.98 199.572
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27.21 3236.18 199.995
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27.49 3292.07 200.452
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27.75 3316.11 200.997
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28.12 3331.22 201.538
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28.39 3381.86 201.955
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28.73 3390.23 202.419
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||||
29.14 3409.65 202.986
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29.51 3392.6 203.584
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29.94 3386.49 204.086
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30.36 3391.61 204.721
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30.61 3422.95 205.419
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31.02 3389.36 206.13
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31.5 3481.4 206.763
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31.93 3500.95 207.362
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32.27 3523.8 208
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32.54 3533.79 208.642
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33.02 3604.73 209.142
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33.2 3687.9 209.637
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33.49 3726.18 210.181
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33.95 3790.44 210.737
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34.36 3892.22 211.192
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||||
34.94 3919.01 211.663
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35.61 3907.08 212.191
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36.29 3947.11 212.708
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37.01 3908.15 213.144
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37.79 3922.57 213.602
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38.96 3879.98 214.147
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40.13 3854.13 214.7
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41.05 3800.93 215.135
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41.66 3835.21 215.652
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42.41 3907.02 216.289
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43.19 3952.48 216.848
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43.69 4044.59 217.314
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44.15 4072.19 217.776
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44.77 4088.49 218.338
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||||
45.57 4126.39 218.917
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46.32 4176.28 219.427
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47.07 4260.08 219.956
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47.66 4329.46 220.573
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48.63 4328.33 221.201
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||||
49.42 4345.51 221.719
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50.41 4510.73 222.281
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51.27 4552.14 222.933
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52.35 4603.65 223.583
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53.51 4605.65 224.152
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54.65 4615.64 224.737
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55.82 4644.93 225.418
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56.92 4656.23 226.117
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58.18 4678.96 226.754
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59.55 4566.62 227.389
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61.01 4562.25 228.07
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62.59 4651.86 228.689
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64.15 4739.16 229.155
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65.37 4696.82 229.674
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66.65 4753.02 230.301
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67.87 4693.76 230.903
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68.86 4615.89 231.395
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69.72 4634.88 231.906
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70.66 4612.08 232.498
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||||
71.44 4618.26 233.074
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||||
72.08 4662.97 233.546
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||||
72.83 4763.57 234.028
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73.48 4849 234.603
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||||
74.19 4939.23 235.153
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||||
75.02 5053.56 235.605
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||||
75.58 5132.87 236.082
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||||
76.25 5170.34 236.657
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76.81 5203.68 237.232
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||||
77.63 5257.26 237.673
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78.25 5283.73 238.176
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78.76 5359.6 238.789
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79.45 5393.57 239.387
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79.81 5460.83 239.861
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80.22 5466.95 240.368
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||||
80.84 5496.29 240.962
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81.45 5526.77 241.539
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82.09 5561.8 242.009
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82.68 5618 242.52
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83.33 5667.39 243.12
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||||
84.09 5750.57 243.721
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||||
84.67 5785.29 244.208
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||||
85.56 5844.05 244.716
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||||
86.66 5878.7 245.354
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||||
87.44 5952.83 245.966
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||||
88.45 6010.96 246.46
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||||
89.39 6055.61 247.017
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||||
90.13 6087.96 247.698
|
||||
90.88 6093.51 248.374
|
||||
92 6152.59 248.928
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||||
93.18 6171.57 249.564
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||||
94.14 6142.1 250.299
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||||
95.11 6078.96 251.031
|
||||
96.27 6047.49 251.65
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||||
97 6074.66 252.295
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||||
97.7 6090.14 253.033
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||||
98.31 6105.25 253.743
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99.13 6175.69 254.338
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||||
99.79 6214.22 255.032
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||||
100.17 6260.74 255.815
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||||
100.88 6327.12 256.543
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||||
101.84 6327.93 257.151
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||||
102.35 6359.9 257.785
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||||
102.83 6393.5 258.516
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103.51 6476.86 259.191
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||||
104.13 6524.5 259.738
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||||
104.71 6600.31 260.351
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105.39 6629.47 261.04
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106.09 6688.61 261.692
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106.75 6717.46 262.236
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107.24 6724.2 262.847
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107.75 6779.53 263.527
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108.29 6825.8 264.169
|
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108.91 6882 264.681
|
||||
109.24 6983.91 265.258
|
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109.74 7020 265.887
|
||||
110.23 7093.12 266.491
|
||||
111 7166.68 266.987
|
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111.43 7236.5 267.545
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111.76 7311.24 268.171
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112.08 7364.63 268.815
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];
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%GDPD GDPQ GPOP
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series = zeros(193,2);
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series(:,2) = data_q(:,1);
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series(:,1) = 1000*data_q(:,2)./data_q(:,3);
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Y_obs = series(:,1);
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P_obs = series(:,2);
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series = series(2:193,:)./series(1:192,:);
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gy_obs = series(:,1);
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gp_obs = series(:,2);
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data_q = [
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18.02 1474.5 150.2
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17.94 1538.2 150.9
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18.01 1584.5 151.4
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18.42 1644.1 152
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18.73 1678.6 152.7
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19.46 1693.1 153.3
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19.55 1724 153.9
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19.56 1758.2 154.7
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19.79 1760.6 155.4
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19.77 1779.2 156
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19.82 1778.8 156.6
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20.03 1790.9 157.3
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20.12 1846 158
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20.1 1882.6 158.6
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20.14 1897.3 159.2
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20.22 1887.4 160
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20.27 1858.2 160.7
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20.34 1849.9 161.4
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20.39 1848.5 162
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20.42 1868.9 162.8
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20.47 1905.6 163.6
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20.56 1959.6 164.3
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20.62 1994.4 164.9
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20.78 2020.1 165.7
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21 2030.5 166.5
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21.2 2023.6 167.2
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||||
21.33 2037.7 167.9
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||||
21.62 2033.4 168.7
|
||||
21.71 2066.2 169.5
|
||||
22.01 2077.5 170.2
|
||||
22.15 2071.9 170.9
|
||||
22.27 2094 171.7
|
||||
22.29 2070.8 172.5
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22.56 2012.6 173.1
|
||||
22.64 2024.7 173.8
|
||||
22.77 2072.3 174.5
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||||
22.88 2120.6 175.3
|
||||
22.92 2165 176.045
|
||||
22.91 2223.3 176.727
|
||||
22.94 2221.4 177.481
|
||||
23.03 2230.95 178.268
|
||||
23.13 2279.22 179.694
|
||||
23.22 2265.48 180.335
|
||||
23.32 2268.29 181.094
|
||||
23.4 2238.57 181.915
|
||||
23.45 2251.68 182.634
|
||||
23.51 2292.02 183.337
|
||||
23.56 2332.61 184.103
|
||||
23.63 2381.01 184.894
|
||||
23.75 2422.59 185.553
|
||||
23.81 2448.01 186.203
|
||||
23.87 2471.86 186.926
|
||||
23.94 2476.67 187.68
|
||||
24 2508.7 188.299
|
||||
24.07 2538.05 188.906
|
||||
24.12 2586.26 189.631
|
||||
24.29 2604.62 190.362
|
||||
24.35 2666.69 190.954
|
||||
24.41 2697.54 191.56
|
||||
24.52 2729.63 192.256
|
||||
24.64 2739.75 192.938
|
||||
24.77 2808.88 193.467
|
||||
24.88 2846.34 193.994
|
||||
25.01 2898.79 194.647
|
||||
25.17 2970.48 195.279
|
||||
25.32 3042.35 195.763
|
||||
25.53 3055.53 196.277
|
||||
25.79 3076.51 196.877
|
||||
26.02 3102.36 197.481
|
||||
26.14 3127.15 197.967
|
||||
26.31 3129.53 198.455
|
||||
26.6 3154.19 199.012
|
||||
26.9 3177.98 199.572
|
||||
27.21 3236.18 199.995
|
||||
27.49 3292.07 200.452
|
||||
27.75 3316.11 200.997
|
||||
28.12 3331.22 201.538
|
||||
28.39 3381.86 201.955
|
||||
28.73 3390.23 202.419
|
||||
29.14 3409.65 202.986
|
||||
29.51 3392.6 203.584
|
||||
29.94 3386.49 204.086
|
||||
30.36 3391.61 204.721
|
||||
30.61 3422.95 205.419
|
||||
31.02 3389.36 206.13
|
||||
31.5 3481.4 206.763
|
||||
31.93 3500.95 207.362
|
||||
32.27 3523.8 208
|
||||
32.54 3533.79 208.642
|
||||
33.02 3604.73 209.142
|
||||
33.2 3687.9 209.637
|
||||
33.49 3726.18 210.181
|
||||
33.95 3790.44 210.737
|
||||
34.36 3892.22 211.192
|
||||
34.94 3919.01 211.663
|
||||
35.61 3907.08 212.191
|
||||
36.29 3947.11 212.708
|
||||
37.01 3908.15 213.144
|
||||
37.79 3922.57 213.602
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38.96 3879.98 214.147
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||||
40.13 3854.13 214.7
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41.05 3800.93 215.135
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41.66 3835.21 215.652
|
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42.41 3907.02 216.289
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||||
43.19 3952.48 216.848
|
||||
43.69 4044.59 217.314
|
||||
44.15 4072.19 217.776
|
||||
44.77 4088.49 218.338
|
||||
45.57 4126.39 218.917
|
||||
46.32 4176.28 219.427
|
||||
47.07 4260.08 219.956
|
||||
47.66 4329.46 220.573
|
||||
48.63 4328.33 221.201
|
||||
49.42 4345.51 221.719
|
||||
50.41 4510.73 222.281
|
||||
51.27 4552.14 222.933
|
||||
52.35 4603.65 223.583
|
||||
53.51 4605.65 224.152
|
||||
54.65 4615.64 224.737
|
||||
55.82 4644.93 225.418
|
||||
56.92 4656.23 226.117
|
||||
58.18 4678.96 226.754
|
||||
59.55 4566.62 227.389
|
||||
61.01 4562.25 228.07
|
||||
62.59 4651.86 228.689
|
||||
64.15 4739.16 229.155
|
||||
65.37 4696.82 229.674
|
||||
66.65 4753.02 230.301
|
||||
67.87 4693.76 230.903
|
||||
68.86 4615.89 231.395
|
||||
69.72 4634.88 231.906
|
||||
70.66 4612.08 232.498
|
||||
71.44 4618.26 233.074
|
||||
72.08 4662.97 233.546
|
||||
72.83 4763.57 234.028
|
||||
73.48 4849 234.603
|
||||
74.19 4939.23 235.153
|
||||
75.02 5053.56 235.605
|
||||
75.58 5132.87 236.082
|
||||
76.25 5170.34 236.657
|
||||
76.81 5203.68 237.232
|
||||
77.63 5257.26 237.673
|
||||
78.25 5283.73 238.176
|
||||
78.76 5359.6 238.789
|
||||
79.45 5393.57 239.387
|
||||
79.81 5460.83 239.861
|
||||
80.22 5466.95 240.368
|
||||
80.84 5496.29 240.962
|
||||
81.45 5526.77 241.539
|
||||
82.09 5561.8 242.009
|
||||
82.68 5618 242.52
|
||||
83.33 5667.39 243.12
|
||||
84.09 5750.57 243.721
|
||||
84.67 5785.29 244.208
|
||||
85.56 5844.05 244.716
|
||||
86.66 5878.7 245.354
|
||||
87.44 5952.83 245.966
|
||||
88.45 6010.96 246.46
|
||||
89.39 6055.61 247.017
|
||||
90.13 6087.96 247.698
|
||||
90.88 6093.51 248.374
|
||||
92 6152.59 248.928
|
||||
93.18 6171.57 249.564
|
||||
94.14 6142.1 250.299
|
||||
95.11 6078.96 251.031
|
||||
96.27 6047.49 251.65
|
||||
97 6074.66 252.295
|
||||
97.7 6090.14 253.033
|
||||
98.31 6105.25 253.743
|
||||
99.13 6175.69 254.338
|
||||
99.79 6214.22 255.032
|
||||
100.17 6260.74 255.815
|
||||
100.88 6327.12 256.543
|
||||
101.84 6327.93 257.151
|
||||
102.35 6359.9 257.785
|
||||
102.83 6393.5 258.516
|
||||
103.51 6476.86 259.191
|
||||
104.13 6524.5 259.738
|
||||
104.71 6600.31 260.351
|
||||
105.39 6629.47 261.04
|
||||
106.09 6688.61 261.692
|
||||
106.75 6717.46 262.236
|
||||
107.24 6724.2 262.847
|
||||
107.75 6779.53 263.527
|
||||
108.29 6825.8 264.169
|
||||
108.91 6882 264.681
|
||||
109.24 6983.91 265.258
|
||||
109.74 7020 265.887
|
||||
110.23 7093.12 266.491
|
||||
111 7166.68 266.987
|
||||
111.43 7236.5 267.545
|
||||
111.76 7311.24 268.171
|
||||
112.08 7364.63 268.815
|
||||
];
|
||||
%GDPD GDPQ GPOP
|
||||
|
||||
series = zeros(193,2);
|
||||
series(:,2) = data_q(:,1);
|
||||
series(:,1) = 1000*data_q(:,2)./data_q(:,3);
|
||||
|
||||
Y_obs = series(:,1);
|
||||
P_obs = series(:,2);
|
||||
|
||||
series = series(2:193,:)./series(1:192,:);
|
||||
|
||||
gy_obs = series(:,1);
|
||||
gp_obs = series(:,2);
|
||||
|
||||
ti = [1950:0.25:1997.75];
|
||||
|
|
@ -1,157 +1,157 @@
|
|||
function [dr,ys,info]=discretionary_policy_1(oo_,Instruments)
|
||||
|
||||
% Copyright (C) 2007-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
global M_ options_
|
||||
persistent Hold
|
||||
|
||||
options_ = set_default_option(options_,'qz_criterium',1.000001);
|
||||
options_ = set_default_option(options_,'solve_maxit',3000);
|
||||
|
||||
% safeguard against issues like running ramsey policy first and then running discretion
|
||||
if isfield(M_,'orig_model')
|
||||
orig_model = M_.orig_model;
|
||||
M_.endo_nbr = orig_model.endo_nbr;
|
||||
M_.endo_names = orig_model.endo_names;
|
||||
M_.lead_lag_incidence = orig_model.lead_lag_incidence;
|
||||
M_.maximum_lead = orig_model.maximum_lead;
|
||||
M_.maximum_endo_lead = orig_model.maximum_endo_lead;
|
||||
M_.maximum_lag = orig_model.maximum_lag;
|
||||
M_.maximum_endo_lag = orig_model.maximum_endo_lag;
|
||||
else
|
||||
M_.orig_model = M_;
|
||||
end
|
||||
|
||||
beta = get_optimal_policy_discount_factor(M_.params,M_.param_names);
|
||||
|
||||
exo_nbr = M_.exo_nbr;
|
||||
if isfield(M_,'orig_model')
|
||||
orig_model = M_.orig_model;
|
||||
endo_nbr = orig_model.endo_nbr;
|
||||
endo_names = orig_model.endo_names;
|
||||
lead_lag_incidence = orig_model.lead_lag_incidence;
|
||||
MaxLead = orig_model.maximum_lead;
|
||||
MaxLag = orig_model.maximum_lag;
|
||||
else
|
||||
endo_names = M_.endo_names;
|
||||
endo_nbr = M_.endo_nbr;
|
||||
MaxLag=M_.maximum_lag;
|
||||
MaxLead=M_.maximum_lead;
|
||||
lead_lag_incidence = M_.lead_lag_incidence;
|
||||
end
|
||||
|
||||
[U,Uy,W] = feval([M_.fname,'_objective_static'],zeros(endo_nbr,1),[], M_.params);
|
||||
if any(any(Uy~=0))
|
||||
error(['discretionary_policy: the objective function must have zero ' ...
|
||||
'first order derivatives'])
|
||||
end
|
||||
|
||||
W=reshape(W,endo_nbr,endo_nbr);
|
||||
|
||||
klen = MaxLag + MaxLead + 1;
|
||||
iyv=lead_lag_incidence';
|
||||
% Find the jacobian
|
||||
z = repmat(zeros(endo_nbr,1),1,klen);
|
||||
z = z(nonzeros(iyv)) ;
|
||||
it_ = MaxLag + 1 ;
|
||||
|
||||
if exo_nbr == 0
|
||||
oo_.exo_steady_state = [] ;
|
||||
end
|
||||
[junk,jacobia_] = feval([M_.fname '_dynamic'],z, [oo_.exo_simul ...
|
||||
oo_.exo_det_simul], M_.params, zeros(endo_nbr,1), it_);
|
||||
if any(junk~=0)
|
||||
error(['discretionary_policy: the model must be written in deviation ' ...
|
||||
'form and not have constant terms'])
|
||||
end
|
||||
|
||||
eq_nbr= size(jacobia_,1);
|
||||
instr_nbr=endo_nbr-eq_nbr;
|
||||
|
||||
instr_id=nan(instr_nbr,1);
|
||||
for j=1:instr_nbr
|
||||
vj=deblank(Instruments(j,:));
|
||||
vj_id=strmatch(vj,endo_names,'exact');
|
||||
if ~isempty(vj_id)
|
||||
instr_id(j)=vj_id;
|
||||
else
|
||||
error([mfilename,':: instrument ',vj,' not found'])
|
||||
end
|
||||
end
|
||||
|
||||
Indices={'lag','0','lead'};
|
||||
iter=1;
|
||||
for j=1:numel(Indices)
|
||||
eval(['A',Indices{j},'=zeros(eq_nbr,endo_nbr);'])
|
||||
if strcmp(Indices{j},'0')||(strcmp(Indices{j},'lag') && MaxLag)||(strcmp(Indices{j},'lead') && MaxLead)
|
||||
[junk,row,col]=find(lead_lag_incidence(iter,:));
|
||||
eval(['A',Indices{j},'(:,row)=jacobia_(:,col);'])
|
||||
iter=iter+1;
|
||||
end
|
||||
end
|
||||
B=jacobia_(:,nnz(iyv)+1:end);
|
||||
|
||||
%%% MAIN ENGINE %%%
|
||||
qz_criterium = options_.qz_criterium;
|
||||
solve_maxit = options_.solve_maxit;
|
||||
discretion_tol = options_.discretionary_tol;
|
||||
|
||||
if ~isempty(Hold)
|
||||
[H,G,info]=discretionary_policy_engine(Alag,A0,Alead,B,W,instr_id,beta,solve_maxit,discretion_tol,qz_criterium,Hold);
|
||||
else
|
||||
[H,G,info]=discretionary_policy_engine(Alag,A0,Alead,B,W,instr_id,beta,solve_maxit,discretion_tol,qz_criterium);
|
||||
end
|
||||
|
||||
if info
|
||||
dr=[];
|
||||
return
|
||||
else
|
||||
Hold=H;
|
||||
% Hold=[]; use this line if persistent command is not used.
|
||||
end
|
||||
% update the following elements
|
||||
|
||||
LLI=lead_lag_incidence;
|
||||
LLI(MaxLag,:)=any(H);
|
||||
|
||||
LLI=LLI';
|
||||
tmp=find(LLI);
|
||||
LLI(tmp)=1:numel(tmp);
|
||||
|
||||
M_.lead_lag_incidence = LLI';
|
||||
|
||||
% set the state
|
||||
dr=oo_.dr;
|
||||
dr.ys =zeros(endo_nbr,1);
|
||||
dr=set_state_space(dr,M_);
|
||||
order_var=dr.order_var;
|
||||
|
||||
T=H(order_var,order_var);
|
||||
dr.ghu=G(order_var,:);
|
||||
Selection=any(T);
|
||||
dr.ghx=T(:,Selection);
|
||||
|
||||
ys=NondistortionarySteadyState(M_);
|
||||
dr.ys=ys; % <--- dr.ys =zeros(NewEndo_nbr,1);
|
||||
|
||||
function ys=NondistortionarySteadyState(M_)
|
||||
if exist([M_.fname,'_steadystate.m'],'file')
|
||||
eval(['ys=',M_.fname,'_steadystate.m;'])
|
||||
else
|
||||
ys=zeros(M_.endo_nbr,1);
|
||||
end
|
||||
function [dr,ys,info]=discretionary_policy_1(oo_,Instruments)
|
||||
|
||||
% Copyright (C) 2007-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
global M_ options_
|
||||
persistent Hold
|
||||
|
||||
options_ = set_default_option(options_,'qz_criterium',1.000001);
|
||||
options_ = set_default_option(options_,'solve_maxit',3000);
|
||||
|
||||
% safeguard against issues like running ramsey policy first and then running discretion
|
||||
if isfield(M_,'orig_model')
|
||||
orig_model = M_.orig_model;
|
||||
M_.endo_nbr = orig_model.endo_nbr;
|
||||
M_.endo_names = orig_model.endo_names;
|
||||
M_.lead_lag_incidence = orig_model.lead_lag_incidence;
|
||||
M_.maximum_lead = orig_model.maximum_lead;
|
||||
M_.maximum_endo_lead = orig_model.maximum_endo_lead;
|
||||
M_.maximum_lag = orig_model.maximum_lag;
|
||||
M_.maximum_endo_lag = orig_model.maximum_endo_lag;
|
||||
else
|
||||
M_.orig_model = M_;
|
||||
end
|
||||
|
||||
beta = get_optimal_policy_discount_factor(M_.params,M_.param_names);
|
||||
|
||||
exo_nbr = M_.exo_nbr;
|
||||
if isfield(M_,'orig_model')
|
||||
orig_model = M_.orig_model;
|
||||
endo_nbr = orig_model.endo_nbr;
|
||||
endo_names = orig_model.endo_names;
|
||||
lead_lag_incidence = orig_model.lead_lag_incidence;
|
||||
MaxLead = orig_model.maximum_lead;
|
||||
MaxLag = orig_model.maximum_lag;
|
||||
else
|
||||
endo_names = M_.endo_names;
|
||||
endo_nbr = M_.endo_nbr;
|
||||
MaxLag=M_.maximum_lag;
|
||||
MaxLead=M_.maximum_lead;
|
||||
lead_lag_incidence = M_.lead_lag_incidence;
|
||||
end
|
||||
|
||||
[U,Uy,W] = feval([M_.fname,'_objective_static'],zeros(endo_nbr,1),[], M_.params);
|
||||
if any(any(Uy~=0))
|
||||
error(['discretionary_policy: the objective function must have zero ' ...
|
||||
'first order derivatives'])
|
||||
end
|
||||
|
||||
W=reshape(W,endo_nbr,endo_nbr);
|
||||
|
||||
klen = MaxLag + MaxLead + 1;
|
||||
iyv=lead_lag_incidence';
|
||||
% Find the jacobian
|
||||
z = repmat(zeros(endo_nbr,1),1,klen);
|
||||
z = z(nonzeros(iyv)) ;
|
||||
it_ = MaxLag + 1 ;
|
||||
|
||||
if exo_nbr == 0
|
||||
oo_.exo_steady_state = [] ;
|
||||
end
|
||||
[junk,jacobia_] = feval([M_.fname '_dynamic'],z, [oo_.exo_simul ...
|
||||
oo_.exo_det_simul], M_.params, zeros(endo_nbr,1), it_);
|
||||
if any(junk~=0)
|
||||
error(['discretionary_policy: the model must be written in deviation ' ...
|
||||
'form and not have constant terms'])
|
||||
end
|
||||
|
||||
eq_nbr= size(jacobia_,1);
|
||||
instr_nbr=endo_nbr-eq_nbr;
|
||||
|
||||
instr_id=nan(instr_nbr,1);
|
||||
for j=1:instr_nbr
|
||||
vj=deblank(Instruments(j,:));
|
||||
vj_id=strmatch(vj,endo_names,'exact');
|
||||
if ~isempty(vj_id)
|
||||
instr_id(j)=vj_id;
|
||||
else
|
||||
error([mfilename,':: instrument ',vj,' not found'])
|
||||
end
|
||||
end
|
||||
|
||||
Indices={'lag','0','lead'};
|
||||
iter=1;
|
||||
for j=1:numel(Indices)
|
||||
eval(['A',Indices{j},'=zeros(eq_nbr,endo_nbr);'])
|
||||
if strcmp(Indices{j},'0')||(strcmp(Indices{j},'lag') && MaxLag)||(strcmp(Indices{j},'lead') && MaxLead)
|
||||
[junk,row,col]=find(lead_lag_incidence(iter,:));
|
||||
eval(['A',Indices{j},'(:,row)=jacobia_(:,col);'])
|
||||
iter=iter+1;
|
||||
end
|
||||
end
|
||||
B=jacobia_(:,nnz(iyv)+1:end);
|
||||
|
||||
%%% MAIN ENGINE %%%
|
||||
qz_criterium = options_.qz_criterium;
|
||||
solve_maxit = options_.solve_maxit;
|
||||
discretion_tol = options_.discretionary_tol;
|
||||
|
||||
if ~isempty(Hold)
|
||||
[H,G,info]=discretionary_policy_engine(Alag,A0,Alead,B,W,instr_id,beta,solve_maxit,discretion_tol,qz_criterium,Hold);
|
||||
else
|
||||
[H,G,info]=discretionary_policy_engine(Alag,A0,Alead,B,W,instr_id,beta,solve_maxit,discretion_tol,qz_criterium);
|
||||
end
|
||||
|
||||
if info
|
||||
dr=[];
|
||||
return
|
||||
else
|
||||
Hold=H;
|
||||
% Hold=[]; use this line if persistent command is not used.
|
||||
end
|
||||
% update the following elements
|
||||
|
||||
LLI=lead_lag_incidence;
|
||||
LLI(MaxLag,:)=any(H);
|
||||
|
||||
LLI=LLI';
|
||||
tmp=find(LLI);
|
||||
LLI(tmp)=1:numel(tmp);
|
||||
|
||||
M_.lead_lag_incidence = LLI';
|
||||
|
||||
% set the state
|
||||
dr=oo_.dr;
|
||||
dr.ys =zeros(endo_nbr,1);
|
||||
dr=set_state_space(dr,M_);
|
||||
order_var=dr.order_var;
|
||||
|
||||
T=H(order_var,order_var);
|
||||
dr.ghu=G(order_var,:);
|
||||
Selection=any(T);
|
||||
dr.ghx=T(:,Selection);
|
||||
|
||||
ys=NondistortionarySteadyState(M_);
|
||||
dr.ys=ys; % <--- dr.ys =zeros(NewEndo_nbr,1);
|
||||
|
||||
function ys=NondistortionarySteadyState(M_)
|
||||
if exist([M_.fname,'_steadystate.m'],'file')
|
||||
eval(['ys=',M_.fname,'_steadystate.m;'])
|
||||
else
|
||||
ys=zeros(M_.endo_nbr,1);
|
||||
end
|
||||
|
|
|
|||
|
|
@ -1,299 +1,299 @@
|
|||
function [H,G,retcode]=discretionary_policy_engine(AAlag,AA0,AAlead,BB,bigw,instr_id,beta,solve_maxit,discretion_tol,qz_criterium,H00,verbose)
|
||||
|
||||
% Solves the discretionary problem for a model of the form:
|
||||
% AAlag*yy_{t-1}+AA0*yy_t+AAlead*yy_{t+1}+BB*e=0, with W the weight on the
|
||||
% variables in vector y_t and instr_id is the location of the instruments
|
||||
% in the yy_t vector.
|
||||
% We use the Dennis (2007, Macroeconomic Dynamics) algorithm and so we need
|
||||
% to re-write the model in the form
|
||||
% A0*y_t=A1*y_{t-1}+A2*y_{t+1}+A3*x_t+A4*x_{t+1}+A5*e_t, with W the
|
||||
% weight on the y_t vector and Q the weight on the x_t vector of
|
||||
% instruments.
|
||||
|
||||
% Copyright (C) 2007-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
if nargin<12
|
||||
verbose=0;
|
||||
if nargin<11
|
||||
H00=[];
|
||||
if nargin<10
|
||||
qz_criterium=1.000001;
|
||||
if nargin<9
|
||||
discretion_tol=sqrt(eps);
|
||||
if nargin<8
|
||||
solve_maxit=3000;
|
||||
if nargin<7
|
||||
beta=.99;
|
||||
if nargin<6
|
||||
error([mfilename,':: Insufficient number of input arguments'])
|
||||
elseif nargin>12
|
||||
error([mfilename,':: Number of input arguments cannot exceed 12'])
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
[A0,A1,A2,A3,A4,A5,W,Q,endo_nbr,exo_nbr,aux,endo_augm_id]=GetDennisMatrices(AAlag,AA0,AAlead,BB,bigw,instr_id);
|
||||
% aux is a logical index of the instruments which appear with lags in the
|
||||
% model. Their location in the state vector is instr_id(aux)
|
||||
% endo_augm_id is index (not logical) of locations of the augmented vector
|
||||
% of non-instrumental variables
|
||||
|
||||
AuxiliaryVariables_nbr=sum(aux);
|
||||
H0=zeros(endo_nbr+AuxiliaryVariables_nbr);
|
||||
if ~isempty(H00)
|
||||
H0(1:endo_nbr,1:endo_nbr)=H00;clear H00
|
||||
end
|
||||
|
||||
H10=H0(endo_augm_id,endo_augm_id);
|
||||
F10=H0(instr_id,endo_augm_id);
|
||||
|
||||
iter=0;
|
||||
H1=H10;
|
||||
F1=F10;
|
||||
while 1
|
||||
iter=iter+1;
|
||||
P=SylvesterDoubling(W+beta*F1'*Q*F1,beta*H1',H1,discretion_tol,solve_maxit);
|
||||
if any(any(isnan(P)))
|
||||
P=SylvesterHessenbergSchur(W+beta*F1'*Q*F1,beta*H1',H1);
|
||||
if any(any(isnan(P)))
|
||||
retcode=2;
|
||||
return
|
||||
end
|
||||
end
|
||||
D=A0-A2*H1-A4*F1;
|
||||
Dinv=inv(D);
|
||||
A3DPD=A3'*Dinv'*P*Dinv;
|
||||
F1=-(Q+A3DPD*A3)\(A3DPD*A1);
|
||||
H1=Dinv*(A1+A3*F1);
|
||||
|
||||
[rcode,NQ]=CheckConvergence([H1;F1]-[H10;F10],iter,solve_maxit,discretion_tol);
|
||||
if rcode
|
||||
break
|
||||
else
|
||||
if verbose
|
||||
disp(NQ)
|
||||
end
|
||||
end
|
||||
H10=H1;
|
||||
F10=F1;
|
||||
end
|
||||
|
||||
retcode = 0;
|
||||
switch rcode
|
||||
case 3 % nan
|
||||
retcode=63;
|
||||
retcode(2)=10000;
|
||||
if verbose
|
||||
disp([mfilename,':: NAN elements in the solution'])
|
||||
end
|
||||
case 2% maxiter
|
||||
retcode = 61
|
||||
if verbose
|
||||
disp([mfilename,':: Maximum Number of Iterations reached'])
|
||||
end
|
||||
case 1
|
||||
BadEig=max(abs(eig(H1)))>qz_criterium;
|
||||
if BadEig
|
||||
retcode=62;
|
||||
retcode(2)=100*max(abs(eig(H1)));
|
||||
if verbose
|
||||
disp([mfilename,':: Some eigenvalues greater than qz_criterium, Model potentially unstable'])
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
if retcode(1)
|
||||
H=[];
|
||||
G=[];
|
||||
else
|
||||
F2=-(Q+A3DPD*A3)\(A3DPD*A5);
|
||||
H2=Dinv*(A5+A3*F2);
|
||||
H=zeros(endo_nbr+AuxiliaryVariables_nbr);
|
||||
G=zeros(endo_nbr+AuxiliaryVariables_nbr,exo_nbr);
|
||||
H(endo_augm_id,endo_augm_id)=H1;
|
||||
H(instr_id,endo_augm_id)=F1;
|
||||
G(endo_augm_id,:)=H2;
|
||||
G(instr_id,:)=F2;
|
||||
|
||||
% Account for auxilliary variables
|
||||
H(:,instr_id(aux))=H(:,end-(AuxiliaryVariables_nbr-1:-1:0));
|
||||
H=H(1:endo_nbr,1:endo_nbr);
|
||||
G=G(1:endo_nbr,:);
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
|
||||
function [rcode,NQ]=CheckConvergence(Q,iter,MaxIter,crit)
|
||||
|
||||
NQ=max(max(abs(Q)));% norm(Q); seems too costly
|
||||
if isnan(NQ)
|
||||
rcode=3;
|
||||
elseif iter>MaxIter;
|
||||
rcode=2;
|
||||
elseif NQ<crit
|
||||
rcode=1;
|
||||
else
|
||||
rcode=0;
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function [A00,A11,A22,A33,A44,A55,WW,Q,endo_nbr,exo_nbr,aux,endo_augm_id]=GetDennisMatrices(AAlag,AA0,AAlead,BB,bigw,instr_id)
|
||||
[eq_nbr,endo_nbr]=size(AAlag);
|
||||
exo_nbr=size(BB,2);
|
||||
y=setdiff(1:endo_nbr,instr_id);
|
||||
instr_nbr=numel(instr_id);
|
||||
|
||||
A0=AA0(:,y);
|
||||
A1=-AAlag(:,y);
|
||||
A2=-AAlead(:,y);
|
||||
A3=-AA0(:,instr_id);
|
||||
A4=-AAlead(:,instr_id);
|
||||
A5=-BB;
|
||||
W=bigw(y,y);
|
||||
Q=bigw(instr_id,instr_id);
|
||||
% Adjust for possible lags in instruments by creating auxiliary equations
|
||||
A6=-AAlag(:,instr_id);
|
||||
aux=any(A6);
|
||||
AuxiliaryVariables_nbr=sum(aux);
|
||||
ny=eq_nbr;
|
||||
m=eq_nbr+AuxiliaryVariables_nbr;
|
||||
A00=zeros(m);A00(1:ny,1:ny)=A0;A00(ny+1:end,ny+1:end)=eye(AuxiliaryVariables_nbr);
|
||||
A11=zeros(m);A11(1:ny,1:ny)=A1;A11(1:ny,ny+1:end)=A6(:,aux);
|
||||
A22=zeros(m);A22(1:ny,1:ny)=A2;
|
||||
A33=zeros(m,instr_nbr);A33(1:ny,1:end)=A3;A33(ny+1:end,aux)=eye(AuxiliaryVariables_nbr);
|
||||
A44=zeros(m,instr_nbr);A44(1:ny,1:end)=A4;
|
||||
A55=zeros(m,exo_nbr);A55(1:ny,1:end)=A5;
|
||||
WW=zeros(m);WW(1:ny,1:ny)=W;
|
||||
endo_augm_id=setdiff(1:endo_nbr+AuxiliaryVariables_nbr,instr_id);
|
||||
|
||||
end
|
||||
|
||||
function v= SylvesterDoubling (d,g,h,tol,maxit)
|
||||
|
||||
% DOUBLES Solves a Sylvester equation using doubling
|
||||
%
|
||||
% [v,info] = doubles (g,d,h,tol,maxit) uses a doubling algorithm
|
||||
% to solve the Sylvester equation v = d + g v h
|
||||
|
||||
v = d;
|
||||
for i =1:maxit,
|
||||
vadd = g*v*h;
|
||||
v = v+vadd;
|
||||
if norm (vadd,1) <= (tol*norm(v,1))
|
||||
break;
|
||||
end
|
||||
g = g*g;
|
||||
h = h*h;
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function v = SylvesterHessenbergSchur(d,g,h)
|
||||
%
|
||||
% DSYLHS Solves a discrete time sylvester equation using the
|
||||
% Hessenberg-Schur algorithm
|
||||
%
|
||||
% v = DSYLHS(g,d,h) computes the matrix v that satisfies the
|
||||
% discrete time sylvester equation
|
||||
%
|
||||
% v = d + g'vh
|
||||
|
||||
if size(g,1) >= size(h,1)
|
||||
[u,gbarp] = hess(g');
|
||||
[t,hbar] = schur(h);
|
||||
[vbar] = sylvest_private(gbarp,u'*d*t,hbar,1e-15);
|
||||
v = u*vbar*t';
|
||||
else
|
||||
[u,gbar] = schur(g);
|
||||
[t,hbarp] = hess(h');
|
||||
[vbar] = sylvest_private(hbarp,t'*d'*u,gbar,1e-15);
|
||||
v = u*vbar'*t';
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
|
||||
function v = sylvest_private(g,d,h,tol)
|
||||
%
|
||||
% SYLVEST Solves a Sylvester equation
|
||||
%
|
||||
% solves the Sylvester equation
|
||||
% v = d + g v h
|
||||
% for v where both g and h must be upper block triangular.
|
||||
% The output info is zero on a successful return.
|
||||
% The input tol indicates when an element of g or h should be considered
|
||||
% zero.
|
||||
|
||||
[m,n] = size(d);
|
||||
v = zeros(m,n);
|
||||
w = eye(m);
|
||||
i = 1;
|
||||
temp = [];
|
||||
|
||||
%First handle the i = 1 case outside the loop
|
||||
|
||||
if i< n,
|
||||
if abs(h(i+1,i)) < tol,
|
||||
v(:,i)= (w - g*h(i,i))\d(:,i);
|
||||
i = i+1;
|
||||
else
|
||||
A = [w-g*h(i,i) (-g*h(i+1,i));...
|
||||
-g*h(i,i+1) w-g*h(i+1,i+1)];
|
||||
C = [d(:,i); d(:,i+1)];
|
||||
X = A\C;
|
||||
v(:,i) = X(1:m,:);
|
||||
v(:,i+1) = X(m+1:2*m, :);
|
||||
i = i+2;
|
||||
end
|
||||
end
|
||||
|
||||
%Handle the rest of the matrix with the possible exception of i=n
|
||||
|
||||
while i<n,
|
||||
b= i-1;
|
||||
temp = [temp g*v(:,size(temp,2)+1:b)]; %#ok<AGROW>
|
||||
if abs(h(i+1,i)) < tol,
|
||||
v(:,i) = (w - g*h(i,i))\(d(:,i) + temp*h(1:b,i));
|
||||
i = i+1;
|
||||
else
|
||||
A = [w - g*h(i,i) (-g*h(i+1,i)); ...
|
||||
-g*h(i,i+1) w - g*h(i+1,i+1)];
|
||||
C = [d(:,i) + temp*h(1:b,i); ...
|
||||
d(:,i+1) + temp*h(1:b,i+1)];
|
||||
X = A\C;
|
||||
v(:,i) = X(1:m,:);
|
||||
v(:,i+1) = X(m+1:2*m, :);
|
||||
i = i+2;
|
||||
end
|
||||
end
|
||||
|
||||
%Handle the i = n case if i=n was not in a 2-2 block
|
||||
|
||||
if i==n,
|
||||
b = i-1;
|
||||
temp = [temp g*v(:,size(temp,2)+1:b)];
|
||||
v(:,i) = (w-g*h(i,i))\(d(:,i) + temp*h(1:b,i));
|
||||
end
|
||||
|
||||
end
|
||||
function [H,G,retcode]=discretionary_policy_engine(AAlag,AA0,AAlead,BB,bigw,instr_id,beta,solve_maxit,discretion_tol,qz_criterium,H00,verbose)
|
||||
|
||||
% Solves the discretionary problem for a model of the form:
|
||||
% AAlag*yy_{t-1}+AA0*yy_t+AAlead*yy_{t+1}+BB*e=0, with W the weight on the
|
||||
% variables in vector y_t and instr_id is the location of the instruments
|
||||
% in the yy_t vector.
|
||||
% We use the Dennis (2007, Macroeconomic Dynamics) algorithm and so we need
|
||||
% to re-write the model in the form
|
||||
% A0*y_t=A1*y_{t-1}+A2*y_{t+1}+A3*x_t+A4*x_{t+1}+A5*e_t, with W the
|
||||
% weight on the y_t vector and Q the weight on the x_t vector of
|
||||
% instruments.
|
||||
|
||||
% Copyright (C) 2007-2012 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
if nargin<12
|
||||
verbose=0;
|
||||
if nargin<11
|
||||
H00=[];
|
||||
if nargin<10
|
||||
qz_criterium=1.000001;
|
||||
if nargin<9
|
||||
discretion_tol=sqrt(eps);
|
||||
if nargin<8
|
||||
solve_maxit=3000;
|
||||
if nargin<7
|
||||
beta=.99;
|
||||
if nargin<6
|
||||
error([mfilename,':: Insufficient number of input arguments'])
|
||||
elseif nargin>12
|
||||
error([mfilename,':: Number of input arguments cannot exceed 12'])
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
[A0,A1,A2,A3,A4,A5,W,Q,endo_nbr,exo_nbr,aux,endo_augm_id]=GetDennisMatrices(AAlag,AA0,AAlead,BB,bigw,instr_id);
|
||||
% aux is a logical index of the instruments which appear with lags in the
|
||||
% model. Their location in the state vector is instr_id(aux)
|
||||
% endo_augm_id is index (not logical) of locations of the augmented vector
|
||||
% of non-instrumental variables
|
||||
|
||||
AuxiliaryVariables_nbr=sum(aux);
|
||||
H0=zeros(endo_nbr+AuxiliaryVariables_nbr);
|
||||
if ~isempty(H00)
|
||||
H0(1:endo_nbr,1:endo_nbr)=H00;clear H00
|
||||
end
|
||||
|
||||
H10=H0(endo_augm_id,endo_augm_id);
|
||||
F10=H0(instr_id,endo_augm_id);
|
||||
|
||||
iter=0;
|
||||
H1=H10;
|
||||
F1=F10;
|
||||
while 1
|
||||
iter=iter+1;
|
||||
P=SylvesterDoubling(W+beta*F1'*Q*F1,beta*H1',H1,discretion_tol,solve_maxit);
|
||||
if any(any(isnan(P)))
|
||||
P=SylvesterHessenbergSchur(W+beta*F1'*Q*F1,beta*H1',H1);
|
||||
if any(any(isnan(P)))
|
||||
retcode=2;
|
||||
return
|
||||
end
|
||||
end
|
||||
D=A0-A2*H1-A4*F1;
|
||||
Dinv=inv(D);
|
||||
A3DPD=A3'*Dinv'*P*Dinv;
|
||||
F1=-(Q+A3DPD*A3)\(A3DPD*A1);
|
||||
H1=Dinv*(A1+A3*F1);
|
||||
|
||||
[rcode,NQ]=CheckConvergence([H1;F1]-[H10;F10],iter,solve_maxit,discretion_tol);
|
||||
if rcode
|
||||
break
|
||||
else
|
||||
if verbose
|
||||
disp(NQ)
|
||||
end
|
||||
end
|
||||
H10=H1;
|
||||
F10=F1;
|
||||
end
|
||||
|
||||
retcode = 0;
|
||||
switch rcode
|
||||
case 3 % nan
|
||||
retcode=63;
|
||||
retcode(2)=10000;
|
||||
if verbose
|
||||
disp([mfilename,':: NAN elements in the solution'])
|
||||
end
|
||||
case 2% maxiter
|
||||
retcode = 61
|
||||
if verbose
|
||||
disp([mfilename,':: Maximum Number of Iterations reached'])
|
||||
end
|
||||
case 1
|
||||
BadEig=max(abs(eig(H1)))>qz_criterium;
|
||||
if BadEig
|
||||
retcode=62;
|
||||
retcode(2)=100*max(abs(eig(H1)));
|
||||
if verbose
|
||||
disp([mfilename,':: Some eigenvalues greater than qz_criterium, Model potentially unstable'])
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
if retcode(1)
|
||||
H=[];
|
||||
G=[];
|
||||
else
|
||||
F2=-(Q+A3DPD*A3)\(A3DPD*A5);
|
||||
H2=Dinv*(A5+A3*F2);
|
||||
H=zeros(endo_nbr+AuxiliaryVariables_nbr);
|
||||
G=zeros(endo_nbr+AuxiliaryVariables_nbr,exo_nbr);
|
||||
H(endo_augm_id,endo_augm_id)=H1;
|
||||
H(instr_id,endo_augm_id)=F1;
|
||||
G(endo_augm_id,:)=H2;
|
||||
G(instr_id,:)=F2;
|
||||
|
||||
% Account for auxilliary variables
|
||||
H(:,instr_id(aux))=H(:,end-(AuxiliaryVariables_nbr-1:-1:0));
|
||||
H=H(1:endo_nbr,1:endo_nbr);
|
||||
G=G(1:endo_nbr,:);
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
|
||||
function [rcode,NQ]=CheckConvergence(Q,iter,MaxIter,crit)
|
||||
|
||||
NQ=max(max(abs(Q)));% norm(Q); seems too costly
|
||||
if isnan(NQ)
|
||||
rcode=3;
|
||||
elseif iter>MaxIter;
|
||||
rcode=2;
|
||||
elseif NQ<crit
|
||||
rcode=1;
|
||||
else
|
||||
rcode=0;
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function [A00,A11,A22,A33,A44,A55,WW,Q,endo_nbr,exo_nbr,aux,endo_augm_id]=GetDennisMatrices(AAlag,AA0,AAlead,BB,bigw,instr_id)
|
||||
[eq_nbr,endo_nbr]=size(AAlag);
|
||||
exo_nbr=size(BB,2);
|
||||
y=setdiff(1:endo_nbr,instr_id);
|
||||
instr_nbr=numel(instr_id);
|
||||
|
||||
A0=AA0(:,y);
|
||||
A1=-AAlag(:,y);
|
||||
A2=-AAlead(:,y);
|
||||
A3=-AA0(:,instr_id);
|
||||
A4=-AAlead(:,instr_id);
|
||||
A5=-BB;
|
||||
W=bigw(y,y);
|
||||
Q=bigw(instr_id,instr_id);
|
||||
% Adjust for possible lags in instruments by creating auxiliary equations
|
||||
A6=-AAlag(:,instr_id);
|
||||
aux=any(A6);
|
||||
AuxiliaryVariables_nbr=sum(aux);
|
||||
ny=eq_nbr;
|
||||
m=eq_nbr+AuxiliaryVariables_nbr;
|
||||
A00=zeros(m);A00(1:ny,1:ny)=A0;A00(ny+1:end,ny+1:end)=eye(AuxiliaryVariables_nbr);
|
||||
A11=zeros(m);A11(1:ny,1:ny)=A1;A11(1:ny,ny+1:end)=A6(:,aux);
|
||||
A22=zeros(m);A22(1:ny,1:ny)=A2;
|
||||
A33=zeros(m,instr_nbr);A33(1:ny,1:end)=A3;A33(ny+1:end,aux)=eye(AuxiliaryVariables_nbr);
|
||||
A44=zeros(m,instr_nbr);A44(1:ny,1:end)=A4;
|
||||
A55=zeros(m,exo_nbr);A55(1:ny,1:end)=A5;
|
||||
WW=zeros(m);WW(1:ny,1:ny)=W;
|
||||
endo_augm_id=setdiff(1:endo_nbr+AuxiliaryVariables_nbr,instr_id);
|
||||
|
||||
end
|
||||
|
||||
function v= SylvesterDoubling (d,g,h,tol,maxit)
|
||||
|
||||
% DOUBLES Solves a Sylvester equation using doubling
|
||||
%
|
||||
% [v,info] = doubles (g,d,h,tol,maxit) uses a doubling algorithm
|
||||
% to solve the Sylvester equation v = d + g v h
|
||||
|
||||
v = d;
|
||||
for i =1:maxit,
|
||||
vadd = g*v*h;
|
||||
v = v+vadd;
|
||||
if norm (vadd,1) <= (tol*norm(v,1))
|
||||
break;
|
||||
end
|
||||
g = g*g;
|
||||
h = h*h;
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function v = SylvesterHessenbergSchur(d,g,h)
|
||||
%
|
||||
% DSYLHS Solves a discrete time sylvester equation using the
|
||||
% Hessenberg-Schur algorithm
|
||||
%
|
||||
% v = DSYLHS(g,d,h) computes the matrix v that satisfies the
|
||||
% discrete time sylvester equation
|
||||
%
|
||||
% v = d + g'vh
|
||||
|
||||
if size(g,1) >= size(h,1)
|
||||
[u,gbarp] = hess(g');
|
||||
[t,hbar] = schur(h);
|
||||
[vbar] = sylvest_private(gbarp,u'*d*t,hbar,1e-15);
|
||||
v = u*vbar*t';
|
||||
else
|
||||
[u,gbar] = schur(g);
|
||||
[t,hbarp] = hess(h');
|
||||
[vbar] = sylvest_private(hbarp,t'*d'*u,gbar,1e-15);
|
||||
v = u*vbar'*t';
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
|
||||
function v = sylvest_private(g,d,h,tol)
|
||||
%
|
||||
% SYLVEST Solves a Sylvester equation
|
||||
%
|
||||
% solves the Sylvester equation
|
||||
% v = d + g v h
|
||||
% for v where both g and h must be upper block triangular.
|
||||
% The output info is zero on a successful return.
|
||||
% The input tol indicates when an element of g or h should be considered
|
||||
% zero.
|
||||
|
||||
[m,n] = size(d);
|
||||
v = zeros(m,n);
|
||||
w = eye(m);
|
||||
i = 1;
|
||||
temp = [];
|
||||
|
||||
%First handle the i = 1 case outside the loop
|
||||
|
||||
if i< n,
|
||||
if abs(h(i+1,i)) < tol,
|
||||
v(:,i)= (w - g*h(i,i))\d(:,i);
|
||||
i = i+1;
|
||||
else
|
||||
A = [w-g*h(i,i) (-g*h(i+1,i));...
|
||||
-g*h(i,i+1) w-g*h(i+1,i+1)];
|
||||
C = [d(:,i); d(:,i+1)];
|
||||
X = A\C;
|
||||
v(:,i) = X(1:m,:);
|
||||
v(:,i+1) = X(m+1:2*m, :);
|
||||
i = i+2;
|
||||
end
|
||||
end
|
||||
|
||||
%Handle the rest of the matrix with the possible exception of i=n
|
||||
|
||||
while i<n,
|
||||
b= i-1;
|
||||
temp = [temp g*v(:,size(temp,2)+1:b)]; %#ok<AGROW>
|
||||
if abs(h(i+1,i)) < tol,
|
||||
v(:,i) = (w - g*h(i,i))\(d(:,i) + temp*h(1:b,i));
|
||||
i = i+1;
|
||||
else
|
||||
A = [w - g*h(i,i) (-g*h(i+1,i)); ...
|
||||
-g*h(i,i+1) w - g*h(i+1,i+1)];
|
||||
C = [d(:,i) + temp*h(1:b,i); ...
|
||||
d(:,i+1) + temp*h(1:b,i+1)];
|
||||
X = A\C;
|
||||
v(:,i) = X(1:m,:);
|
||||
v(:,i+1) = X(m+1:2*m, :);
|
||||
i = i+2;
|
||||
end
|
||||
end
|
||||
|
||||
%Handle the i = n case if i=n was not in a 2-2 block
|
||||
|
||||
if i==n,
|
||||
b = i-1;
|
||||
temp = [temp g*v(:,size(temp,2)+1:b)];
|
||||
v(:,i) = (w-g*h(i,i))\(d(:,i) + temp*h(1:b,i));
|
||||
end
|
||||
|
||||
end
|
||||
|
|
|
|||
|
|
@ -1,102 +1,102 @@
|
|||
function [pars, cosnJ] = ident_bruteforce(J,n,TeX, pnames_TeX)
|
||||
% function [pars, cosnJ] = ident_bruteforce(J,n,TeX, pnames_TeX)
|
||||
%
|
||||
% given the Jacobian matrix J of moment derivatives w.r.t. parameters
|
||||
% computes, for each column of J, the groups of columns from 1 to n that
|
||||
% can repliate at best the derivatives of that column
|
||||
%
|
||||
% OUTPUTS
|
||||
% pars : cell array with groupf of params for each column of J for 1 to n
|
||||
% cosnJ : the cosn of each column with the selected group of columns
|
||||
|
||||
% Copyright (C) 2009-2011 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licen
|
||||
global M_ options_
|
||||
|
||||
OutputDirectoryName = CheckPath('Identification',M_.dname);
|
||||
|
||||
k = size(J,2); % number of parameters
|
||||
|
||||
if nargin<2 || isempty(n)
|
||||
n = 4; % max n-tuple
|
||||
end
|
||||
if nargin<3 || isempty(TeX)
|
||||
TeX = 0; % max n-tuple
|
||||
end
|
||||
|
||||
cosnJ=zeros(k,n);
|
||||
pars{k,n}=[];
|
||||
for ll = 1:n,
|
||||
h = dyn_waitbar(0,['Brute force collinearity for ' int2str(ll) ' parameters.']);
|
||||
for ii = 1:k
|
||||
tmp = find([1:k]~=ii);
|
||||
tmp2 = nchoosek(tmp,ll);
|
||||
cosnJ2=zeros(size(tmp2,1),1);
|
||||
b=[];
|
||||
for jj = 1:size(tmp2,1)
|
||||
[cosnJ2(jj,1), b(:,jj)] = cosn([J(:,ii),J(:,tmp2(jj,:))]);
|
||||
end
|
||||
cosnJ(ii,ll) = max(cosnJ2(:,1));
|
||||
if cosnJ(ii,ll)>1.e-8,
|
||||
if ll>1 && ((cosnJ(ii,ll)-cosnJ(ii,ll-1))<1.e-8),
|
||||
pars{ii,ll} = [pars{ii,ll-1} NaN];
|
||||
cosnJ(ii,ll) = cosnJ(ii,ll-1);
|
||||
else
|
||||
pars{ii,ll} = tmp2(find(cosnJ2(:,1)==max(cosnJ2(:,1))),:);
|
||||
end
|
||||
else
|
||||
pars{ii,ll} = NaN(1,ll);
|
||||
end
|
||||
dyn_waitbar(ii/k,h)
|
||||
end
|
||||
dyn_waitbar_close(h);
|
||||
if TeX
|
||||
filename = [OutputDirectoryName '/' M_.fname '_collinearity_patterns' int2str(ll) '.TeX'];
|
||||
fidTeX = fopen(filename,'w');
|
||||
fprintf(fidTeX,'%% TeX-table generated by ident_bruteforce (Dynare).\n');
|
||||
fprintf(fidTeX,['%% Collinearity patterns with ',int2str(ll),' parameter(s)\n']);
|
||||
fprintf(fidTeX,['%% ' datestr(now,0)]);
|
||||
fprintf(fidTeX,' \n');
|
||||
fprintf(fidTeX,' \n');
|
||||
fprintf(fidTeX,'{\\tiny \n');
|
||||
fprintf(fidTeX,'\\begin{table}\n');
|
||||
fprintf(fidTeX,'\\centering\n');
|
||||
fprintf(fidTeX,'\\begin{tabular}{l|lc} \n');
|
||||
fprintf(fidTeX,'\\hline\\hline \\\\ \n');
|
||||
fprintf(fidTeX,' Parameter & Explanatory & cosn \\\\ \n');
|
||||
fprintf(fidTeX,' & parameter(s) & \\\\ \n');
|
||||
fprintf(fidTeX,'\\hline \\\\ \n');
|
||||
for i=1:k,
|
||||
plist='';
|
||||
for ii=1:ll,
|
||||
plist = [plist ' $' pnames_TeX(pars{i,ll}(ii),:) '$ '];
|
||||
end
|
||||
fprintf(fidTeX,'$%s$ & [%s] & %7.3f \\\\ \n',...
|
||||
pnames_TeX(i,:),...
|
||||
plist,...
|
||||
cosnJ(i,ll));
|
||||
end
|
||||
fprintf(fidTeX,'\\hline\\hline \n');
|
||||
fprintf(fidTeX,'\\end{tabular}\n ');
|
||||
fprintf(fidTeX,['\\caption{Collinearity patterns with ',int2str(ll),' parameter(s)}\n ']);
|
||||
fprintf(fidTeX,['\\label{Table:CollinearityPatterns:',int2str(ll),'}\n']);
|
||||
fprintf(fidTeX,'\\end{table}\n');
|
||||
fprintf(fidTeX,'} \n');
|
||||
fprintf(fidTeX,'%% End of TeX file.\n');
|
||||
fclose(fidTeX);
|
||||
end
|
||||
function [pars, cosnJ] = ident_bruteforce(J,n,TeX, pnames_TeX)
|
||||
% function [pars, cosnJ] = ident_bruteforce(J,n,TeX, pnames_TeX)
|
||||
%
|
||||
% given the Jacobian matrix J of moment derivatives w.r.t. parameters
|
||||
% computes, for each column of J, the groups of columns from 1 to n that
|
||||
% can repliate at best the derivatives of that column
|
||||
%
|
||||
% OUTPUTS
|
||||
% pars : cell array with groupf of params for each column of J for 1 to n
|
||||
% cosnJ : the cosn of each column with the selected group of columns
|
||||
|
||||
% Copyright (C) 2009-2011 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licen
|
||||
global M_ options_
|
||||
|
||||
OutputDirectoryName = CheckPath('Identification',M_.dname);
|
||||
|
||||
k = size(J,2); % number of parameters
|
||||
|
||||
if nargin<2 || isempty(n)
|
||||
n = 4; % max n-tuple
|
||||
end
|
||||
if nargin<3 || isempty(TeX)
|
||||
TeX = 0; % max n-tuple
|
||||
end
|
||||
|
||||
cosnJ=zeros(k,n);
|
||||
pars{k,n}=[];
|
||||
for ll = 1:n,
|
||||
h = dyn_waitbar(0,['Brute force collinearity for ' int2str(ll) ' parameters.']);
|
||||
for ii = 1:k
|
||||
tmp = find([1:k]~=ii);
|
||||
tmp2 = nchoosek(tmp,ll);
|
||||
cosnJ2=zeros(size(tmp2,1),1);
|
||||
b=[];
|
||||
for jj = 1:size(tmp2,1)
|
||||
[cosnJ2(jj,1), b(:,jj)] = cosn([J(:,ii),J(:,tmp2(jj,:))]);
|
||||
end
|
||||
cosnJ(ii,ll) = max(cosnJ2(:,1));
|
||||
if cosnJ(ii,ll)>1.e-8,
|
||||
if ll>1 && ((cosnJ(ii,ll)-cosnJ(ii,ll-1))<1.e-8),
|
||||
pars{ii,ll} = [pars{ii,ll-1} NaN];
|
||||
cosnJ(ii,ll) = cosnJ(ii,ll-1);
|
||||
else
|
||||
pars{ii,ll} = tmp2(find(cosnJ2(:,1)==max(cosnJ2(:,1))),:);
|
||||
end
|
||||
else
|
||||
pars{ii,ll} = NaN(1,ll);
|
||||
end
|
||||
dyn_waitbar(ii/k,h)
|
||||
end
|
||||
dyn_waitbar_close(h);
|
||||
if TeX
|
||||
filename = [OutputDirectoryName '/' M_.fname '_collinearity_patterns' int2str(ll) '.TeX'];
|
||||
fidTeX = fopen(filename,'w');
|
||||
fprintf(fidTeX,'%% TeX-table generated by ident_bruteforce (Dynare).\n');
|
||||
fprintf(fidTeX,['%% Collinearity patterns with ',int2str(ll),' parameter(s)\n']);
|
||||
fprintf(fidTeX,['%% ' datestr(now,0)]);
|
||||
fprintf(fidTeX,' \n');
|
||||
fprintf(fidTeX,' \n');
|
||||
fprintf(fidTeX,'{\\tiny \n');
|
||||
fprintf(fidTeX,'\\begin{table}\n');
|
||||
fprintf(fidTeX,'\\centering\n');
|
||||
fprintf(fidTeX,'\\begin{tabular}{l|lc} \n');
|
||||
fprintf(fidTeX,'\\hline\\hline \\\\ \n');
|
||||
fprintf(fidTeX,' Parameter & Explanatory & cosn \\\\ \n');
|
||||
fprintf(fidTeX,' & parameter(s) & \\\\ \n');
|
||||
fprintf(fidTeX,'\\hline \\\\ \n');
|
||||
for i=1:k,
|
||||
plist='';
|
||||
for ii=1:ll,
|
||||
plist = [plist ' $' pnames_TeX(pars{i,ll}(ii),:) '$ '];
|
||||
end
|
||||
fprintf(fidTeX,'$%s$ & [%s] & %7.3f \\\\ \n',...
|
||||
pnames_TeX(i,:),...
|
||||
plist,...
|
||||
cosnJ(i,ll));
|
||||
end
|
||||
fprintf(fidTeX,'\\hline\\hline \n');
|
||||
fprintf(fidTeX,'\\end{tabular}\n ');
|
||||
fprintf(fidTeX,['\\caption{Collinearity patterns with ',int2str(ll),' parameter(s)}\n ']);
|
||||
fprintf(fidTeX,['\\label{Table:CollinearityPatterns:',int2str(ll),'}\n']);
|
||||
fprintf(fidTeX,'\\end{table}\n');
|
||||
fprintf(fidTeX,'} \n');
|
||||
fprintf(fidTeX,'%% End of TeX file.\n');
|
||||
fclose(fidTeX);
|
||||
end
|
||||
end
|
||||
|
|
@ -1,345 +1,345 @@
|
|||
function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
|
||||
% function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
|
||||
% Evaluates the posterior kernel of a dsge model.
|
||||
%
|
||||
% INPUTS
|
||||
% xparam1 [double] vector of model parameters.
|
||||
% gend [integer] scalar specifying the number of observations.
|
||||
% data [double] matrix of data
|
||||
% data_index [cell] cell of column vectors
|
||||
% number_of_observations [integer]
|
||||
% no_more_missing_observations [integer]
|
||||
% OUTPUTS
|
||||
% fval : value of the posterior kernel at xparam1.
|
||||
% cost_flag : zero if the function returns a penalty, one otherwise.
|
||||
% ys : steady state of original endogenous variables
|
||||
% trend_coeff :
|
||||
% info : vector of informations about the penalty:
|
||||
% 41: one (many) parameter(s) do(es) not satisfied the lower bound
|
||||
% 42: one (many) parameter(s) do(es) not satisfied the upper bound
|
||||
%
|
||||
% SPECIAL REQUIREMENTS
|
||||
%
|
||||
|
||||
% Copyright (C) 2004-2010 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
global bayestopt_ estim_params_ options_ trend_coeff_ M_ oo_
|
||||
fval = [];
|
||||
ys = [];
|
||||
trend_coeff = [];
|
||||
cost_flag = 1;
|
||||
nobs = size(options_.varobs,1);
|
||||
%------------------------------------------------------------------------------
|
||||
% 1. Get the structural parameters & define penalties
|
||||
%------------------------------------------------------------------------------
|
||||
if options_.mode_compute ~= 1 & any(xparam1 < bayestopt_.lb)
|
||||
k = find(xparam1 < bayestopt_.lb);
|
||||
fval = bayestopt_.penalty+sum((bayestopt_.lb(k)-xparam1(k)).^2);
|
||||
cost_flag = 0;
|
||||
info = 41;
|
||||
return;
|
||||
end
|
||||
if options_.mode_compute ~= 1 & any(xparam1 > bayestopt_.ub)
|
||||
k = find(xparam1 > bayestopt_.ub);
|
||||
fval = bayestopt_.penalty+sum((xparam1(k)-bayestopt_.ub(k)).^2);
|
||||
cost_flag = 0;
|
||||
info = 42;
|
||||
return;
|
||||
end
|
||||
Q = M_.Sigma_e;
|
||||
H = M_.H;
|
||||
for i=1:estim_params_.nvx
|
||||
k =estim_params_.var_exo(i,1);
|
||||
Q(k,k) = xparam1(i)*xparam1(i);
|
||||
end
|
||||
offset = estim_params_.nvx;
|
||||
if estim_params_.nvn
|
||||
for i=1:estim_params_.nvn
|
||||
k = estim_params_.var_endo(i,1);
|
||||
H(k,k) = xparam1(i+offset)*xparam1(i+offset);
|
||||
end
|
||||
offset = offset+estim_params_.nvn;
|
||||
end
|
||||
if estim_params_.ncx
|
||||
for i=1:estim_params_.ncx
|
||||
k1 =estim_params_.corrx(i,1);
|
||||
k2 =estim_params_.corrx(i,2);
|
||||
Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
|
||||
Q(k2,k1) = Q(k1,k2);
|
||||
end
|
||||
[CholQ,testQ] = chol(Q);
|
||||
if testQ %% The variance-covariance matrix of the structural innovations is not definite positive.
|
||||
%% We have to compute the eigenvalues of this matrix in order to build the penalty.
|
||||
a = diag(eig(Q));
|
||||
k = find(a < 0);
|
||||
if k > 0
|
||||
fval = bayestopt_.penalty+sum(-a(k));
|
||||
cost_flag = 0;
|
||||
info = 43;
|
||||
return
|
||||
end
|
||||
end
|
||||
offset = offset+estim_params_.ncx;
|
||||
end
|
||||
if estim_params_.ncn
|
||||
for i=1:estim_params_.ncn
|
||||
k1 = options_.lgyidx2varobs(estim_params_.corrn(i,1));
|
||||
k2 = options_.lgyidx2varobs(estim_params_.corrn(i,2));
|
||||
H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
|
||||
H(k2,k1) = H(k1,k2);
|
||||
end
|
||||
[CholH,testH] = chol(H);
|
||||
if testH
|
||||
a = diag(eig(H));
|
||||
k = find(a < 0);
|
||||
if k > 0
|
||||
fval = bayestopt_.penalty+sum(-a(k));
|
||||
cost_flag = 0;
|
||||
info = 44;
|
||||
return
|
||||
end
|
||||
end
|
||||
offset = offset+estim_params_.ncn;
|
||||
end
|
||||
if estim_params_.np > 0
|
||||
M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
|
||||
end
|
||||
M_.Sigma_e = Q;
|
||||
M_.H = H;
|
||||
%------------------------------------------------------------------------------
|
||||
% 2. call model setup & reduction program
|
||||
%------------------------------------------------------------------------------
|
||||
[T,R,SteadyState,info] = dynare_resolve(bayestopt_.restrict_var_list,...
|
||||
bayestopt_.restrict_columns,...
|
||||
bayestopt_.restrict_aux);
|
||||
if info(1) == 1 || info(1) == 2 || info(1) == 5
|
||||
fval = bayestopt_.penalty+1;
|
||||
cost_flag = 0;
|
||||
return
|
||||
elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21
|
||||
fval = bayestopt_.penalty+info(2);
|
||||
cost_flag = 0;
|
||||
return
|
||||
end
|
||||
bayestopt_.mf = bayestopt_.mf1;
|
||||
if options_.noconstant
|
||||
constant = zeros(nobs,1);
|
||||
else
|
||||
if options_.loglinear
|
||||
constant = log(SteadyState(bayestopt_.mfys));
|
||||
else
|
||||
constant = SteadyState(bayestopt_.mfys);
|
||||
end
|
||||
end
|
||||
if bayestopt_.with_trend
|
||||
trend_coeff = zeros(nobs,1);
|
||||
t = options_.trend_coeffs;
|
||||
for i=1:length(t)
|
||||
if ~isempty(t{i})
|
||||
trend_coeff(i) = evalin('base',t{i});
|
||||
end
|
||||
end
|
||||
trend = repmat(constant,1,gend)+trend_coeff*[1:gend];
|
||||
else
|
||||
trend = repmat(constant,1,gend);
|
||||
end
|
||||
start = options_.presample+1;
|
||||
np = size(T,1);
|
||||
mf = bayestopt_.mf;
|
||||
no_missing_data_flag = (number_of_observations==gend*nobs);
|
||||
%------------------------------------------------------------------------------
|
||||
% 3. Initial condition of the Kalman filter
|
||||
%------------------------------------------------------------------------------
|
||||
T
|
||||
R
|
||||
Q
|
||||
R*Q*R'
|
||||
pause
|
||||
options_.lik_init = 1;
|
||||
kalman_algo = options_.kalman_algo;
|
||||
if options_.lik_init == 1 % Kalman filter
|
||||
if kalman_algo ~= 2
|
||||
kalman_algo = 1;
|
||||
end
|
||||
Pstar = lyapunov_symm(T,R*Q*R',options_.qz_criterium,options_.lyapunov_complex_threshold);
|
||||
Pinf = [];
|
||||
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
|
||||
if kalman_algo ~= 2
|
||||
kalman_algo = 1;
|
||||
end
|
||||
Pstar = options_.Harvey_scale_factor*eye(np);
|
||||
Pinf = [];
|
||||
elseif options_.lik_init == 3 % Diffuse Kalman filter
|
||||
if kalman_algo ~= 4
|
||||
kalman_algo = 3;
|
||||
end
|
||||
[QT,ST] = schur(T);
|
||||
e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
|
||||
[QT,ST] = ordschur(QT,ST,e1);
|
||||
k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
|
||||
nk = length(k);
|
||||
nk1 = nk+1;
|
||||
Pinf = zeros(np,np);
|
||||
Pinf(1:nk,1:nk) = eye(nk);
|
||||
Pstar = zeros(np,np);
|
||||
B = QT'*R*Q*R'*QT;
|
||||
for i=np:-1:nk+2
|
||||
if ST(i,i-1) == 0
|
||||
if i == np
|
||||
c = zeros(np-nk,1);
|
||||
else
|
||||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||||
end
|
||||
q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
|
||||
Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
|
||||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||||
else
|
||||
if i == np
|
||||
c = zeros(np-nk,1);
|
||||
c1 = zeros(np-nk,1);
|
||||
else
|
||||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
|
||||
ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
|
||||
c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
|
||||
ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
|
||||
ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||||
end
|
||||
q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
|
||||
-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
|
||||
z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
|
||||
Pstar(nk1:i,i) = z(1:(i-nk));
|
||||
Pstar(nk1:i,i-1) = z(i-nk+1:end);
|
||||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||||
Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
|
||||
i = i - 1;
|
||||
end
|
||||
end
|
||||
if i == nk+2
|
||||
c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
|
||||
Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
|
||||
end
|
||||
Z = QT(mf,:);
|
||||
R1 = QT'*R;
|
||||
[QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
|
||||
k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
|
||||
if length(k) > 0
|
||||
k1 = EE(:,k);
|
||||
dd =ones(nk,1);
|
||||
dd(k1) = zeros(length(k1),1);
|
||||
Pinf(1:nk,1:nk) = diag(dd);
|
||||
end
|
||||
end
|
||||
if kalman_algo == 2
|
||||
end
|
||||
kalman_tol = options_.kalman_tol;
|
||||
riccati_tol = options_.riccati_tol;
|
||||
mf = bayestopt_.mf1;
|
||||
Y = data-trend;
|
||||
Pstar
|
||||
pause
|
||||
%------------------------------------------------------------------------------
|
||||
% 4. Likelihood evaluation
|
||||
%------------------------------------------------------------------------------
|
||||
if (kalman_algo==1)% Multivariate Kalman Filter
|
||||
if no_missing_data_flag
|
||||
LIK = kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol);
|
||||
else
|
||||
LIK = ...
|
||||
missing_observations_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol, ...
|
||||
data_index,number_of_observations,no_more_missing_observations);
|
||||
end
|
||||
if isinf(LIK)
|
||||
kalman_algo = 2;
|
||||
end
|
||||
end
|
||||
if (kalman_algo==2)% Univariate Kalman Filter
|
||||
no_correlation_flag = 1;
|
||||
if length(H)==1 & H == 0
|
||||
H = zeros(nobs,1);
|
||||
else
|
||||
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
||||
H = diag(H);
|
||||
else
|
||||
no_correlation_flag = 0;
|
||||
end
|
||||
end
|
||||
if no_correlation_flag
|
||||
LIK = univariate_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
|
||||
else
|
||||
LIK = univariate_kalman_filter_corr(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
|
||||
end
|
||||
end
|
||||
if (kalman_algo==3)% Multivariate Diffuse Kalman Filter
|
||||
if no_missing_data_flag
|
||||
LIK = diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol, ...
|
||||
riccati_tol);
|
||||
else
|
||||
LIK = missing_observations_diffuse_kalman_filter(ST,R1,Q,H,Pinf, ...
|
||||
Pstar,Y,start,Z,kalman_tol,riccati_tol,...
|
||||
data_index,number_of_observations,...
|
||||
no_more_missing_observations);
|
||||
end
|
||||
if isinf(LIK)
|
||||
kalman_algo = 4;
|
||||
end
|
||||
end
|
||||
if (kalman_algo==4)% Univariate Diffuse Kalman Filter
|
||||
no_correlation_flag = 1;
|
||||
if length(H)==1 & H == 0
|
||||
H = zeros(nobs,1);
|
||||
else
|
||||
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
||||
H = diag(H);
|
||||
else
|
||||
no_correlation_flag = 0;
|
||||
end
|
||||
end
|
||||
if no_correlation_flag
|
||||
LIK = univariate_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y, ...
|
||||
start,Z,kalman_tol,riccati_tol,data_index,...
|
||||
number_of_observations,no_more_missing_observations);
|
||||
else
|
||||
LIK = univariate_diffuse_kalman_filter_corr(ST,R1,Q,H,Pinf,Pstar, ...
|
||||
Y,start,Z,kalman_tol,riccati_tol,...
|
||||
data_index,number_of_observations,...
|
||||
no_more_missing_observations);
|
||||
end
|
||||
end
|
||||
if isnan(LIK)
|
||||
cost_flag = 0;
|
||||
return
|
||||
end
|
||||
if imag(LIK)~=0
|
||||
likelihood = bayestopt_.penalty;
|
||||
else
|
||||
likelihood = LIK;
|
||||
end
|
||||
% ------------------------------------------------------------------------------
|
||||
% Adds prior if necessary
|
||||
% ------------------------------------------------------------------------------
|
||||
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||||
fval = (likelihood-lnprior);
|
||||
likelihood
|
||||
lnprior
|
||||
fval
|
||||
pause
|
||||
LIKDLL=logposterior(xparam1,Y,mexext)
|
||||
pause
|
||||
options_.kalman_algo = kalman_algo;
|
||||
function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
|
||||
% function [fval,cost_flag,ys,trend_coeff,info] = DsgeLikelihood(xparam1,gend,data,data_index,number_of_observations,no_more_missing_observations)
|
||||
% Evaluates the posterior kernel of a dsge model.
|
||||
%
|
||||
% INPUTS
|
||||
% xparam1 [double] vector of model parameters.
|
||||
% gend [integer] scalar specifying the number of observations.
|
||||
% data [double] matrix of data
|
||||
% data_index [cell] cell of column vectors
|
||||
% number_of_observations [integer]
|
||||
% no_more_missing_observations [integer]
|
||||
% OUTPUTS
|
||||
% fval : value of the posterior kernel at xparam1.
|
||||
% cost_flag : zero if the function returns a penalty, one otherwise.
|
||||
% ys : steady state of original endogenous variables
|
||||
% trend_coeff :
|
||||
% info : vector of informations about the penalty:
|
||||
% 41: one (many) parameter(s) do(es) not satisfied the lower bound
|
||||
% 42: one (many) parameter(s) do(es) not satisfied the upper bound
|
||||
%
|
||||
% SPECIAL REQUIREMENTS
|
||||
%
|
||||
|
||||
% Copyright (C) 2004-2010 Dynare Team
|
||||
%
|
||||
% This file is part of Dynare.
|
||||
%
|
||||
% Dynare is free software: you can redistribute it and/or modify
|
||||
% it under the terms of the GNU General Public License as published by
|
||||
% the Free Software Foundation, either version 3 of the License, or
|
||||
% (at your option) any later version.
|
||||
%
|
||||
% Dynare is distributed in the hope that it will be useful,
|
||||
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
% GNU General Public License for more details.
|
||||
%
|
||||
% You should have received a copy of the GNU General Public License
|
||||
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
||||
|
||||
global bayestopt_ estim_params_ options_ trend_coeff_ M_ oo_
|
||||
fval = [];
|
||||
ys = [];
|
||||
trend_coeff = [];
|
||||
cost_flag = 1;
|
||||
nobs = size(options_.varobs,1);
|
||||
%------------------------------------------------------------------------------
|
||||
% 1. Get the structural parameters & define penalties
|
||||
%------------------------------------------------------------------------------
|
||||
if options_.mode_compute ~= 1 & any(xparam1 < bayestopt_.lb)
|
||||
k = find(xparam1 < bayestopt_.lb);
|
||||
fval = bayestopt_.penalty+sum((bayestopt_.lb(k)-xparam1(k)).^2);
|
||||
cost_flag = 0;
|
||||
info = 41;
|
||||
return;
|
||||
end
|
||||
if options_.mode_compute ~= 1 & any(xparam1 > bayestopt_.ub)
|
||||
k = find(xparam1 > bayestopt_.ub);
|
||||
fval = bayestopt_.penalty+sum((xparam1(k)-bayestopt_.ub(k)).^2);
|
||||
cost_flag = 0;
|
||||
info = 42;
|
||||
return;
|
||||
end
|
||||
Q = M_.Sigma_e;
|
||||
H = M_.H;
|
||||
for i=1:estim_params_.nvx
|
||||
k =estim_params_.var_exo(i,1);
|
||||
Q(k,k) = xparam1(i)*xparam1(i);
|
||||
end
|
||||
offset = estim_params_.nvx;
|
||||
if estim_params_.nvn
|
||||
for i=1:estim_params_.nvn
|
||||
k = estim_params_.var_endo(i,1);
|
||||
H(k,k) = xparam1(i+offset)*xparam1(i+offset);
|
||||
end
|
||||
offset = offset+estim_params_.nvn;
|
||||
end
|
||||
if estim_params_.ncx
|
||||
for i=1:estim_params_.ncx
|
||||
k1 =estim_params_.corrx(i,1);
|
||||
k2 =estim_params_.corrx(i,2);
|
||||
Q(k1,k2) = xparam1(i+offset)*sqrt(Q(k1,k1)*Q(k2,k2));
|
||||
Q(k2,k1) = Q(k1,k2);
|
||||
end
|
||||
[CholQ,testQ] = chol(Q);
|
||||
if testQ %% The variance-covariance matrix of the structural innovations is not definite positive.
|
||||
%% We have to compute the eigenvalues of this matrix in order to build the penalty.
|
||||
a = diag(eig(Q));
|
||||
k = find(a < 0);
|
||||
if k > 0
|
||||
fval = bayestopt_.penalty+sum(-a(k));
|
||||
cost_flag = 0;
|
||||
info = 43;
|
||||
return
|
||||
end
|
||||
end
|
||||
offset = offset+estim_params_.ncx;
|
||||
end
|
||||
if estim_params_.ncn
|
||||
for i=1:estim_params_.ncn
|
||||
k1 = options_.lgyidx2varobs(estim_params_.corrn(i,1));
|
||||
k2 = options_.lgyidx2varobs(estim_params_.corrn(i,2));
|
||||
H(k1,k2) = xparam1(i+offset)*sqrt(H(k1,k1)*H(k2,k2));
|
||||
H(k2,k1) = H(k1,k2);
|
||||
end
|
||||
[CholH,testH] = chol(H);
|
||||
if testH
|
||||
a = diag(eig(H));
|
||||
k = find(a < 0);
|
||||
if k > 0
|
||||
fval = bayestopt_.penalty+sum(-a(k));
|
||||
cost_flag = 0;
|
||||
info = 44;
|
||||
return
|
||||
end
|
||||
end
|
||||
offset = offset+estim_params_.ncn;
|
||||
end
|
||||
if estim_params_.np > 0
|
||||
M_.params(estim_params_.param_vals(:,1)) = xparam1(offset+1:end);
|
||||
end
|
||||
M_.Sigma_e = Q;
|
||||
M_.H = H;
|
||||
%------------------------------------------------------------------------------
|
||||
% 2. call model setup & reduction program
|
||||
%------------------------------------------------------------------------------
|
||||
[T,R,SteadyState,info] = dynare_resolve(bayestopt_.restrict_var_list,...
|
||||
bayestopt_.restrict_columns,...
|
||||
bayestopt_.restrict_aux);
|
||||
if info(1) == 1 || info(1) == 2 || info(1) == 5
|
||||
fval = bayestopt_.penalty+1;
|
||||
cost_flag = 0;
|
||||
return
|
||||
elseif info(1) == 3 || info(1) == 4 || info(1)==6 ||info(1) == 19 || info(1) == 20 || info(1) == 21
|
||||
fval = bayestopt_.penalty+info(2);
|
||||
cost_flag = 0;
|
||||
return
|
||||
end
|
||||
bayestopt_.mf = bayestopt_.mf1;
|
||||
if options_.noconstant
|
||||
constant = zeros(nobs,1);
|
||||
else
|
||||
if options_.loglinear
|
||||
constant = log(SteadyState(bayestopt_.mfys));
|
||||
else
|
||||
constant = SteadyState(bayestopt_.mfys);
|
||||
end
|
||||
end
|
||||
if bayestopt_.with_trend
|
||||
trend_coeff = zeros(nobs,1);
|
||||
t = options_.trend_coeffs;
|
||||
for i=1:length(t)
|
||||
if ~isempty(t{i})
|
||||
trend_coeff(i) = evalin('base',t{i});
|
||||
end
|
||||
end
|
||||
trend = repmat(constant,1,gend)+trend_coeff*[1:gend];
|
||||
else
|
||||
trend = repmat(constant,1,gend);
|
||||
end
|
||||
start = options_.presample+1;
|
||||
np = size(T,1);
|
||||
mf = bayestopt_.mf;
|
||||
no_missing_data_flag = (number_of_observations==gend*nobs);
|
||||
%------------------------------------------------------------------------------
|
||||
% 3. Initial condition of the Kalman filter
|
||||
%------------------------------------------------------------------------------
|
||||
T
|
||||
R
|
||||
Q
|
||||
R*Q*R'
|
||||
pause
|
||||
options_.lik_init = 1;
|
||||
kalman_algo = options_.kalman_algo;
|
||||
if options_.lik_init == 1 % Kalman filter
|
||||
if kalman_algo ~= 2
|
||||
kalman_algo = 1;
|
||||
end
|
||||
Pstar = lyapunov_symm(T,R*Q*R',options_.qz_criterium,options_.lyapunov_complex_threshold);
|
||||
Pinf = [];
|
||||
elseif options_.lik_init == 2 % Old Diffuse Kalman filter
|
||||
if kalman_algo ~= 2
|
||||
kalman_algo = 1;
|
||||
end
|
||||
Pstar = options_.Harvey_scale_factor*eye(np);
|
||||
Pinf = [];
|
||||
elseif options_.lik_init == 3 % Diffuse Kalman filter
|
||||
if kalman_algo ~= 4
|
||||
kalman_algo = 3;
|
||||
end
|
||||
[QT,ST] = schur(T);
|
||||
e1 = abs(ordeig(ST)) > 2-options_.qz_criterium;
|
||||
[QT,ST] = ordschur(QT,ST,e1);
|
||||
k = find(abs(ordeig(ST)) > 2-options_.qz_criterium);
|
||||
nk = length(k);
|
||||
nk1 = nk+1;
|
||||
Pinf = zeros(np,np);
|
||||
Pinf(1:nk,1:nk) = eye(nk);
|
||||
Pstar = zeros(np,np);
|
||||
B = QT'*R*Q*R'*QT;
|
||||
for i=np:-1:nk+2
|
||||
if ST(i,i-1) == 0
|
||||
if i == np
|
||||
c = zeros(np-nk,1);
|
||||
else
|
||||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||||
end
|
||||
q = eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i);
|
||||
Pstar(nk1:i,i) = q\(B(nk1:i,i)+c);
|
||||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||||
else
|
||||
if i == np
|
||||
c = zeros(np-nk,1);
|
||||
c1 = zeros(np-nk,1);
|
||||
else
|
||||
c = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i,i+1:end)')+...
|
||||
ST(i,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i)+...
|
||||
ST(i,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1);
|
||||
c1 = ST(nk1:i,:)*(Pstar(:,i+1:end)*ST(i-1,i+1:end)')+...
|
||||
ST(i-1,i-1)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i-1)+...
|
||||
ST(i-1,i)*ST(nk1:i,i+1:end)*Pstar(i+1:end,i);
|
||||
end
|
||||
q = [eye(i-nk)-ST(nk1:i,nk1:i)*ST(i,i) -ST(nk1:i,nk1:i)*ST(i,i-1);...
|
||||
-ST(nk1:i,nk1:i)*ST(i-1,i) eye(i-nk)-ST(nk1:i,nk1:i)*ST(i-1,i-1)];
|
||||
z = q\[B(nk1:i,i)+c;B(nk1:i,i-1)+c1];
|
||||
Pstar(nk1:i,i) = z(1:(i-nk));
|
||||
Pstar(nk1:i,i-1) = z(i-nk+1:end);
|
||||
Pstar(i,nk1:i-1) = Pstar(nk1:i-1,i)';
|
||||
Pstar(i-1,nk1:i-2) = Pstar(nk1:i-2,i-1)';
|
||||
i = i - 1;
|
||||
end
|
||||
end
|
||||
if i == nk+2
|
||||
c = ST(nk+1,:)*(Pstar(:,nk+2:end)*ST(nk1,nk+2:end)')+ST(nk1,nk1)*ST(nk1,nk+2:end)*Pstar(nk+2:end,nk1);
|
||||
Pstar(nk1,nk1)=(B(nk1,nk1)+c)/(1-ST(nk1,nk1)*ST(nk1,nk1));
|
||||
end
|
||||
Z = QT(mf,:);
|
||||
R1 = QT'*R;
|
||||
[QQ,RR,EE] = qr(Z*ST(:,1:nk),0);
|
||||
k = find(abs(diag([RR; zeros(nk-size(Z,1),size(RR,2))])) < 1e-8);
|
||||
if length(k) > 0
|
||||
k1 = EE(:,k);
|
||||
dd =ones(nk,1);
|
||||
dd(k1) = zeros(length(k1),1);
|
||||
Pinf(1:nk,1:nk) = diag(dd);
|
||||
end
|
||||
end
|
||||
if kalman_algo == 2
|
||||
end
|
||||
kalman_tol = options_.kalman_tol;
|
||||
riccati_tol = options_.riccati_tol;
|
||||
mf = bayestopt_.mf1;
|
||||
Y = data-trend;
|
||||
Pstar
|
||||
pause
|
||||
%------------------------------------------------------------------------------
|
||||
% 4. Likelihood evaluation
|
||||
%------------------------------------------------------------------------------
|
||||
if (kalman_algo==1)% Multivariate Kalman Filter
|
||||
if no_missing_data_flag
|
||||
LIK = kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol);
|
||||
else
|
||||
LIK = ...
|
||||
missing_observations_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol, ...
|
||||
data_index,number_of_observations,no_more_missing_observations);
|
||||
end
|
||||
if isinf(LIK)
|
||||
kalman_algo = 2;
|
||||
end
|
||||
end
|
||||
if (kalman_algo==2)% Univariate Kalman Filter
|
||||
no_correlation_flag = 1;
|
||||
if length(H)==1 & H == 0
|
||||
H = zeros(nobs,1);
|
||||
else
|
||||
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
||||
H = diag(H);
|
||||
else
|
||||
no_correlation_flag = 0;
|
||||
end
|
||||
end
|
||||
if no_correlation_flag
|
||||
LIK = univariate_kalman_filter(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
|
||||
else
|
||||
LIK = univariate_kalman_filter_corr(T,R,Q,H,Pstar,Y,start,mf,kalman_tol,riccati_tol,data_index,number_of_observations,no_more_missing_observations);
|
||||
end
|
||||
end
|
||||
if (kalman_algo==3)% Multivariate Diffuse Kalman Filter
|
||||
if no_missing_data_flag
|
||||
LIK = diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y,start,Z,kalman_tol, ...
|
||||
riccati_tol);
|
||||
else
|
||||
LIK = missing_observations_diffuse_kalman_filter(ST,R1,Q,H,Pinf, ...
|
||||
Pstar,Y,start,Z,kalman_tol,riccati_tol,...
|
||||
data_index,number_of_observations,...
|
||||
no_more_missing_observations);
|
||||
end
|
||||
if isinf(LIK)
|
||||
kalman_algo = 4;
|
||||
end
|
||||
end
|
||||
if (kalman_algo==4)% Univariate Diffuse Kalman Filter
|
||||
no_correlation_flag = 1;
|
||||
if length(H)==1 & H == 0
|
||||
H = zeros(nobs,1);
|
||||
else
|
||||
if all(all(abs(H-diag(diag(H)))<1e-14))% ie, the covariance matrix is diagonal...
|
||||
H = diag(H);
|
||||
else
|
||||
no_correlation_flag = 0;
|
||||
end
|
||||
end
|
||||
if no_correlation_flag
|
||||
LIK = univariate_diffuse_kalman_filter(ST,R1,Q,H,Pinf,Pstar,Y, ...
|
||||
start,Z,kalman_tol,riccati_tol,data_index,...
|
||||
number_of_observations,no_more_missing_observations);
|
||||
else
|
||||
LIK = univariate_diffuse_kalman_filter_corr(ST,R1,Q,H,Pinf,Pstar, ...
|
||||
Y,start,Z,kalman_tol,riccati_tol,...
|
||||
data_index,number_of_observations,...
|
||||
no_more_missing_observations);
|
||||
end
|
||||
end
|
||||
if isnan(LIK)
|
||||
cost_flag = 0;
|
||||
return
|
||||
end
|
||||
if imag(LIK)~=0
|
||||
likelihood = bayestopt_.penalty;
|
||||
else
|
||||
likelihood = LIK;
|
||||
end
|
||||
% ------------------------------------------------------------------------------
|
||||
% Adds prior if necessary
|
||||
% ------------------------------------------------------------------------------
|
||||
lnprior = priordens(xparam1,bayestopt_.pshape,bayestopt_.p6,bayestopt_.p7,bayestopt_.p3,bayestopt_.p4);
|
||||
fval = (likelihood-lnprior);
|
||||
likelihood
|
||||
lnprior
|
||||
fval
|
||||
pause
|
||||
LIKDLL=logposterior(xparam1,Y,mexext)
|
||||
pause
|
||||
options_.kalman_algo = kalman_algo;
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,184 +1,184 @@
|
|||
//options_.usePartInfo=1;
|
||||
|
||||
var MC E EF R_KF QF CF IF YF LF PIEF WF RF R_K Q C I Y L PIE W R EE_A PIE_BAR EE_B EE_G EE_L EE_I KF K one BIGTHETA;
|
||||
|
||||
varexo E_A E_B E_G E_L E_I ETA_R E_PIE_BAR ETA_Q ETA_P ETA_W ;
|
||||
|
||||
parameters
|
||||
xi_e lambda_w alpha czcap beta phi_i tau sig_c hab ccs cinvs phi_y gamma_w xi_w gamma_p xi_p sig_l r_dpi
|
||||
r_pie r_dy r_y rho rho_a rho_pb rho_b rho_g rho_l rho_i LMP ;
|
||||
|
||||
|
||||
|
||||
alpha=.30;
|
||||
beta=.99;
|
||||
tau=0.025;
|
||||
ccs=0.6;
|
||||
cinvs=.22; //% alpha*(tau+ctrend)/R_K R_K=ctrend/beta-1+tau
|
||||
lambda_w = 0.5;
|
||||
phi_i= 6.771;
|
||||
sig_c= 1.353;
|
||||
hab= 0.573;
|
||||
xi_w= 0.737;
|
||||
sig_l= 2.400;
|
||||
xi_p= 0.908;
|
||||
xi_e= 0.599;
|
||||
gamma_w= 0.763;
|
||||
gamma_p= 0.469;
|
||||
czcap= 0.169;
|
||||
phi_y= 1.408;
|
||||
r_pie= 1.684;
|
||||
r_dpi= 0.14;
|
||||
rho= 0.961;
|
||||
r_y= 0.099;
|
||||
r_dy= 0.159;
|
||||
rho_a= 0.823;
|
||||
rho_b= 0.855;
|
||||
rho_g= 0.949;
|
||||
rho_l= 0.889;
|
||||
rho_i= 0.927;
|
||||
rho_pb= 0.924;
|
||||
LMP = 0.0 ; //NEW.
|
||||
|
||||
model(linear, use_dll);
|
||||
CF = (1/(1+hab))*(CF(1)+hab*CF(-1))-((1-hab)/((1+hab)*sig_c))*(RF-PIEF(1)-EE_B) ;
|
||||
0 = alpha*R_KF+(1-alpha)*WF -EE_A ;
|
||||
PIEF = 0*one;
|
||||
IF = (1/(1+beta))* (( IF(-1) + beta*(IF(1)))+(1/phi_i)*QF)+0*ETA_Q+EE_I ;
|
||||
QF = -(RF-PIEF(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_KF(1)+beta*(1-tau)*QF(1) +0*EE_I ;
|
||||
KF = (1-tau)*KF(-1)+tau*IF(-1) ;
|
||||
YF = (ccs*CF+cinvs*IF)+EE_G ;
|
||||
|
||||
YF = 1*phi_y*( alpha*KF+alpha*(1/czcap)*R_KF+(1-alpha)*LF+EE_A ) ;
|
||||
WF = (sig_c/(1-hab))*(CF-hab*CF(-1)) + sig_l*LF - EE_L ;
|
||||
LF = R_KF*((1+czcap)/czcap)-WF+KF ;
|
||||
EF = EF(-1)+EF(1)-EF+(LF-EF)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
C = (hab/(1+hab))*C(-1)+(1/(1+hab))*C(1)-((1-hab)/((1+hab)*sig_c))*(R-PIE(1)-EE_B) ;
|
||||
I = (1/(1+beta))* (( I(-1) + beta*(I(1)))+(1/phi_i)*Q )+1*ETA_Q+1*EE_I ;
|
||||
Q = -(R-PIE(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_K(1)+beta*(1-tau)*Q(1) +EE_I*0+0*ETA_Q ;
|
||||
K = (1-tau)*K(-1)+tau*I(-1) ;
|
||||
Y = (ccs*C+cinvs*I)+ EE_G ;
|
||||
Y = phi_y*( alpha*K+alpha*(1/czcap)*R_K+(1-alpha)*L ) +phi_y*EE_A ;
|
||||
PIE = (1/(1+beta*gamma_p))*
|
||||
(
|
||||
(beta)*(PIE(1)) +(gamma_p)*(PIE(-1))
|
||||
+((1-xi_p)*(1-beta*xi_p)/(xi_p))*(MC)
|
||||
) + ETA_P ;
|
||||
|
||||
MC = alpha*R_K+(1-alpha)*W -EE_A;
|
||||
W = (1/(1+beta))*(beta*W(+1)+W(-1))
|
||||
+(beta/(1+beta))*(PIE(+1))
|
||||
-((1+beta*gamma_w)/(1+beta))*(PIE)
|
||||
+(gamma_w/(1+beta))*(PIE(-1))
|
||||
-(1/(1+beta))*(((1-beta*xi_w)*(1-xi_w))/(((1+(((1+lambda_w)*sig_l)/(lambda_w))))*xi_w))*(W-sig_l*L-(sig_c/(1-hab))*(C-hab*C(-1))+EE_L)
|
||||
+ETA_W;
|
||||
L = R_K*((1+czcap)/czcap)-W+K ;
|
||||
|
||||
// R = r_dpi*(PIE-PIE(-1))
|
||||
// +(1-rho)*(r_pie*(PIE(-1)-PIE_BAR)+r_y*(Y-YF))
|
||||
// +r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
// +rho*(R(-1)-PIE_BAR)
|
||||
// +PIE_BAR
|
||||
// +ETA_R;
|
||||
|
||||
|
||||
R =
|
||||
|
||||
r_dpi*(PIE-PIE(-1))
|
||||
|
||||
+(1-rho)*(r_pie*(BIGTHETA)+r_y*(Y-YF))
|
||||
+r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
+rho*(R(-1)-PIE_BAR)
|
||||
+PIE_BAR
|
||||
+ETA_R;
|
||||
|
||||
|
||||
E = E(-1)+E(1)-E+(L-E)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
|
||||
EE_A = (rho_a)*EE_A(-1) + E_A;
|
||||
PIE_BAR = rho_pb*PIE_BAR(-1)+ E_PIE_BAR ;
|
||||
EE_B = rho_b*EE_B(-1) + E_B ;
|
||||
EE_G = rho_g*EE_G(-1) + E_G ;
|
||||
EE_L = rho_l*EE_L(-1) + E_L ;
|
||||
EE_I = rho_i*EE_I(-1) + E_I ;
|
||||
one = 0*one(-1) ;
|
||||
|
||||
LMP*BIGTHETA(1) = BIGTHETA - (PIE(-1) - PIE_BAR) ;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
shocks;
|
||||
var E_A; stderr 0.598;
|
||||
var E_B; stderr 0.336;
|
||||
var E_G; stderr 0.325;
|
||||
var E_I; stderr 0.085;
|
||||
var E_L; stderr 3.520;
|
||||
var ETA_P; stderr 0.160;
|
||||
var ETA_W; stderr 0.289;
|
||||
var ETA_R; stderr 0.081;
|
||||
var ETA_Q; stderr 0.604;
|
||||
var E_PIE_BAR; stderr 0.017;
|
||||
end;
|
||||
|
||||
//stoch_simul(irf=20) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
// stoch_simul generates what kind of standard errors for the shocks ?
|
||||
|
||||
//steady;
|
||||
//check;
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE MC R W R_K E L I ;
|
||||
|
||||
//datatomfile('ddd',[]);
|
||||
|
||||
// new syntax
|
||||
|
||||
estimated_params;
|
||||
// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE
|
||||
// PRIOR_SHAPE: BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF
|
||||
stderr E_A,0.543,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr E_PIE_BAR,0.072,0.001,4,INV_GAMMA_PDF,0.02,10;
|
||||
stderr E_B,0.2694,0.01,4,INV_GAMMA_PDF,0.2,2;
|
||||
stderr E_G,0.3052,0.01,4,INV_GAMMA_PDF,0.3,2;
|
||||
stderr E_L,1.4575,0.1,6,INV_GAMMA_PDF,1,2;
|
||||
stderr E_I,0.1318,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_R,0.1363,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_Q,0.4842,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr ETA_P,0.1731,0.01,4,INV_GAMMA_PDF,0.15,2;
|
||||
stderr ETA_W,0.2462,0.1,4,INV_GAMMA_PDF,0.25,2;
|
||||
rho_a,.9722,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_pb,.85,.1,.999,BETA_PDF,0.85,0.1;
|
||||
rho_b,.7647,.1,.99,BETA_PDF,0.85,0.1;
|
||||
rho_g,.9502,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_l,.9542,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_i,.6705,.1,.99,BETA_PDF,0.85,0.1;
|
||||
phi_i,5.2083,1,15,NORMAL_PDF,4,1.5;
|
||||
sig_c,0.9817,0.25,3,NORMAL_PDF,1,0.375;
|
||||
hab,0.5612,0.3,0.95,BETA_PDF,0.7,0.1;
|
||||
xi_w,0.7661,0.3,0.9,BETA_PDF,0.75,0.05;
|
||||
sig_l,1.7526,0.5,5,NORMAL_PDF,2,0.75;
|
||||
xi_p,0.8684,0.3,0.95,BETA_PDF,0.75,0.05;
|
||||
xi_e,0.5724,0.1,0.95,BETA_PDF,0.5,0.15;
|
||||
gamma_w,0.6202,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
gamma_p,0.6638,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
czcap,0.2516,0.01,2,NORMAL_PDF,0.2,0.075;
|
||||
phi_y,1.3011,1.001,2,NORMAL_PDF,1.45,0.125;
|
||||
r_pie,1.4616,1.2,2,NORMAL_PDF,1.7,0.1;
|
||||
r_dpi,0.1144,0.01,0.5,NORMAL_PDF,0.3,0.1;
|
||||
rho,0.8865,0.5,0.99,BETA_PDF,0.8,0.10;
|
||||
r_y,0.0571,0.01,0.2,NORMAL_PDF,0.125,0.05;
|
||||
r_dy,0.2228,0.05,0.5,NORMAL_PDF,0.0625,0.05;
|
||||
end;
|
||||
|
||||
varobs Y C I E PIE W R;
|
||||
|
||||
//estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118, lik_init=2, mode_compute=1,mh_replic=0);
|
||||
estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118,mh_jscale=0.2,mh_replic=1000
|
||||
//,mode_compute=0,mode_file=sweuromodel_dll_mode
|
||||
);
|
||||
|
||||
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
//options_.usePartInfo=1;
|
||||
|
||||
var MC E EF R_KF QF CF IF YF LF PIEF WF RF R_K Q C I Y L PIE W R EE_A PIE_BAR EE_B EE_G EE_L EE_I KF K one BIGTHETA;
|
||||
|
||||
varexo E_A E_B E_G E_L E_I ETA_R E_PIE_BAR ETA_Q ETA_P ETA_W ;
|
||||
|
||||
parameters
|
||||
xi_e lambda_w alpha czcap beta phi_i tau sig_c hab ccs cinvs phi_y gamma_w xi_w gamma_p xi_p sig_l r_dpi
|
||||
r_pie r_dy r_y rho rho_a rho_pb rho_b rho_g rho_l rho_i LMP ;
|
||||
|
||||
|
||||
|
||||
alpha=.30;
|
||||
beta=.99;
|
||||
tau=0.025;
|
||||
ccs=0.6;
|
||||
cinvs=.22; //% alpha*(tau+ctrend)/R_K R_K=ctrend/beta-1+tau
|
||||
lambda_w = 0.5;
|
||||
phi_i= 6.771;
|
||||
sig_c= 1.353;
|
||||
hab= 0.573;
|
||||
xi_w= 0.737;
|
||||
sig_l= 2.400;
|
||||
xi_p= 0.908;
|
||||
xi_e= 0.599;
|
||||
gamma_w= 0.763;
|
||||
gamma_p= 0.469;
|
||||
czcap= 0.169;
|
||||
phi_y= 1.408;
|
||||
r_pie= 1.684;
|
||||
r_dpi= 0.14;
|
||||
rho= 0.961;
|
||||
r_y= 0.099;
|
||||
r_dy= 0.159;
|
||||
rho_a= 0.823;
|
||||
rho_b= 0.855;
|
||||
rho_g= 0.949;
|
||||
rho_l= 0.889;
|
||||
rho_i= 0.927;
|
||||
rho_pb= 0.924;
|
||||
LMP = 0.0 ; //NEW.
|
||||
|
||||
model(linear, use_dll);
|
||||
CF = (1/(1+hab))*(CF(1)+hab*CF(-1))-((1-hab)/((1+hab)*sig_c))*(RF-PIEF(1)-EE_B) ;
|
||||
0 = alpha*R_KF+(1-alpha)*WF -EE_A ;
|
||||
PIEF = 0*one;
|
||||
IF = (1/(1+beta))* (( IF(-1) + beta*(IF(1)))+(1/phi_i)*QF)+0*ETA_Q+EE_I ;
|
||||
QF = -(RF-PIEF(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_KF(1)+beta*(1-tau)*QF(1) +0*EE_I ;
|
||||
KF = (1-tau)*KF(-1)+tau*IF(-1) ;
|
||||
YF = (ccs*CF+cinvs*IF)+EE_G ;
|
||||
|
||||
YF = 1*phi_y*( alpha*KF+alpha*(1/czcap)*R_KF+(1-alpha)*LF+EE_A ) ;
|
||||
WF = (sig_c/(1-hab))*(CF-hab*CF(-1)) + sig_l*LF - EE_L ;
|
||||
LF = R_KF*((1+czcap)/czcap)-WF+KF ;
|
||||
EF = EF(-1)+EF(1)-EF+(LF-EF)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
C = (hab/(1+hab))*C(-1)+(1/(1+hab))*C(1)-((1-hab)/((1+hab)*sig_c))*(R-PIE(1)-EE_B) ;
|
||||
I = (1/(1+beta))* (( I(-1) + beta*(I(1)))+(1/phi_i)*Q )+1*ETA_Q+1*EE_I ;
|
||||
Q = -(R-PIE(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_K(1)+beta*(1-tau)*Q(1) +EE_I*0+0*ETA_Q ;
|
||||
K = (1-tau)*K(-1)+tau*I(-1) ;
|
||||
Y = (ccs*C+cinvs*I)+ EE_G ;
|
||||
Y = phi_y*( alpha*K+alpha*(1/czcap)*R_K+(1-alpha)*L ) +phi_y*EE_A ;
|
||||
PIE = (1/(1+beta*gamma_p))*
|
||||
(
|
||||
(beta)*(PIE(1)) +(gamma_p)*(PIE(-1))
|
||||
+((1-xi_p)*(1-beta*xi_p)/(xi_p))*(MC)
|
||||
) + ETA_P ;
|
||||
|
||||
MC = alpha*R_K+(1-alpha)*W -EE_A;
|
||||
W = (1/(1+beta))*(beta*W(+1)+W(-1))
|
||||
+(beta/(1+beta))*(PIE(+1))
|
||||
-((1+beta*gamma_w)/(1+beta))*(PIE)
|
||||
+(gamma_w/(1+beta))*(PIE(-1))
|
||||
-(1/(1+beta))*(((1-beta*xi_w)*(1-xi_w))/(((1+(((1+lambda_w)*sig_l)/(lambda_w))))*xi_w))*(W-sig_l*L-(sig_c/(1-hab))*(C-hab*C(-1))+EE_L)
|
||||
+ETA_W;
|
||||
L = R_K*((1+czcap)/czcap)-W+K ;
|
||||
|
||||
// R = r_dpi*(PIE-PIE(-1))
|
||||
// +(1-rho)*(r_pie*(PIE(-1)-PIE_BAR)+r_y*(Y-YF))
|
||||
// +r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
// +rho*(R(-1)-PIE_BAR)
|
||||
// +PIE_BAR
|
||||
// +ETA_R;
|
||||
|
||||
|
||||
R =
|
||||
|
||||
r_dpi*(PIE-PIE(-1))
|
||||
|
||||
+(1-rho)*(r_pie*(BIGTHETA)+r_y*(Y-YF))
|
||||
+r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
+rho*(R(-1)-PIE_BAR)
|
||||
+PIE_BAR
|
||||
+ETA_R;
|
||||
|
||||
|
||||
E = E(-1)+E(1)-E+(L-E)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
|
||||
EE_A = (rho_a)*EE_A(-1) + E_A;
|
||||
PIE_BAR = rho_pb*PIE_BAR(-1)+ E_PIE_BAR ;
|
||||
EE_B = rho_b*EE_B(-1) + E_B ;
|
||||
EE_G = rho_g*EE_G(-1) + E_G ;
|
||||
EE_L = rho_l*EE_L(-1) + E_L ;
|
||||
EE_I = rho_i*EE_I(-1) + E_I ;
|
||||
one = 0*one(-1) ;
|
||||
|
||||
LMP*BIGTHETA(1) = BIGTHETA - (PIE(-1) - PIE_BAR) ;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
shocks;
|
||||
var E_A; stderr 0.598;
|
||||
var E_B; stderr 0.336;
|
||||
var E_G; stderr 0.325;
|
||||
var E_I; stderr 0.085;
|
||||
var E_L; stderr 3.520;
|
||||
var ETA_P; stderr 0.160;
|
||||
var ETA_W; stderr 0.289;
|
||||
var ETA_R; stderr 0.081;
|
||||
var ETA_Q; stderr 0.604;
|
||||
var E_PIE_BAR; stderr 0.017;
|
||||
end;
|
||||
|
||||
//stoch_simul(irf=20) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
// stoch_simul generates what kind of standard errors for the shocks ?
|
||||
|
||||
//steady;
|
||||
//check;
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE MC R W R_K E L I ;
|
||||
|
||||
//datatomfile('ddd',[]);
|
||||
|
||||
// new syntax
|
||||
|
||||
estimated_params;
|
||||
// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE
|
||||
// PRIOR_SHAPE: BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF
|
||||
stderr E_A,0.543,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr E_PIE_BAR,0.072,0.001,4,INV_GAMMA_PDF,0.02,10;
|
||||
stderr E_B,0.2694,0.01,4,INV_GAMMA_PDF,0.2,2;
|
||||
stderr E_G,0.3052,0.01,4,INV_GAMMA_PDF,0.3,2;
|
||||
stderr E_L,1.4575,0.1,6,INV_GAMMA_PDF,1,2;
|
||||
stderr E_I,0.1318,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_R,0.1363,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_Q,0.4842,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr ETA_P,0.1731,0.01,4,INV_GAMMA_PDF,0.15,2;
|
||||
stderr ETA_W,0.2462,0.1,4,INV_GAMMA_PDF,0.25,2;
|
||||
rho_a,.9722,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_pb,.85,.1,.999,BETA_PDF,0.85,0.1;
|
||||
rho_b,.7647,.1,.99,BETA_PDF,0.85,0.1;
|
||||
rho_g,.9502,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_l,.9542,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_i,.6705,.1,.99,BETA_PDF,0.85,0.1;
|
||||
phi_i,5.2083,1,15,NORMAL_PDF,4,1.5;
|
||||
sig_c,0.9817,0.25,3,NORMAL_PDF,1,0.375;
|
||||
hab,0.5612,0.3,0.95,BETA_PDF,0.7,0.1;
|
||||
xi_w,0.7661,0.3,0.9,BETA_PDF,0.75,0.05;
|
||||
sig_l,1.7526,0.5,5,NORMAL_PDF,2,0.75;
|
||||
xi_p,0.8684,0.3,0.95,BETA_PDF,0.75,0.05;
|
||||
xi_e,0.5724,0.1,0.95,BETA_PDF,0.5,0.15;
|
||||
gamma_w,0.6202,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
gamma_p,0.6638,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
czcap,0.2516,0.01,2,NORMAL_PDF,0.2,0.075;
|
||||
phi_y,1.3011,1.001,2,NORMAL_PDF,1.45,0.125;
|
||||
r_pie,1.4616,1.2,2,NORMAL_PDF,1.7,0.1;
|
||||
r_dpi,0.1144,0.01,0.5,NORMAL_PDF,0.3,0.1;
|
||||
rho,0.8865,0.5,0.99,BETA_PDF,0.8,0.10;
|
||||
r_y,0.0571,0.01,0.2,NORMAL_PDF,0.125,0.05;
|
||||
r_dy,0.2228,0.05,0.5,NORMAL_PDF,0.0625,0.05;
|
||||
end;
|
||||
|
||||
varobs Y C I E PIE W R;
|
||||
|
||||
//estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118, lik_init=2, mode_compute=1,mh_replic=0);
|
||||
estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118,mh_jscale=0.2,mh_replic=1000
|
||||
//,mode_compute=0,mode_file=sweuromodel_dll_mode
|
||||
);
|
||||
|
||||
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,182 +1,182 @@
|
|||
//options_.usePartInfo=1;
|
||||
|
||||
var MC E EF R_KF QF CF IF YF LF PIEF WF RF R_K Q C I Y L PIE W R EE_A PIE_BAR EE_B EE_G EE_L EE_I KF K one BIGTHETA;
|
||||
|
||||
varexo E_A E_B E_G E_L E_I ETA_R E_PIE_BAR ETA_Q ETA_P ETA_W ;
|
||||
|
||||
parameters
|
||||
xi_e lambda_w alpha czcap beta phi_i tau sig_c hab ccs cinvs phi_y gamma_w xi_w gamma_p xi_p sig_l r_dpi
|
||||
r_pie r_dy r_y rho rho_a rho_pb rho_b rho_g rho_l rho_i LMP ;
|
||||
|
||||
|
||||
|
||||
alpha=.30;
|
||||
beta=.99;
|
||||
tau=0.025;
|
||||
ccs=0.6;
|
||||
cinvs=.22; //% alpha*(tau+ctrend)/R_K R_K=ctrend/beta-1+tau
|
||||
lambda_w = 0.5;
|
||||
phi_i= 6.771;
|
||||
sig_c= 1.353;
|
||||
hab= 0.573;
|
||||
xi_w= 0.737;
|
||||
sig_l= 2.400;
|
||||
xi_p= 0.908;
|
||||
xi_e= 0.599;
|
||||
gamma_w= 0.763;
|
||||
gamma_p= 0.469;
|
||||
czcap= 0.169;
|
||||
phi_y= 1.408;
|
||||
r_pie= 1.684;
|
||||
r_dpi= 0.14;
|
||||
rho= 0.961;
|
||||
r_y= 0.099;
|
||||
r_dy= 0.159;
|
||||
rho_a= 0.823;
|
||||
rho_b= 0.855;
|
||||
rho_g= 0.949;
|
||||
rho_l= 0.889;
|
||||
rho_i= 0.927;
|
||||
rho_pb= 0.924;
|
||||
LMP = 0.0 ; //NEW.
|
||||
|
||||
model(linear, use_dll);
|
||||
CF = (1/(1+hab))*(CF(1)+hab*CF(-1))-((1-hab)/((1+hab)*sig_c))*(RF-PIEF(1)-EE_B) ;
|
||||
0 = alpha*R_KF+(1-alpha)*WF -EE_A ;
|
||||
PIEF = 0*one;
|
||||
IF = (1/(1+beta))* (( IF(-1) + beta*(IF(1)))+(1/phi_i)*QF)+0*ETA_Q+EE_I ;
|
||||
QF = -(RF-PIEF(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_KF(1)+beta*(1-tau)*QF(1) +0*EE_I ;
|
||||
KF = (1-tau)*KF(-1)+tau*IF(-1) ;
|
||||
YF = (ccs*CF+cinvs*IF)+EE_G ;
|
||||
|
||||
YF = 1*phi_y*( alpha*KF+alpha*(1/czcap)*R_KF+(1-alpha)*LF+EE_A ) ;
|
||||
WF = (sig_c/(1-hab))*(CF-hab*CF(-1)) + sig_l*LF - EE_L ;
|
||||
LF = R_KF*((1+czcap)/czcap)-WF+KF ;
|
||||
EF = EF(-1)+EF(1)-EF+(LF-EF)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
C = (hab/(1+hab))*C(-1)+(1/(1+hab))*C(1)-((1-hab)/((1+hab)*sig_c))*(R-PIE(1)-EE_B) ;
|
||||
I = (1/(1+beta))* (( I(-1) + beta*(I(1)))+(1/phi_i)*Q )+1*ETA_Q+1*EE_I ;
|
||||
Q = -(R-PIE(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_K(1)+beta*(1-tau)*Q(1) +EE_I*0+0*ETA_Q ;
|
||||
K = (1-tau)*K(-1)+tau*I(-1) ;
|
||||
Y = (ccs*C+cinvs*I)+ EE_G ;
|
||||
Y = phi_y*( alpha*K+alpha*(1/czcap)*R_K+(1-alpha)*L ) +phi_y*EE_A ;
|
||||
PIE = (1/(1+beta*gamma_p))*
|
||||
(
|
||||
(beta)*(PIE(1)) +(gamma_p)*(PIE(-1))
|
||||
+((1-xi_p)*(1-beta*xi_p)/(xi_p))*(MC)
|
||||
) + ETA_P ;
|
||||
|
||||
MC = alpha*R_K+(1-alpha)*W -EE_A;
|
||||
W = (1/(1+beta))*(beta*W(+1)+W(-1))
|
||||
+(beta/(1+beta))*(PIE(+1))
|
||||
-((1+beta*gamma_w)/(1+beta))*(PIE)
|
||||
+(gamma_w/(1+beta))*(PIE(-1))
|
||||
-(1/(1+beta))*(((1-beta*xi_w)*(1-xi_w))/(((1+(((1+lambda_w)*sig_l)/(lambda_w))))*xi_w))*(W-sig_l*L-(sig_c/(1-hab))*(C-hab*C(-1))+EE_L)
|
||||
+ETA_W;
|
||||
L = R_K*((1+czcap)/czcap)-W+K ;
|
||||
|
||||
// R = r_dpi*(PIE-PIE(-1))
|
||||
// +(1-rho)*(r_pie*(PIE(-1)-PIE_BAR)+r_y*(Y-YF))
|
||||
// +r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
// +rho*(R(-1)-PIE_BAR)
|
||||
// +PIE_BAR
|
||||
// +ETA_R;
|
||||
|
||||
|
||||
R =
|
||||
|
||||
r_dpi*(PIE-PIE(-1))
|
||||
|
||||
+(1-rho)*(r_pie*(BIGTHETA)+r_y*(Y-YF))
|
||||
+r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
+rho*(R(-1)-PIE_BAR)
|
||||
+PIE_BAR
|
||||
+ETA_R;
|
||||
|
||||
|
||||
E = E(-1)+E(1)-E+(L-E)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
|
||||
EE_A = (rho_a)*EE_A(-1) + E_A;
|
||||
PIE_BAR = rho_pb*PIE_BAR(-1)+ E_PIE_BAR ;
|
||||
EE_B = rho_b*EE_B(-1) + E_B ;
|
||||
EE_G = rho_g*EE_G(-1) + E_G ;
|
||||
EE_L = rho_l*EE_L(-1) + E_L ;
|
||||
EE_I = rho_i*EE_I(-1) + E_I ;
|
||||
one = 0*one(-1) ;
|
||||
|
||||
LMP*BIGTHETA(1) = BIGTHETA - (PIE(-1) - PIE_BAR) ;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
shocks;
|
||||
var E_A; stderr 0.598;
|
||||
var E_B; stderr 0.336;
|
||||
var E_G; stderr 0.325;
|
||||
var E_I; stderr 0.085;
|
||||
var E_L; stderr 3.520;
|
||||
var ETA_P; stderr 0.160;
|
||||
var ETA_W; stderr 0.289;
|
||||
var ETA_R; stderr 0.081;
|
||||
var ETA_Q; stderr 0.604;
|
||||
var E_PIE_BAR; stderr 0.017;
|
||||
end;
|
||||
|
||||
//stoch_simul(irf=20) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
// stoch_simul generates what kind of standard errors for the shocks ?
|
||||
|
||||
//steady;
|
||||
//check;
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE MC R W R_K E L I ;
|
||||
|
||||
//datatomfile('ddd',[]);
|
||||
|
||||
// new syntax
|
||||
|
||||
estimated_params;
|
||||
// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE
|
||||
// PRIOR_SHAPE: BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF
|
||||
stderr E_A,0.543,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr E_PIE_BAR,0.072,0.001,4,INV_GAMMA_PDF,0.02,10;
|
||||
stderr E_B,0.2694,0.01,4,INV_GAMMA_PDF,0.2,2;
|
||||
stderr E_G,0.3052,0.01,4,INV_GAMMA_PDF,0.3,2;
|
||||
stderr E_L,1.4575,0.1,6,INV_GAMMA_PDF,1,2;
|
||||
stderr E_I,0.1318,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_R,0.1363,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_Q,0.4842,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr ETA_P,0.1731,0.01,4,INV_GAMMA_PDF,0.15,2;
|
||||
stderr ETA_W,0.2462,0.1,4,INV_GAMMA_PDF,0.25,2;
|
||||
rho_a,.9722,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_pb,.85,.1,.999,BETA_PDF,0.85,0.1;
|
||||
rho_b,.7647,.1,.99,BETA_PDF,0.85,0.1;
|
||||
rho_g,.9502,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_l,.9542,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_i,.6705,.1,.99,BETA_PDF,0.85,0.1;
|
||||
phi_i,5.2083,1,15,NORMAL_PDF,4,1.5;
|
||||
sig_c,0.9817,0.25,3,NORMAL_PDF,1,0.375;
|
||||
hab,0.5612,0.3,0.95,BETA_PDF,0.7,0.1;
|
||||
xi_w,0.7661,0.3,0.9,BETA_PDF,0.75,0.05;
|
||||
sig_l,1.7526,0.5,5,NORMAL_PDF,2,0.75;
|
||||
xi_p,0.8684,0.3,0.95,BETA_PDF,0.75,0.05;
|
||||
xi_e,0.5724,0.1,0.95,BETA_PDF,0.5,0.15;
|
||||
gamma_w,0.6202,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
gamma_p,0.6638,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
czcap,0.2516,0.01,2,NORMAL_PDF,0.2,0.075;
|
||||
phi_y,1.3011,1.001,2,NORMAL_PDF,1.45,0.125;
|
||||
r_pie,1.4616,1.2,2,NORMAL_PDF,1.7,0.1;
|
||||
r_dpi,0.1144,0.01,0.5,NORMAL_PDF,0.3,0.1;
|
||||
rho,0.8865,0.5,0.99,BETA_PDF,0.8,0.10;
|
||||
r_y,0.0571,0.01,0.2,NORMAL_PDF,0.125,0.05;
|
||||
r_dy,0.2228,0.05,0.5,NORMAL_PDF,0.0625,0.05;
|
||||
end;
|
||||
|
||||
varobs Y C I E PIE W R;
|
||||
|
||||
//estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118, lik_init=2, mode_compute=1,mh_replic=0);
|
||||
estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118,mh_jscale=0.2,mh_replic=150000, mode_check); //
|
||||
|
||||
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
//options_.usePartInfo=1;
|
||||
|
||||
var MC E EF R_KF QF CF IF YF LF PIEF WF RF R_K Q C I Y L PIE W R EE_A PIE_BAR EE_B EE_G EE_L EE_I KF K one BIGTHETA;
|
||||
|
||||
varexo E_A E_B E_G E_L E_I ETA_R E_PIE_BAR ETA_Q ETA_P ETA_W ;
|
||||
|
||||
parameters
|
||||
xi_e lambda_w alpha czcap beta phi_i tau sig_c hab ccs cinvs phi_y gamma_w xi_w gamma_p xi_p sig_l r_dpi
|
||||
r_pie r_dy r_y rho rho_a rho_pb rho_b rho_g rho_l rho_i LMP ;
|
||||
|
||||
|
||||
|
||||
alpha=.30;
|
||||
beta=.99;
|
||||
tau=0.025;
|
||||
ccs=0.6;
|
||||
cinvs=.22; //% alpha*(tau+ctrend)/R_K R_K=ctrend/beta-1+tau
|
||||
lambda_w = 0.5;
|
||||
phi_i= 6.771;
|
||||
sig_c= 1.353;
|
||||
hab= 0.573;
|
||||
xi_w= 0.737;
|
||||
sig_l= 2.400;
|
||||
xi_p= 0.908;
|
||||
xi_e= 0.599;
|
||||
gamma_w= 0.763;
|
||||
gamma_p= 0.469;
|
||||
czcap= 0.169;
|
||||
phi_y= 1.408;
|
||||
r_pie= 1.684;
|
||||
r_dpi= 0.14;
|
||||
rho= 0.961;
|
||||
r_y= 0.099;
|
||||
r_dy= 0.159;
|
||||
rho_a= 0.823;
|
||||
rho_b= 0.855;
|
||||
rho_g= 0.949;
|
||||
rho_l= 0.889;
|
||||
rho_i= 0.927;
|
||||
rho_pb= 0.924;
|
||||
LMP = 0.0 ; //NEW.
|
||||
|
||||
model(linear, use_dll);
|
||||
CF = (1/(1+hab))*(CF(1)+hab*CF(-1))-((1-hab)/((1+hab)*sig_c))*(RF-PIEF(1)-EE_B) ;
|
||||
0 = alpha*R_KF+(1-alpha)*WF -EE_A ;
|
||||
PIEF = 0*one;
|
||||
IF = (1/(1+beta))* (( IF(-1) + beta*(IF(1)))+(1/phi_i)*QF)+0*ETA_Q+EE_I ;
|
||||
QF = -(RF-PIEF(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_KF(1)+beta*(1-tau)*QF(1) +0*EE_I ;
|
||||
KF = (1-tau)*KF(-1)+tau*IF(-1) ;
|
||||
YF = (ccs*CF+cinvs*IF)+EE_G ;
|
||||
|
||||
YF = 1*phi_y*( alpha*KF+alpha*(1/czcap)*R_KF+(1-alpha)*LF+EE_A ) ;
|
||||
WF = (sig_c/(1-hab))*(CF-hab*CF(-1)) + sig_l*LF - EE_L ;
|
||||
LF = R_KF*((1+czcap)/czcap)-WF+KF ;
|
||||
EF = EF(-1)+EF(1)-EF+(LF-EF)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
C = (hab/(1+hab))*C(-1)+(1/(1+hab))*C(1)-((1-hab)/((1+hab)*sig_c))*(R-PIE(1)-EE_B) ;
|
||||
I = (1/(1+beta))* (( I(-1) + beta*(I(1)))+(1/phi_i)*Q )+1*ETA_Q+1*EE_I ;
|
||||
Q = -(R-PIE(1))+(1-beta*(1-tau))*((0+czcap)/czcap)*R_K(1)+beta*(1-tau)*Q(1) +EE_I*0+0*ETA_Q ;
|
||||
K = (1-tau)*K(-1)+tau*I(-1) ;
|
||||
Y = (ccs*C+cinvs*I)+ EE_G ;
|
||||
Y = phi_y*( alpha*K+alpha*(1/czcap)*R_K+(1-alpha)*L ) +phi_y*EE_A ;
|
||||
PIE = (1/(1+beta*gamma_p))*
|
||||
(
|
||||
(beta)*(PIE(1)) +(gamma_p)*(PIE(-1))
|
||||
+((1-xi_p)*(1-beta*xi_p)/(xi_p))*(MC)
|
||||
) + ETA_P ;
|
||||
|
||||
MC = alpha*R_K+(1-alpha)*W -EE_A;
|
||||
W = (1/(1+beta))*(beta*W(+1)+W(-1))
|
||||
+(beta/(1+beta))*(PIE(+1))
|
||||
-((1+beta*gamma_w)/(1+beta))*(PIE)
|
||||
+(gamma_w/(1+beta))*(PIE(-1))
|
||||
-(1/(1+beta))*(((1-beta*xi_w)*(1-xi_w))/(((1+(((1+lambda_w)*sig_l)/(lambda_w))))*xi_w))*(W-sig_l*L-(sig_c/(1-hab))*(C-hab*C(-1))+EE_L)
|
||||
+ETA_W;
|
||||
L = R_K*((1+czcap)/czcap)-W+K ;
|
||||
|
||||
// R = r_dpi*(PIE-PIE(-1))
|
||||
// +(1-rho)*(r_pie*(PIE(-1)-PIE_BAR)+r_y*(Y-YF))
|
||||
// +r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
// +rho*(R(-1)-PIE_BAR)
|
||||
// +PIE_BAR
|
||||
// +ETA_R;
|
||||
|
||||
|
||||
R =
|
||||
|
||||
r_dpi*(PIE-PIE(-1))
|
||||
|
||||
+(1-rho)*(r_pie*(BIGTHETA)+r_y*(Y-YF))
|
||||
+r_dy*(Y-YF-(Y(-1)-YF(-1)))
|
||||
+rho*(R(-1)-PIE_BAR)
|
||||
+PIE_BAR
|
||||
+ETA_R;
|
||||
|
||||
|
||||
E = E(-1)+E(1)-E+(L-E)*((1-xi_e)*(1-xi_e*beta)/(xi_e));
|
||||
|
||||
|
||||
EE_A = (rho_a)*EE_A(-1) + E_A;
|
||||
PIE_BAR = rho_pb*PIE_BAR(-1)+ E_PIE_BAR ;
|
||||
EE_B = rho_b*EE_B(-1) + E_B ;
|
||||
EE_G = rho_g*EE_G(-1) + E_G ;
|
||||
EE_L = rho_l*EE_L(-1) + E_L ;
|
||||
EE_I = rho_i*EE_I(-1) + E_I ;
|
||||
one = 0*one(-1) ;
|
||||
|
||||
LMP*BIGTHETA(1) = BIGTHETA - (PIE(-1) - PIE_BAR) ;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
shocks;
|
||||
var E_A; stderr 0.598;
|
||||
var E_B; stderr 0.336;
|
||||
var E_G; stderr 0.325;
|
||||
var E_I; stderr 0.085;
|
||||
var E_L; stderr 3.520;
|
||||
var ETA_P; stderr 0.160;
|
||||
var ETA_W; stderr 0.289;
|
||||
var ETA_R; stderr 0.081;
|
||||
var ETA_Q; stderr 0.604;
|
||||
var E_PIE_BAR; stderr 0.017;
|
||||
end;
|
||||
|
||||
//stoch_simul(irf=20) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
// stoch_simul generates what kind of standard errors for the shocks ?
|
||||
|
||||
//steady;
|
||||
//check;
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE MC R W R_K E L I ;
|
||||
|
||||
//datatomfile('ddd',[]);
|
||||
|
||||
// new syntax
|
||||
|
||||
estimated_params;
|
||||
// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE
|
||||
// PRIOR_SHAPE: BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF
|
||||
stderr E_A,0.543,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr E_PIE_BAR,0.072,0.001,4,INV_GAMMA_PDF,0.02,10;
|
||||
stderr E_B,0.2694,0.01,4,INV_GAMMA_PDF,0.2,2;
|
||||
stderr E_G,0.3052,0.01,4,INV_GAMMA_PDF,0.3,2;
|
||||
stderr E_L,1.4575,0.1,6,INV_GAMMA_PDF,1,2;
|
||||
stderr E_I,0.1318,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_R,0.1363,0.01,4,INV_GAMMA_PDF,0.1,2;
|
||||
stderr ETA_Q,0.4842,0.01,4,INV_GAMMA_PDF,0.4,2;
|
||||
stderr ETA_P,0.1731,0.01,4,INV_GAMMA_PDF,0.15,2;
|
||||
stderr ETA_W,0.2462,0.1,4,INV_GAMMA_PDF,0.25,2;
|
||||
rho_a,.9722,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_pb,.85,.1,.999,BETA_PDF,0.85,0.1;
|
||||
rho_b,.7647,.1,.99,BETA_PDF,0.85,0.1;
|
||||
rho_g,.9502,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_l,.9542,.1,.9999,BETA_PDF,0.85,0.1;
|
||||
rho_i,.6705,.1,.99,BETA_PDF,0.85,0.1;
|
||||
phi_i,5.2083,1,15,NORMAL_PDF,4,1.5;
|
||||
sig_c,0.9817,0.25,3,NORMAL_PDF,1,0.375;
|
||||
hab,0.5612,0.3,0.95,BETA_PDF,0.7,0.1;
|
||||
xi_w,0.7661,0.3,0.9,BETA_PDF,0.75,0.05;
|
||||
sig_l,1.7526,0.5,5,NORMAL_PDF,2,0.75;
|
||||
xi_p,0.8684,0.3,0.95,BETA_PDF,0.75,0.05;
|
||||
xi_e,0.5724,0.1,0.95,BETA_PDF,0.5,0.15;
|
||||
gamma_w,0.6202,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
gamma_p,0.6638,0.1,0.99,BETA_PDF,0.75,0.15;
|
||||
czcap,0.2516,0.01,2,NORMAL_PDF,0.2,0.075;
|
||||
phi_y,1.3011,1.001,2,NORMAL_PDF,1.45,0.125;
|
||||
r_pie,1.4616,1.2,2,NORMAL_PDF,1.7,0.1;
|
||||
r_dpi,0.1144,0.01,0.5,NORMAL_PDF,0.3,0.1;
|
||||
rho,0.8865,0.5,0.99,BETA_PDF,0.8,0.10;
|
||||
r_y,0.0571,0.01,0.2,NORMAL_PDF,0.125,0.05;
|
||||
r_dy,0.2228,0.05,0.5,NORMAL_PDF,0.0625,0.05;
|
||||
end;
|
||||
|
||||
varobs Y C I E PIE W R;
|
||||
|
||||
//estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118, lik_init=2, mode_compute=1,mh_replic=0);
|
||||
estimation(datafile=rawdata_euromodel_1,presample=40, first_obs=1, nobs=118,mh_jscale=0.2,mh_replic=150000, mode_check); //
|
||||
|
||||
|
||||
//stoch_simul(periods=200,irf=20,simul_seed=3) Y C PIE R W R_K L Q I K ;
|
||||
|
||||
|
|
|
|||
|
|
@ -1,119 +1,119 @@
|
|||
// This file replicates the estimation of the CIA model from
|
||||
// Frank Schorfheide (2000) "Loss function-based evaluation of DSGE models"
|
||||
// Journal of Applied Econometrics, 15, 645-670.
|
||||
// the data are the ones provided on Schorfheide's web site with the programs.
|
||||
// http://www.econ.upenn.edu/~schorf/programs/dsgesel.ZIP
|
||||
// You need to have fsdat.m in the same directory as this file.
|
||||
// This file replicates:
|
||||
// -the posterior mode as computed by Frank's Gauss programs
|
||||
// -the parameter mean posterior estimates reported in the paper
|
||||
// -the model probability (harmonic mean) reported in the paper
|
||||
// This file was tested with dyn_mat_test_0218.zip
|
||||
// the smooth shocks are probably stil buggy
|
||||
//
|
||||
// The equations are taken from J. Nason and T. Cogley (1994)
|
||||
// "Testing the implications of long-run neutrality for monetary business
|
||||
// cycle models" Journal of Applied Econometrics, 9, S37-S70.
|
||||
// Note that there is an initial minus sign missing in equation (A1), p. S63.
|
||||
//
|
||||
// Michel Juillard, February 2004
|
||||
// Modified for testing k_order_perturbation by GP, Jan-Feb 09
|
||||
|
||||
options_.usePartInfo=0;
|
||||
options_.use_k_order=0;
|
||||
|
||||
//var m m_1 P P_1 c e W R k d n l gy_obs gp_obs Y_obs P_obs y dA P2 c2;
|
||||
var m m_1 P P_1 c e W R k d n l gy_obs gp_obs y dA P2 c2;
|
||||
varexo e_a e_m;
|
||||
|
||||
parameters alp bet gam mst rho psi del;
|
||||
|
||||
alp = 0.33;
|
||||
bet = 0.99;
|
||||
gam = 0.003;
|
||||
mst = 1.011;
|
||||
rho = 0.7;
|
||||
psi = 0.787;
|
||||
del = 0.02;
|
||||
|
||||
model (use_dll);
|
||||
dA = exp(gam+e_a);
|
||||
log(m) = (1-rho)*log(mst) + rho*log(m_1(-1))+e_m;
|
||||
-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c2(+1)*P2(+1)*m(+1))=0;
|
||||
W = l/n;
|
||||
-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
|
||||
R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
|
||||
1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
|
||||
c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
|
||||
P*c = m;
|
||||
m-1+d = l;
|
||||
e = exp(e_a);
|
||||
y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
|
||||
gy_obs = dA*y/y(-1);
|
||||
gp_obs = (P/P_1(-1))*m_1(-1)/dA;
|
||||
//Y_obs/Y_obs(-1) = gy_obs;
|
||||
//P_obs/P_obs(-1) = gp_obs;
|
||||
P2 = P(+1);
|
||||
c2 = c(+1);
|
||||
m_1 = m;
|
||||
P_1 = P;
|
||||
end;
|
||||
|
||||
initval;
|
||||
m = mst;
|
||||
m_1=mst;
|
||||
P = 2.25;
|
||||
P_1 = 2.25;
|
||||
c = 0.45;
|
||||
e = 1;
|
||||
W = 4;
|
||||
R = 1.02;
|
||||
k = 6;
|
||||
d = 0.85;
|
||||
n = 0.19;
|
||||
l = 0.86;
|
||||
y = 0.6;
|
||||
gy_obs = exp(gam);
|
||||
gp_obs = exp(-gam);
|
||||
dA = exp(gam);
|
||||
P2=P;
|
||||
c2=c;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e_a; stderr 0.014;
|
||||
var e_m; stderr 0.005;
|
||||
end;
|
||||
|
||||
//unit_root_vars P_obs Y_obs;
|
||||
|
||||
steady(solve_algo = 2);
|
||||
|
||||
check;
|
||||
|
||||
estimated_params;
|
||||
alp, beta_pdf, 0.356, 0.02;
|
||||
bet, beta_pdf, 0.993, 0.002;
|
||||
gam, normal_pdf, 0.0085, 0.003;
|
||||
mst, normal_pdf, 1.0002, 0.007;
|
||||
rho, beta_pdf, 0.129, 0.223;
|
||||
psi, beta_pdf, 0.65, 0.05;
|
||||
del, beta_pdf, 0.01, 0.005;
|
||||
stderr e_a, inv_gamma_pdf, 0.035449, inf;
|
||||
stderr e_m, inv_gamma_pdf, 0.008862, inf;
|
||||
end;
|
||||
|
||||
//varobs P_obs Y_obs;
|
||||
varobs gp_obs gy_obs;
|
||||
|
||||
steady(solve_algo = 2);
|
||||
|
||||
//observation_trends;
|
||||
//P_obs (log(mst)-gam);
|
||||
//Y_obs (gam);
|
||||
//end;
|
||||
|
||||
//options_.useAIM = 1;
|
||||
estimation(datafile=fsdat,nobs=192,loglinear,mh_replic=2000,
|
||||
mode_compute=4,mh_nblocks=2,mh_drop=0.45,mh_jscale=0.65);
|
||||
|
||||
// This file replicates the estimation of the CIA model from
|
||||
// Frank Schorfheide (2000) "Loss function-based evaluation of DSGE models"
|
||||
// Journal of Applied Econometrics, 15, 645-670.
|
||||
// the data are the ones provided on Schorfheide's web site with the programs.
|
||||
// http://www.econ.upenn.edu/~schorf/programs/dsgesel.ZIP
|
||||
// You need to have fsdat.m in the same directory as this file.
|
||||
// This file replicates:
|
||||
// -the posterior mode as computed by Frank's Gauss programs
|
||||
// -the parameter mean posterior estimates reported in the paper
|
||||
// -the model probability (harmonic mean) reported in the paper
|
||||
// This file was tested with dyn_mat_test_0218.zip
|
||||
// the smooth shocks are probably stil buggy
|
||||
//
|
||||
// The equations are taken from J. Nason and T. Cogley (1994)
|
||||
// "Testing the implications of long-run neutrality for monetary business
|
||||
// cycle models" Journal of Applied Econometrics, 9, S37-S70.
|
||||
// Note that there is an initial minus sign missing in equation (A1), p. S63.
|
||||
//
|
||||
// Michel Juillard, February 2004
|
||||
// Modified for testing k_order_perturbation by GP, Jan-Feb 09
|
||||
|
||||
options_.usePartInfo=0;
|
||||
options_.use_k_order=0;
|
||||
|
||||
//var m m_1 P P_1 c e W R k d n l gy_obs gp_obs Y_obs P_obs y dA P2 c2;
|
||||
var m m_1 P P_1 c e W R k d n l gy_obs gp_obs y dA P2 c2;
|
||||
varexo e_a e_m;
|
||||
|
||||
parameters alp bet gam mst rho psi del;
|
||||
|
||||
alp = 0.33;
|
||||
bet = 0.99;
|
||||
gam = 0.003;
|
||||
mst = 1.011;
|
||||
rho = 0.7;
|
||||
psi = 0.787;
|
||||
del = 0.02;
|
||||
|
||||
model (use_dll);
|
||||
dA = exp(gam+e_a);
|
||||
log(m) = (1-rho)*log(mst) + rho*log(m_1(-1))+e_m;
|
||||
-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c2(+1)*P2(+1)*m(+1))=0;
|
||||
W = l/n;
|
||||
-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
|
||||
R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
|
||||
1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
|
||||
c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
|
||||
P*c = m;
|
||||
m-1+d = l;
|
||||
e = exp(e_a);
|
||||
y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
|
||||
gy_obs = dA*y/y(-1);
|
||||
gp_obs = (P/P_1(-1))*m_1(-1)/dA;
|
||||
//Y_obs/Y_obs(-1) = gy_obs;
|
||||
//P_obs/P_obs(-1) = gp_obs;
|
||||
P2 = P(+1);
|
||||
c2 = c(+1);
|
||||
m_1 = m;
|
||||
P_1 = P;
|
||||
end;
|
||||
|
||||
initval;
|
||||
m = mst;
|
||||
m_1=mst;
|
||||
P = 2.25;
|
||||
P_1 = 2.25;
|
||||
c = 0.45;
|
||||
e = 1;
|
||||
W = 4;
|
||||
R = 1.02;
|
||||
k = 6;
|
||||
d = 0.85;
|
||||
n = 0.19;
|
||||
l = 0.86;
|
||||
y = 0.6;
|
||||
gy_obs = exp(gam);
|
||||
gp_obs = exp(-gam);
|
||||
dA = exp(gam);
|
||||
P2=P;
|
||||
c2=c;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e_a; stderr 0.014;
|
||||
var e_m; stderr 0.005;
|
||||
end;
|
||||
|
||||
//unit_root_vars P_obs Y_obs;
|
||||
|
||||
steady(solve_algo = 2);
|
||||
|
||||
check;
|
||||
|
||||
estimated_params;
|
||||
alp, beta_pdf, 0.356, 0.02;
|
||||
bet, beta_pdf, 0.993, 0.002;
|
||||
gam, normal_pdf, 0.0085, 0.003;
|
||||
mst, normal_pdf, 1.0002, 0.007;
|
||||
rho, beta_pdf, 0.129, 0.223;
|
||||
psi, beta_pdf, 0.65, 0.05;
|
||||
del, beta_pdf, 0.01, 0.005;
|
||||
stderr e_a, inv_gamma_pdf, 0.035449, inf;
|
||||
stderr e_m, inv_gamma_pdf, 0.008862, inf;
|
||||
end;
|
||||
|
||||
//varobs P_obs Y_obs;
|
||||
varobs gp_obs gy_obs;
|
||||
|
||||
steady(solve_algo = 2);
|
||||
|
||||
//observation_trends;
|
||||
//P_obs (log(mst)-gam);
|
||||
//Y_obs (gam);
|
||||
//end;
|
||||
|
||||
//options_.useAIM = 1;
|
||||
estimation(datafile=fsdat,nobs=192,loglinear,mh_replic=2000,
|
||||
mode_compute=4,mh_nblocks=2,mh_drop=0.45,mh_jscale=0.65);
|
||||
|
||||
|
|
|
|||
|
|
@ -1,100 +1,100 @@
|
|||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
1.68081431462 3.34729969129 10 1.41159342106 -1.59065680853 ...
|
||||
-0.343321601133 5.05563513564 12 1.75117366498 -2.40127764642 ...
|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
-0.562233624818 3.88598638237 9.75 -0.0505384765105 0.332826708151 ...
|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
0.842215068977 3.11164509647 12.25 -1.08290421696 0.014323281961 ...
|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
-0.418465249225 3.75861110232 14.75 -1.03131674824 0.188507675831 ...
|
||||
-0.644028342116 4.15104788154 13.75 -1.48911756546 0.204560913792 ...
|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
-0.00264276644799 3.07989972052 8.75 -2.56342461535 2.105998353 ...
|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
1.68081431462 3.34729969129 10 1.41159342106 -1.59065680853 ...
|
||||
-0.343321601133 5.05563513564 12 1.75117366498 -2.40127764642 ...
|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
-0.562233624818 3.88598638237 9.75 -0.0505384765105 0.332826708151 ...
|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
0.842215068977 3.11164509647 12.25 -1.08290421696 0.014323281961 ...
|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
-0.418465249225 3.75861110232 14.75 -1.03131674824 0.188507675831 ...
|
||||
-0.644028342116 4.15104788154 13.75 -1.48911756546 0.204560913792 ...
|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
-0.00264276644799 3.07989972052 8.75 -2.56342461535 2.105998353 ...
|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
|
|
|
|||
|
|
@ -1,65 +1,65 @@
|
|||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000k_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
P2=P;
|
||||
c2=c;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
dA
|
||||
P2
|
||||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000k_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
P2=P;
|
||||
c2=c;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
dA
|
||||
P2
|
||||
c2 ];
|
||||
|
|
@ -1,65 +1,65 @@
|
|||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000k_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
P2=P;
|
||||
c2=c;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
dA
|
||||
P2
|
||||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000k_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
P2=P;
|
||||
c2=c;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
dA
|
||||
P2
|
||||
c2 ];
|
||||
|
|
@ -1,210 +1,210 @@
|
|||
data_q = [
|
||||
18.02 1474.5 150.2
|
||||
17.94 1538.2 150.9
|
||||
18.01 1584.5 151.4
|
||||
18.42 1644.1 152
|
||||
18.73 1678.6 152.7
|
||||
19.46 1693.1 153.3
|
||||
19.55 1724 153.9
|
||||
19.56 1758.2 154.7
|
||||
19.79 1760.6 155.4
|
||||
19.77 1779.2 156
|
||||
19.82 1778.8 156.6
|
||||
20.03 1790.9 157.3
|
||||
20.12 1846 158
|
||||
20.1 1882.6 158.6
|
||||
20.14 1897.3 159.2
|
||||
20.22 1887.4 160
|
||||
20.27 1858.2 160.7
|
||||
20.34 1849.9 161.4
|
||||
20.39 1848.5 162
|
||||
20.42 1868.9 162.8
|
||||
20.47 1905.6 163.6
|
||||
20.56 1959.6 164.3
|
||||
20.62 1994.4 164.9
|
||||
20.78 2020.1 165.7
|
||||
21 2030.5 166.5
|
||||
21.2 2023.6 167.2
|
||||
21.33 2037.7 167.9
|
||||
21.62 2033.4 168.7
|
||||
21.71 2066.2 169.5
|
||||
22.01 2077.5 170.2
|
||||
22.15 2071.9 170.9
|
||||
22.27 2094 171.7
|
||||
22.29 2070.8 172.5
|
||||
22.56 2012.6 173.1
|
||||
22.64 2024.7 173.8
|
||||
22.77 2072.3 174.5
|
||||
22.88 2120.6 175.3
|
||||
22.92 2165 176.045
|
||||
22.91 2223.3 176.727
|
||||
22.94 2221.4 177.481
|
||||
23.03 2230.95 178.268
|
||||
23.13 2279.22 179.694
|
||||
23.22 2265.48 180.335
|
||||
23.32 2268.29 181.094
|
||||
23.4 2238.57 181.915
|
||||
23.45 2251.68 182.634
|
||||
23.51 2292.02 183.337
|
||||
23.56 2332.61 184.103
|
||||
23.63 2381.01 184.894
|
||||
23.75 2422.59 185.553
|
||||
23.81 2448.01 186.203
|
||||
23.87 2471.86 186.926
|
||||
23.94 2476.67 187.68
|
||||
24 2508.7 188.299
|
||||
24.07 2538.05 188.906
|
||||
24.12 2586.26 189.631
|
||||
24.29 2604.62 190.362
|
||||
24.35 2666.69 190.954
|
||||
24.41 2697.54 191.56
|
||||
24.52 2729.63 192.256
|
||||
24.64 2739.75 192.938
|
||||
24.77 2808.88 193.467
|
||||
24.88 2846.34 193.994
|
||||
25.01 2898.79 194.647
|
||||
25.17 2970.48 195.279
|
||||
25.32 3042.35 195.763
|
||||
25.53 3055.53 196.277
|
||||
25.79 3076.51 196.877
|
||||
26.02 3102.36 197.481
|
||||
26.14 3127.15 197.967
|
||||
26.31 3129.53 198.455
|
||||
26.6 3154.19 199.012
|
||||
26.9 3177.98 199.572
|
||||
27.21 3236.18 199.995
|
||||
27.49 3292.07 200.452
|
||||
27.75 3316.11 200.997
|
||||
28.12 3331.22 201.538
|
||||
28.39 3381.86 201.955
|
||||
28.73 3390.23 202.419
|
||||
29.14 3409.65 202.986
|
||||
29.51 3392.6 203.584
|
||||
29.94 3386.49 204.086
|
||||
30.36 3391.61 204.721
|
||||
30.61 3422.95 205.419
|
||||
31.02 3389.36 206.13
|
||||
31.5 3481.4 206.763
|
||||
31.93 3500.95 207.362
|
||||
32.27 3523.8 208
|
||||
32.54 3533.79 208.642
|
||||
33.02 3604.73 209.142
|
||||
33.2 3687.9 209.637
|
||||
33.49 3726.18 210.181
|
||||
33.95 3790.44 210.737
|
||||
34.36 3892.22 211.192
|
||||
34.94 3919.01 211.663
|
||||
35.61 3907.08 212.191
|
||||
36.29 3947.11 212.708
|
||||
37.01 3908.15 213.144
|
||||
37.79 3922.57 213.602
|
||||
38.96 3879.98 214.147
|
||||
40.13 3854.13 214.7
|
||||
41.05 3800.93 215.135
|
||||
41.66 3835.21 215.652
|
||||
42.41 3907.02 216.289
|
||||
43.19 3952.48 216.848
|
||||
43.69 4044.59 217.314
|
||||
44.15 4072.19 217.776
|
||||
44.77 4088.49 218.338
|
||||
45.57 4126.39 218.917
|
||||
46.32 4176.28 219.427
|
||||
47.07 4260.08 219.956
|
||||
47.66 4329.46 220.573
|
||||
48.63 4328.33 221.201
|
||||
49.42 4345.51 221.719
|
||||
50.41 4510.73 222.281
|
||||
51.27 4552.14 222.933
|
||||
52.35 4603.65 223.583
|
||||
53.51 4605.65 224.152
|
||||
54.65 4615.64 224.737
|
||||
55.82 4644.93 225.418
|
||||
56.92 4656.23 226.117
|
||||
58.18 4678.96 226.754
|
||||
59.55 4566.62 227.389
|
||||
61.01 4562.25 228.07
|
||||
62.59 4651.86 228.689
|
||||
64.15 4739.16 229.155
|
||||
65.37 4696.82 229.674
|
||||
66.65 4753.02 230.301
|
||||
67.87 4693.76 230.903
|
||||
68.86 4615.89 231.395
|
||||
69.72 4634.88 231.906
|
||||
70.66 4612.08 232.498
|
||||
71.44 4618.26 233.074
|
||||
72.08 4662.97 233.546
|
||||
72.83 4763.57 234.028
|
||||
73.48 4849 234.603
|
||||
74.19 4939.23 235.153
|
||||
75.02 5053.56 235.605
|
||||
75.58 5132.87 236.082
|
||||
76.25 5170.34 236.657
|
||||
76.81 5203.68 237.232
|
||||
77.63 5257.26 237.673
|
||||
78.25 5283.73 238.176
|
||||
78.76 5359.6 238.789
|
||||
79.45 5393.57 239.387
|
||||
79.81 5460.83 239.861
|
||||
80.22 5466.95 240.368
|
||||
80.84 5496.29 240.962
|
||||
81.45 5526.77 241.539
|
||||
82.09 5561.8 242.009
|
||||
82.68 5618 242.52
|
||||
83.33 5667.39 243.12
|
||||
84.09 5750.57 243.721
|
||||
84.67 5785.29 244.208
|
||||
85.56 5844.05 244.716
|
||||
86.66 5878.7 245.354
|
||||
87.44 5952.83 245.966
|
||||
88.45 6010.96 246.46
|
||||
89.39 6055.61 247.017
|
||||
90.13 6087.96 247.698
|
||||
90.88 6093.51 248.374
|
||||
92 6152.59 248.928
|
||||
93.18 6171.57 249.564
|
||||
94.14 6142.1 250.299
|
||||
95.11 6078.96 251.031
|
||||
96.27 6047.49 251.65
|
||||
97 6074.66 252.295
|
||||
97.7 6090.14 253.033
|
||||
98.31 6105.25 253.743
|
||||
99.13 6175.69 254.338
|
||||
99.79 6214.22 255.032
|
||||
100.17 6260.74 255.815
|
||||
100.88 6327.12 256.543
|
||||
101.84 6327.93 257.151
|
||||
102.35 6359.9 257.785
|
||||
102.83 6393.5 258.516
|
||||
103.51 6476.86 259.191
|
||||
104.13 6524.5 259.738
|
||||
104.71 6600.31 260.351
|
||||
105.39 6629.47 261.04
|
||||
106.09 6688.61 261.692
|
||||
106.75 6717.46 262.236
|
||||
107.24 6724.2 262.847
|
||||
107.75 6779.53 263.527
|
||||
108.29 6825.8 264.169
|
||||
108.91 6882 264.681
|
||||
109.24 6983.91 265.258
|
||||
109.74 7020 265.887
|
||||
110.23 7093.12 266.491
|
||||
111 7166.68 266.987
|
||||
111.43 7236.5 267.545
|
||||
111.76 7311.24 268.171
|
||||
112.08 7364.63 268.815
|
||||
];
|
||||
%GDPD GDPQ GPOP
|
||||
|
||||
series = zeros(193,2);
|
||||
series(:,2) = data_q(:,1);
|
||||
series(:,1) = 1000*data_q(:,2)./data_q(:,3);
|
||||
|
||||
Y_obs = series(:,1);
|
||||
P_obs = series(:,2);
|
||||
|
||||
series = series(2:193,:)./series(1:192,:);
|
||||
|
||||
gy_obs = series(:,1);
|
||||
gp_obs = series(:,2);
|
||||
|
||||
data_q = [
|
||||
18.02 1474.5 150.2
|
||||
17.94 1538.2 150.9
|
||||
18.01 1584.5 151.4
|
||||
18.42 1644.1 152
|
||||
18.73 1678.6 152.7
|
||||
19.46 1693.1 153.3
|
||||
19.55 1724 153.9
|
||||
19.56 1758.2 154.7
|
||||
19.79 1760.6 155.4
|
||||
19.77 1779.2 156
|
||||
19.82 1778.8 156.6
|
||||
20.03 1790.9 157.3
|
||||
20.12 1846 158
|
||||
20.1 1882.6 158.6
|
||||
20.14 1897.3 159.2
|
||||
20.22 1887.4 160
|
||||
20.27 1858.2 160.7
|
||||
20.34 1849.9 161.4
|
||||
20.39 1848.5 162
|
||||
20.42 1868.9 162.8
|
||||
20.47 1905.6 163.6
|
||||
20.56 1959.6 164.3
|
||||
20.62 1994.4 164.9
|
||||
20.78 2020.1 165.7
|
||||
21 2030.5 166.5
|
||||
21.2 2023.6 167.2
|
||||
21.33 2037.7 167.9
|
||||
21.62 2033.4 168.7
|
||||
21.71 2066.2 169.5
|
||||
22.01 2077.5 170.2
|
||||
22.15 2071.9 170.9
|
||||
22.27 2094 171.7
|
||||
22.29 2070.8 172.5
|
||||
22.56 2012.6 173.1
|
||||
22.64 2024.7 173.8
|
||||
22.77 2072.3 174.5
|
||||
22.88 2120.6 175.3
|
||||
22.92 2165 176.045
|
||||
22.91 2223.3 176.727
|
||||
22.94 2221.4 177.481
|
||||
23.03 2230.95 178.268
|
||||
23.13 2279.22 179.694
|
||||
23.22 2265.48 180.335
|
||||
23.32 2268.29 181.094
|
||||
23.4 2238.57 181.915
|
||||
23.45 2251.68 182.634
|
||||
23.51 2292.02 183.337
|
||||
23.56 2332.61 184.103
|
||||
23.63 2381.01 184.894
|
||||
23.75 2422.59 185.553
|
||||
23.81 2448.01 186.203
|
||||
23.87 2471.86 186.926
|
||||
23.94 2476.67 187.68
|
||||
24 2508.7 188.299
|
||||
24.07 2538.05 188.906
|
||||
24.12 2586.26 189.631
|
||||
24.29 2604.62 190.362
|
||||
24.35 2666.69 190.954
|
||||
24.41 2697.54 191.56
|
||||
24.52 2729.63 192.256
|
||||
24.64 2739.75 192.938
|
||||
24.77 2808.88 193.467
|
||||
24.88 2846.34 193.994
|
||||
25.01 2898.79 194.647
|
||||
25.17 2970.48 195.279
|
||||
25.32 3042.35 195.763
|
||||
25.53 3055.53 196.277
|
||||
25.79 3076.51 196.877
|
||||
26.02 3102.36 197.481
|
||||
26.14 3127.15 197.967
|
||||
26.31 3129.53 198.455
|
||||
26.6 3154.19 199.012
|
||||
26.9 3177.98 199.572
|
||||
27.21 3236.18 199.995
|
||||
27.49 3292.07 200.452
|
||||
27.75 3316.11 200.997
|
||||
28.12 3331.22 201.538
|
||||
28.39 3381.86 201.955
|
||||
28.73 3390.23 202.419
|
||||
29.14 3409.65 202.986
|
||||
29.51 3392.6 203.584
|
||||
29.94 3386.49 204.086
|
||||
30.36 3391.61 204.721
|
||||
30.61 3422.95 205.419
|
||||
31.02 3389.36 206.13
|
||||
31.5 3481.4 206.763
|
||||
31.93 3500.95 207.362
|
||||
32.27 3523.8 208
|
||||
32.54 3533.79 208.642
|
||||
33.02 3604.73 209.142
|
||||
33.2 3687.9 209.637
|
||||
33.49 3726.18 210.181
|
||||
33.95 3790.44 210.737
|
||||
34.36 3892.22 211.192
|
||||
34.94 3919.01 211.663
|
||||
35.61 3907.08 212.191
|
||||
36.29 3947.11 212.708
|
||||
37.01 3908.15 213.144
|
||||
37.79 3922.57 213.602
|
||||
38.96 3879.98 214.147
|
||||
40.13 3854.13 214.7
|
||||
41.05 3800.93 215.135
|
||||
41.66 3835.21 215.652
|
||||
42.41 3907.02 216.289
|
||||
43.19 3952.48 216.848
|
||||
43.69 4044.59 217.314
|
||||
44.15 4072.19 217.776
|
||||
44.77 4088.49 218.338
|
||||
45.57 4126.39 218.917
|
||||
46.32 4176.28 219.427
|
||||
47.07 4260.08 219.956
|
||||
47.66 4329.46 220.573
|
||||
48.63 4328.33 221.201
|
||||
49.42 4345.51 221.719
|
||||
50.41 4510.73 222.281
|
||||
51.27 4552.14 222.933
|
||||
52.35 4603.65 223.583
|
||||
53.51 4605.65 224.152
|
||||
54.65 4615.64 224.737
|
||||
55.82 4644.93 225.418
|
||||
56.92 4656.23 226.117
|
||||
58.18 4678.96 226.754
|
||||
59.55 4566.62 227.389
|
||||
61.01 4562.25 228.07
|
||||
62.59 4651.86 228.689
|
||||
64.15 4739.16 229.155
|
||||
65.37 4696.82 229.674
|
||||
66.65 4753.02 230.301
|
||||
67.87 4693.76 230.903
|
||||
68.86 4615.89 231.395
|
||||
69.72 4634.88 231.906
|
||||
70.66 4612.08 232.498
|
||||
71.44 4618.26 233.074
|
||||
72.08 4662.97 233.546
|
||||
72.83 4763.57 234.028
|
||||
73.48 4849 234.603
|
||||
74.19 4939.23 235.153
|
||||
75.02 5053.56 235.605
|
||||
75.58 5132.87 236.082
|
||||
76.25 5170.34 236.657
|
||||
76.81 5203.68 237.232
|
||||
77.63 5257.26 237.673
|
||||
78.25 5283.73 238.176
|
||||
78.76 5359.6 238.789
|
||||
79.45 5393.57 239.387
|
||||
79.81 5460.83 239.861
|
||||
80.22 5466.95 240.368
|
||||
80.84 5496.29 240.962
|
||||
81.45 5526.77 241.539
|
||||
82.09 5561.8 242.009
|
||||
82.68 5618 242.52
|
||||
83.33 5667.39 243.12
|
||||
84.09 5750.57 243.721
|
||||
84.67 5785.29 244.208
|
||||
85.56 5844.05 244.716
|
||||
86.66 5878.7 245.354
|
||||
87.44 5952.83 245.966
|
||||
88.45 6010.96 246.46
|
||||
89.39 6055.61 247.017
|
||||
90.13 6087.96 247.698
|
||||
90.88 6093.51 248.374
|
||||
92 6152.59 248.928
|
||||
93.18 6171.57 249.564
|
||||
94.14 6142.1 250.299
|
||||
95.11 6078.96 251.031
|
||||
96.27 6047.49 251.65
|
||||
97 6074.66 252.295
|
||||
97.7 6090.14 253.033
|
||||
98.31 6105.25 253.743
|
||||
99.13 6175.69 254.338
|
||||
99.79 6214.22 255.032
|
||||
100.17 6260.74 255.815
|
||||
100.88 6327.12 256.543
|
||||
101.84 6327.93 257.151
|
||||
102.35 6359.9 257.785
|
||||
102.83 6393.5 258.516
|
||||
103.51 6476.86 259.191
|
||||
104.13 6524.5 259.738
|
||||
104.71 6600.31 260.351
|
||||
105.39 6629.47 261.04
|
||||
106.09 6688.61 261.692
|
||||
106.75 6717.46 262.236
|
||||
107.24 6724.2 262.847
|
||||
107.75 6779.53 263.527
|
||||
108.29 6825.8 264.169
|
||||
108.91 6882 264.681
|
||||
109.24 6983.91 265.258
|
||||
109.74 7020 265.887
|
||||
110.23 7093.12 266.491
|
||||
111 7166.68 266.987
|
||||
111.43 7236.5 267.545
|
||||
111.76 7311.24 268.171
|
||||
112.08 7364.63 268.815
|
||||
];
|
||||
%GDPD GDPQ GPOP
|
||||
|
||||
series = zeros(193,2);
|
||||
series(:,2) = data_q(:,1);
|
||||
series(:,1) = 1000*data_q(:,2)./data_q(:,3);
|
||||
|
||||
Y_obs = series(:,1);
|
||||
P_obs = series(:,2);
|
||||
|
||||
series = series(2:193,:)./series(1:192,:);
|
||||
|
||||
gy_obs = series(:,1);
|
||||
gp_obs = series(:,2);
|
||||
|
||||
ti = [1950:0.25:1997.75];
|
||||
|
|
@ -1,58 +1,58 @@
|
|||
// Test for varexo_det and forecast command at order 1
|
||||
|
||||
var y, c, k, a, h, b;
|
||||
varexo e,u;
|
||||
varexo_det ahat, bhat;
|
||||
|
||||
parameters beta, rho, alpha, delta, theta, psi, tau;
|
||||
|
||||
alpha = 0.36;
|
||||
rho = 0.95;
|
||||
tau = 0.025;
|
||||
beta = 0.99;
|
||||
delta = 0.025;
|
||||
psi = 0;
|
||||
theta = 2.95;
|
||||
|
||||
phi = 0.1;
|
||||
|
||||
//model(bytecode);
|
||||
model;
|
||||
c*theta*h^(1+psi)=(1-alpha)*y;
|
||||
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
|
||||
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
|
||||
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
|
||||
k = exp(b)*(y-c)+(1-delta)*k(-1);
|
||||
a = ahat+ rho*a(-1)+tau*b(-1) + e;
|
||||
b = bhat+ tau*a(-1)+rho*b(-1) + u;
|
||||
end;
|
||||
|
||||
initval;
|
||||
y = 1.08068253095672;
|
||||
c = 0.80359242014163;
|
||||
h = 0.29175631001732;
|
||||
k = 5;
|
||||
a = 0;
|
||||
b = 0;
|
||||
e = 0;
|
||||
u = 0;
|
||||
ahat = 0;
|
||||
bhat = 0;
|
||||
end;
|
||||
|
||||
//simul(periods=20);
|
||||
shocks;
|
||||
var e; stderr 0.009;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0.009;
|
||||
var ahat;
|
||||
periods 1;
|
||||
values 0.1;
|
||||
var bhat;
|
||||
periods 2;
|
||||
values 0.2;
|
||||
end;
|
||||
|
||||
stoch_simul(order=1,irf=0,noprint);
|
||||
|
||||
forecast(periods=20);
|
||||
// Test for varexo_det and forecast command at order 1
|
||||
|
||||
var y, c, k, a, h, b;
|
||||
varexo e,u;
|
||||
varexo_det ahat, bhat;
|
||||
|
||||
parameters beta, rho, alpha, delta, theta, psi, tau;
|
||||
|
||||
alpha = 0.36;
|
||||
rho = 0.95;
|
||||
tau = 0.025;
|
||||
beta = 0.99;
|
||||
delta = 0.025;
|
||||
psi = 0;
|
||||
theta = 2.95;
|
||||
|
||||
phi = 0.1;
|
||||
|
||||
//model(bytecode);
|
||||
model;
|
||||
c*theta*h^(1+psi)=(1-alpha)*y;
|
||||
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
|
||||
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
|
||||
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
|
||||
k = exp(b)*(y-c)+(1-delta)*k(-1);
|
||||
a = ahat+ rho*a(-1)+tau*b(-1) + e;
|
||||
b = bhat+ tau*a(-1)+rho*b(-1) + u;
|
||||
end;
|
||||
|
||||
initval;
|
||||
y = 1.08068253095672;
|
||||
c = 0.80359242014163;
|
||||
h = 0.29175631001732;
|
||||
k = 5;
|
||||
a = 0;
|
||||
b = 0;
|
||||
e = 0;
|
||||
u = 0;
|
||||
ahat = 0;
|
||||
bhat = 0;
|
||||
end;
|
||||
|
||||
//simul(periods=20);
|
||||
shocks;
|
||||
var e; stderr 0.009;
|
||||
var u; stderr 0.009;
|
||||
var e, u = phi*0.009*0.009;
|
||||
var ahat;
|
||||
periods 1;
|
||||
values 0.1;
|
||||
var bhat;
|
||||
periods 2;
|
||||
values 0.2;
|
||||
end;
|
||||
|
||||
stoch_simul(order=1,irf=0,noprint);
|
||||
|
||||
forecast(periods=20);
|
||||
|
|
|
|||
|
|
@ -1,79 +1,79 @@
|
|||
//$ Declaration of the endogenous variables of the DSGE model.
|
||||
var a g mc mrs n winf pie r rw y;
|
||||
|
||||
//$ Declaration of the exogenous variables of the DSGE model.
|
||||
varexo e_a e_g e_lam e_ms;
|
||||
|
||||
//$ Declaration of the deep parameters
|
||||
parameters invsig delta gam rho gampie gamy rhoa rhog bet
|
||||
thetabig omega eps ;
|
||||
|
||||
eps=6;
|
||||
thetabig=2;
|
||||
bet=0.99;
|
||||
invsig=2.5;
|
||||
gampie=1.5;
|
||||
gamy=0.125;
|
||||
gam=1;
|
||||
delta=0.36;
|
||||
omega=0.54;
|
||||
rhoa=0.5;
|
||||
rhog=0.5;
|
||||
rho=0.5;
|
||||
|
||||
|
||||
//$ Specification of the DSGE model used as a prior of the VAR model.
|
||||
model(linear);
|
||||
|
||||
y=y(+1)-(1/invsig)*(r-pie(+1)+g(+1)-g);
|
||||
y=a+(1-delta)*n;
|
||||
mc=rw+n-y;
|
||||
mrs=invsig*y+gam*n-g;
|
||||
r=rho*r(-1)+(1-rho)*(gampie*pie+gamy*y)+e_ms;
|
||||
rw=rw(-1)+winf-pie;
|
||||
a=rhoa*a(-1)+e_a;
|
||||
g=rhog*g(-1)+e_g;
|
||||
rw=mrs;
|
||||
|
||||
//$ HYBRID PHILLIPS CURVED USED FOR THE SUMULATIONS:
|
||||
// pie = (omega/(1+omega*bet))*pie(-1)+(bet/(1+omega*bet))*pie(1)+(1-delta)*
|
||||
// (1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))/(1+omega*bet)*(mc+e_lam);
|
||||
|
||||
//$ FORWARD LOOKING PHILLIPS CURVE:
|
||||
pie=bet*pie(+1)+(1-delta)*(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))*(mc+e_lam);
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//$ Declaration of the prior beliefs about the deep parameters.
|
||||
estimated_params;
|
||||
stderr e_a, uniform_pdf,,,0,2;
|
||||
stderr e_g, uniform_pdf,,,0,2;
|
||||
stderr e_ms, uniform_pdf,,,0,2;
|
||||
stderr e_lam, uniform_pdf,,,0,2;
|
||||
|
||||
invsig, gamma_pdf, 2.5, 1.76;
|
||||
gam, normal_pdf, 1, 0.5;
|
||||
rho, uniform_pdf,,,0,1;
|
||||
gampie, normal_pdf, 1.5, 0.25;
|
||||
gamy, gamma_pdf, 0.125, 0.075;
|
||||
rhoa, uniform_pdf,,,0,1;
|
||||
rhog, uniform_pdf,,,0,1;
|
||||
thetabig, gamma_pdf, 3, 1.42, 1, ;
|
||||
|
||||
//$Parameter for the hybrid Phillips curve
|
||||
//omega, uniform_pdf,,,0,1;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
//$ Declaration of the observed endogenous variables. Note that they are the variables of the VAR (4 by default) and that we must
|
||||
//$ have as many observed variables as exogenous variables.
|
||||
varobs pie r rw y;
|
||||
|
||||
options_.gradient_method = 3;
|
||||
|
||||
//$ The option bayesian_irf triggers the computation of the DSGE-VAR and DSGE posterior distribution of the IRFs.
|
||||
//$ The Dashed lines are the first, fifth (ie the median) and ninth posterior deciles of the DSGE-VAR's IRFs, the bold dark curve is the
|
||||
//$ posterior median of the DSGE's IRfs and the shaded surface covers the space between the first and ninth posterior deciles of the DSGE's IRFs.
|
||||
estimation(datafile=datarabanal_hybrid,first_obs=50,mh_nblocks = 1,nobs=90,dsge_var=.8,mode_compute=4,mh_replic=2000,bayesian_irf);
|
||||
//$ Declaration of the endogenous variables of the DSGE model.
|
||||
var a g mc mrs n winf pie r rw y;
|
||||
|
||||
//$ Declaration of the exogenous variables of the DSGE model.
|
||||
varexo e_a e_g e_lam e_ms;
|
||||
|
||||
//$ Declaration of the deep parameters
|
||||
parameters invsig delta gam rho gampie gamy rhoa rhog bet
|
||||
thetabig omega eps ;
|
||||
|
||||
eps=6;
|
||||
thetabig=2;
|
||||
bet=0.99;
|
||||
invsig=2.5;
|
||||
gampie=1.5;
|
||||
gamy=0.125;
|
||||
gam=1;
|
||||
delta=0.36;
|
||||
omega=0.54;
|
||||
rhoa=0.5;
|
||||
rhog=0.5;
|
||||
rho=0.5;
|
||||
|
||||
|
||||
//$ Specification of the DSGE model used as a prior of the VAR model.
|
||||
model(linear);
|
||||
|
||||
y=y(+1)-(1/invsig)*(r-pie(+1)+g(+1)-g);
|
||||
y=a+(1-delta)*n;
|
||||
mc=rw+n-y;
|
||||
mrs=invsig*y+gam*n-g;
|
||||
r=rho*r(-1)+(1-rho)*(gampie*pie+gamy*y)+e_ms;
|
||||
rw=rw(-1)+winf-pie;
|
||||
a=rhoa*a(-1)+e_a;
|
||||
g=rhog*g(-1)+e_g;
|
||||
rw=mrs;
|
||||
|
||||
//$ HYBRID PHILLIPS CURVED USED FOR THE SUMULATIONS:
|
||||
// pie = (omega/(1+omega*bet))*pie(-1)+(bet/(1+omega*bet))*pie(1)+(1-delta)*
|
||||
// (1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))/(1+omega*bet)*(mc+e_lam);
|
||||
|
||||
//$ FORWARD LOOKING PHILLIPS CURVE:
|
||||
pie=bet*pie(+1)+(1-delta)*(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))*(mc+e_lam);
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//$ Declaration of the prior beliefs about the deep parameters.
|
||||
estimated_params;
|
||||
stderr e_a, uniform_pdf,,,0,2;
|
||||
stderr e_g, uniform_pdf,,,0,2;
|
||||
stderr e_ms, uniform_pdf,,,0,2;
|
||||
stderr e_lam, uniform_pdf,,,0,2;
|
||||
|
||||
invsig, gamma_pdf, 2.5, 1.76;
|
||||
gam, normal_pdf, 1, 0.5;
|
||||
rho, uniform_pdf,,,0,1;
|
||||
gampie, normal_pdf, 1.5, 0.25;
|
||||
gamy, gamma_pdf, 0.125, 0.075;
|
||||
rhoa, uniform_pdf,,,0,1;
|
||||
rhog, uniform_pdf,,,0,1;
|
||||
thetabig, gamma_pdf, 3, 1.42, 1, ;
|
||||
|
||||
//$Parameter for the hybrid Phillips curve
|
||||
//omega, uniform_pdf,,,0,1;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
//$ Declaration of the observed endogenous variables. Note that they are the variables of the VAR (4 by default) and that we must
|
||||
//$ have as many observed variables as exogenous variables.
|
||||
varobs pie r rw y;
|
||||
|
||||
options_.gradient_method = 3;
|
||||
|
||||
//$ The option bayesian_irf triggers the computation of the DSGE-VAR and DSGE posterior distribution of the IRFs.
|
||||
//$ The Dashed lines are the first, fifth (ie the median) and ninth posterior deciles of the DSGE-VAR's IRFs, the bold dark curve is the
|
||||
//$ posterior median of the DSGE's IRfs and the shaded surface covers the space between the first and ninth posterior deciles of the DSGE's IRFs.
|
||||
estimation(datafile=datarabanal_hybrid,first_obs=50,mh_nblocks = 1,nobs=90,dsge_var=.8,mode_compute=4,mh_replic=2000,bayesian_irf);
|
||||
|
|
|
|||
|
|
@ -1,80 +1,80 @@
|
|||
//$ Declaration of the endogenous variables of the DSGE model.
|
||||
var a g mc mrs n winf pie r rw y;
|
||||
|
||||
//$ Declaration of the exogenous variables of the DSGE model.
|
||||
varexo e_a e_g e_lam e_ms;
|
||||
|
||||
//$ Declaration of the deep parameters and of dsge_prior_weight
|
||||
parameters invsig delta gam rho gampie gamy rhoa rhog bet
|
||||
thetabig omega eps ;
|
||||
|
||||
eps=6;
|
||||
thetabig=2;
|
||||
bet=0.99;
|
||||
invsig=2.5;
|
||||
gampie=1.5;
|
||||
gamy=0.125;
|
||||
gam=1;
|
||||
delta=0.36;
|
||||
omega=0.54;
|
||||
rhoa=0.5;
|
||||
rhog=0.5;
|
||||
rho=0.5;
|
||||
|
||||
|
||||
//$ Specification of the DSGE model used as a prior of the VAR model.
|
||||
model(linear);
|
||||
|
||||
y=y(+1)-(1/invsig)*(r-pie(+1)+g(+1)-g);
|
||||
y=a+(1-delta)*n;
|
||||
mc=rw+n-y;
|
||||
mrs=invsig*y+gam*n-g;
|
||||
r=rho*r(-1)+(1-rho)*(gampie*pie+gamy*y)+e_ms;
|
||||
rw=rw(-1)+winf-pie;
|
||||
a=rhoa*a(-1)+e_a;
|
||||
g=rhog*g(-1)+e_g;
|
||||
rw=mrs;
|
||||
|
||||
//$ HYBRID PHILLIPS CURVED USED FOR THE SUMULATIONS:
|
||||
// pie = (omega/(1+omega*bet))*pie(-1)+(bet/(1+omega*bet))*pie(1)+(1-delta)*
|
||||
// (1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))/(1+omega*bet)*(mc+e_lam);
|
||||
|
||||
//$ FORWARD LOOKING PHILLIPS CURVE:
|
||||
pie=bet*pie(+1)+(1-delta)*(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))*(mc+e_lam);
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//$ Declaration of the prior beliefs about the deep parameters and the weight of the DSGE prior.
|
||||
estimated_params;
|
||||
stderr e_a, uniform_pdf,,,0,2;
|
||||
stderr e_g, uniform_pdf,,,0,2;
|
||||
stderr e_ms, uniform_pdf,,,0,2;
|
||||
stderr e_lam, uniform_pdf,,,0,2;
|
||||
|
||||
invsig, gamma_pdf, 2.5, 1.76;
|
||||
gam, normal_pdf, 1, 0.5;
|
||||
rho, uniform_pdf,,,0,1;
|
||||
gampie, normal_pdf, 1.5, 0.25;
|
||||
gamy, gamma_pdf, 0.125, 0.075;
|
||||
rhoa, uniform_pdf,,,0,1;
|
||||
rhog, uniform_pdf,,,0,1;
|
||||
thetabig, gamma_pdf, 3, 1.42, 1, ;
|
||||
|
||||
//$Parameter for the hybrid Phillips curve
|
||||
//omega, uniform_pdf,,,0,1;
|
||||
|
||||
dsge_prior_weight, uniform_pdf,,,0,1.9;
|
||||
end;
|
||||
|
||||
|
||||
//$ Declaration of the observed endogenous variables. Note that they are the variables of the VAR (4 by default) and that we must
|
||||
//$ have as many observed variables as exogenous variables.
|
||||
varobs pie r rw y;
|
||||
|
||||
options_.gradient_method = 3;
|
||||
|
||||
//$ The option bayesian_irf triggers the computation of the DSGE-VAR and DSGE posterior distribution of the IRFs.
|
||||
//$ The Dashed lines are the first, fifth (ie the median) and ninth posterior deciles of the DSGE-VAR's IRFs, the bold dark curve is the
|
||||
//$ posterior median of the DSGE's IRfs and the shaded surface covers the space between the first and ninth posterior deciles of the DSGE's IRFs.
|
||||
estimation(datafile=datarabanal_hybrid,first_obs=50,mh_nblocks = 1,nobs=90,dsge_var,mode_compute=4,mh_replic=2000,bayesian_irf);
|
||||
//$ Declaration of the endogenous variables of the DSGE model.
|
||||
var a g mc mrs n winf pie r rw y;
|
||||
|
||||
//$ Declaration of the exogenous variables of the DSGE model.
|
||||
varexo e_a e_g e_lam e_ms;
|
||||
|
||||
//$ Declaration of the deep parameters and of dsge_prior_weight
|
||||
parameters invsig delta gam rho gampie gamy rhoa rhog bet
|
||||
thetabig omega eps ;
|
||||
|
||||
eps=6;
|
||||
thetabig=2;
|
||||
bet=0.99;
|
||||
invsig=2.5;
|
||||
gampie=1.5;
|
||||
gamy=0.125;
|
||||
gam=1;
|
||||
delta=0.36;
|
||||
omega=0.54;
|
||||
rhoa=0.5;
|
||||
rhog=0.5;
|
||||
rho=0.5;
|
||||
|
||||
|
||||
//$ Specification of the DSGE model used as a prior of the VAR model.
|
||||
model(linear);
|
||||
|
||||
y=y(+1)-(1/invsig)*(r-pie(+1)+g(+1)-g);
|
||||
y=a+(1-delta)*n;
|
||||
mc=rw+n-y;
|
||||
mrs=invsig*y+gam*n-g;
|
||||
r=rho*r(-1)+(1-rho)*(gampie*pie+gamy*y)+e_ms;
|
||||
rw=rw(-1)+winf-pie;
|
||||
a=rhoa*a(-1)+e_a;
|
||||
g=rhog*g(-1)+e_g;
|
||||
rw=mrs;
|
||||
|
||||
//$ HYBRID PHILLIPS CURVED USED FOR THE SUMULATIONS:
|
||||
// pie = (omega/(1+omega*bet))*pie(-1)+(bet/(1+omega*bet))*pie(1)+(1-delta)*
|
||||
// (1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))/(1+omega*bet)*(mc+e_lam);
|
||||
|
||||
//$ FORWARD LOOKING PHILLIPS CURVE:
|
||||
pie=bet*pie(+1)+(1-delta)*(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))*(mc+e_lam);
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//$ Declaration of the prior beliefs about the deep parameters and the weight of the DSGE prior.
|
||||
estimated_params;
|
||||
stderr e_a, uniform_pdf,,,0,2;
|
||||
stderr e_g, uniform_pdf,,,0,2;
|
||||
stderr e_ms, uniform_pdf,,,0,2;
|
||||
stderr e_lam, uniform_pdf,,,0,2;
|
||||
|
||||
invsig, gamma_pdf, 2.5, 1.76;
|
||||
gam, normal_pdf, 1, 0.5;
|
||||
rho, uniform_pdf,,,0,1;
|
||||
gampie, normal_pdf, 1.5, 0.25;
|
||||
gamy, gamma_pdf, 0.125, 0.075;
|
||||
rhoa, uniform_pdf,,,0,1;
|
||||
rhog, uniform_pdf,,,0,1;
|
||||
thetabig, gamma_pdf, 3, 1.42, 1, ;
|
||||
|
||||
//$Parameter for the hybrid Phillips curve
|
||||
//omega, uniform_pdf,,,0,1;
|
||||
|
||||
dsge_prior_weight, uniform_pdf,,,0,1.9;
|
||||
end;
|
||||
|
||||
|
||||
//$ Declaration of the observed endogenous variables. Note that they are the variables of the VAR (4 by default) and that we must
|
||||
//$ have as many observed variables as exogenous variables.
|
||||
varobs pie r rw y;
|
||||
|
||||
options_.gradient_method = 3;
|
||||
|
||||
//$ The option bayesian_irf triggers the computation of the DSGE-VAR and DSGE posterior distribution of the IRFs.
|
||||
//$ The Dashed lines are the first, fifth (ie the median) and ninth posterior deciles of the DSGE-VAR's IRFs, the bold dark curve is the
|
||||
//$ posterior median of the DSGE's IRfs and the shaded surface covers the space between the first and ninth posterior deciles of the DSGE's IRFs.
|
||||
estimation(datafile=datarabanal_hybrid,first_obs=50,mh_nblocks = 1,nobs=90,dsge_var,mode_compute=4,mh_replic=2000,bayesian_irf);
|
||||
|
|
|
|||
|
|
@ -1,51 +1,51 @@
|
|||
var a g mc mrs n pie r rw winf y;
|
||||
varexo e_a e_g e_lam e_ms;
|
||||
|
||||
parameters invsig delta gam rho gampie gamy rhoa rhog bet
|
||||
thetabig omega eps;
|
||||
|
||||
eps=6;
|
||||
thetabig=2;
|
||||
bet=0.99;
|
||||
invsig=2.5;
|
||||
gampie=1.5;
|
||||
gamy=0.125;
|
||||
gam=1;
|
||||
delta=0.36;
|
||||
omega=0.54;
|
||||
rhoa=0.5;
|
||||
rhog=0.5;
|
||||
rho=0.5;
|
||||
|
||||
|
||||
model(linear);
|
||||
y=y(+1)-(1/invsig)*(r-pie(+1)+g(+1)-g);
|
||||
y=a+(1-delta)*n;
|
||||
mc=rw+n-y;
|
||||
mrs=invsig*y+gam*n-g;
|
||||
r=rho*r(-1)+(1-rho)*(gampie*pie+gamy*y)+e_ms;
|
||||
rw=rw(-1)+winf-pie;
|
||||
a=rhoa*a(-1)+e_a;
|
||||
g=rhog*g(-1)+e_g;
|
||||
rw=mrs;
|
||||
|
||||
// HYBRID PHILLIPS CURVED USED FOR THE SUMULATIONS:
|
||||
pie = (omega/(1+omega*bet))*pie(-1)+(bet/(1+omega*bet))*pie(1)+(1-delta)*
|
||||
(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))/(1+omega*bet)*(mc+e_lam);
|
||||
|
||||
// FORWARD LOOKING PHILLIPS CURVE:
|
||||
// pie=bet*pie(+1)+(1-delta)*(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))*(mc+e_lam);
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e_a; stderr 1;
|
||||
var e_g; stderr 1;
|
||||
var e_ms; stderr 1;
|
||||
var e_lam; stderr 1;
|
||||
end;
|
||||
|
||||
steady;
|
||||
check;
|
||||
|
||||
stoch_simul(periods=500,irf=0);
|
||||
var a g mc mrs n pie r rw winf y;
|
||||
varexo e_a e_g e_lam e_ms;
|
||||
|
||||
parameters invsig delta gam rho gampie gamy rhoa rhog bet
|
||||
thetabig omega eps;
|
||||
|
||||
eps=6;
|
||||
thetabig=2;
|
||||
bet=0.99;
|
||||
invsig=2.5;
|
||||
gampie=1.5;
|
||||
gamy=0.125;
|
||||
gam=1;
|
||||
delta=0.36;
|
||||
omega=0.54;
|
||||
rhoa=0.5;
|
||||
rhog=0.5;
|
||||
rho=0.5;
|
||||
|
||||
|
||||
model(linear);
|
||||
y=y(+1)-(1/invsig)*(r-pie(+1)+g(+1)-g);
|
||||
y=a+(1-delta)*n;
|
||||
mc=rw+n-y;
|
||||
mrs=invsig*y+gam*n-g;
|
||||
r=rho*r(-1)+(1-rho)*(gampie*pie+gamy*y)+e_ms;
|
||||
rw=rw(-1)+winf-pie;
|
||||
a=rhoa*a(-1)+e_a;
|
||||
g=rhog*g(-1)+e_g;
|
||||
rw=mrs;
|
||||
|
||||
// HYBRID PHILLIPS CURVED USED FOR THE SUMULATIONS:
|
||||
pie = (omega/(1+omega*bet))*pie(-1)+(bet/(1+omega*bet))*pie(1)+(1-delta)*
|
||||
(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))/(1+omega*bet)*(mc+e_lam);
|
||||
|
||||
// FORWARD LOOKING PHILLIPS CURVE:
|
||||
// pie=bet*pie(+1)+(1-delta)*(1-(1-1/thetabig)*bet)*(1-(1-1/thetabig))/((1-1/thetabig)*(1+delta*(eps-1)))*(mc+e_lam);
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e_a; stderr 1;
|
||||
var e_g; stderr 1;
|
||||
var e_ms; stderr 1;
|
||||
var e_lam; stderr 1;
|
||||
end;
|
||||
|
||||
steady;
|
||||
check;
|
||||
|
||||
stoch_simul(periods=500,irf=0);
|
||||
datatomfile('datarabanal_hybrid',[]);
|
||||
|
|
@ -1,45 +1,45 @@
|
|||
var y pie r;
|
||||
varexo e_y e_pie;
|
||||
|
||||
parameters delta sigma alpha kappa gamma1 gamma2;
|
||||
|
||||
delta = 0.44;
|
||||
kappa = 0.18;
|
||||
alpha = 0.48;
|
||||
sigma = -0.06;
|
||||
|
||||
gamma1 = 1.5;
|
||||
gamma2 = 0.5;
|
||||
|
||||
model(use_dll);
|
||||
y = delta * y(-1) + (1-delta)*y(+1)+sigma *(r - pie(+1)) + e_y;
|
||||
pie = alpha * pie(-1) + (1-alpha) * pie(+1) + kappa*y + e_pie;
|
||||
r = gamma1*pie+gamma2*y;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e_y;
|
||||
stderr 0.63;
|
||||
var e_pie;
|
||||
stderr 0.4;
|
||||
end;
|
||||
|
||||
steady;
|
||||
|
||||
options_.maxit_ = 100;
|
||||
options_.ep.verbosity = 0;
|
||||
options_.ep.stochastic.status = 0;
|
||||
options_.ep.order = 0;
|
||||
options_.ep.nnodes = 0;
|
||||
options_.console_mode = 0;
|
||||
|
||||
ts = extended_path([],100);
|
||||
|
||||
options_.ep.stochastic.status = 1;
|
||||
options_.ep.order = 1;
|
||||
options_.ep.nnodes = 3;
|
||||
sts = extended_path([],100);
|
||||
|
||||
if max(max(abs(ts-sts))) > 1e-12
|
||||
error('extended path algorithm fails in ./tests/ep/linear.mod')
|
||||
var y pie r;
|
||||
varexo e_y e_pie;
|
||||
|
||||
parameters delta sigma alpha kappa gamma1 gamma2;
|
||||
|
||||
delta = 0.44;
|
||||
kappa = 0.18;
|
||||
alpha = 0.48;
|
||||
sigma = -0.06;
|
||||
|
||||
gamma1 = 1.5;
|
||||
gamma2 = 0.5;
|
||||
|
||||
model(use_dll);
|
||||
y = delta * y(-1) + (1-delta)*y(+1)+sigma *(r - pie(+1)) + e_y;
|
||||
pie = alpha * pie(-1) + (1-alpha) * pie(+1) + kappa*y + e_pie;
|
||||
r = gamma1*pie+gamma2*y;
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e_y;
|
||||
stderr 0.63;
|
||||
var e_pie;
|
||||
stderr 0.4;
|
||||
end;
|
||||
|
||||
steady;
|
||||
|
||||
options_.maxit_ = 100;
|
||||
options_.ep.verbosity = 0;
|
||||
options_.ep.stochastic.status = 0;
|
||||
options_.ep.order = 0;
|
||||
options_.ep.nnodes = 0;
|
||||
options_.console_mode = 0;
|
||||
|
||||
ts = extended_path([],100);
|
||||
|
||||
options_.ep.stochastic.status = 1;
|
||||
options_.ep.order = 1;
|
||||
options_.ep.nnodes = 3;
|
||||
sts = extended_path([],100);
|
||||
|
||||
if max(max(abs(ts-sts))) > 1e-12
|
||||
error('extended path algorithm fails in ./tests/ep/linear.mod')
|
||||
end
|
||||
|
|
@ -1,60 +1,60 @@
|
|||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000a_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000a_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
dA ];
|
||||
|
|
@ -1,60 +1,60 @@
|
|||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000a_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
% computes the steady state of fs2000 analyticaly
|
||||
% largely inspired by the program of F. Schorfheide
|
||||
function [ys,check] = fs2000a_steadystate(ys,exe)
|
||||
global M_
|
||||
|
||||
alp = M_.params(1);
|
||||
bet = M_.params(2);
|
||||
gam = M_.params(3);
|
||||
mst = M_.params(4);
|
||||
rho = M_.params(5);
|
||||
psi = M_.params(6);
|
||||
del = M_.params(7);
|
||||
|
||||
check = 0;
|
||||
|
||||
dA = exp(gam);
|
||||
gst = 1/dA;
|
||||
m = mst;
|
||||
|
||||
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
|
||||
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
|
||||
nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
|
||||
n = xist/(nust+xist);
|
||||
P = xist + nust;
|
||||
k = khst*n;
|
||||
|
||||
l = psi*mst*n/( (1-psi)*(1-n) );
|
||||
c = mst/P;
|
||||
d = l - mst + 1;
|
||||
y = k^alp*n^(1-alp)*gst^alp;
|
||||
R = mst/bet;
|
||||
W = l/n;
|
||||
ist = y-c;
|
||||
q = 1 - d;
|
||||
|
||||
e = 1;
|
||||
|
||||
gp_obs = m/dA;
|
||||
gy_obs = dA;
|
||||
|
||||
P_obs = 1;
|
||||
Y_obs = 1;
|
||||
|
||||
ys =[
|
||||
m
|
||||
P
|
||||
c
|
||||
e
|
||||
W
|
||||
R
|
||||
k
|
||||
d
|
||||
n
|
||||
l
|
||||
gy_obs
|
||||
gp_obs
|
||||
Y_obs
|
||||
P_obs
|
||||
y
|
||||
dA ];
|
||||
|
|
@ -1,56 +1,56 @@
|
|||
load test
|
||||
% $$$ Y = Y(1:2,:);
|
||||
% $$$ mf = mf(1:2);
|
||||
% $$$ H=H(1:2,1:2);
|
||||
% $$$ pp = pp-1;
|
||||
% $$$ trend =trend(1:2,:);
|
||||
Pinf1(1,1) = 1;
|
||||
Pstar1(1,1) = 0;
|
||||
Pstar1(4,1) = 0;
|
||||
Pstar1(1,4) = 0;
|
||||
[alphahat1,epsilonhat1,etahat1,a11, aK1] = DiffuseKalmanSmootherH1(T,R,Q,H, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,epsilonhat2,etahat2,a12, aK2] = DiffuseKalmanSmootherH3(T,R,Q,H, ...
|
||||
Pinf1,Pstar1,Y,trend, ...
|
||||
pp,mm,smpl,mf);
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(epsilonhat1-epsilonhat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
max(max(abs(aK1-aK2)))
|
||||
|
||||
return
|
||||
[alphahat1,etahat1,a11, aK1] = DiffuseKalmanSmoother1(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,etahat2,a12, aK2] = DiffuseKalmanSmoother3(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend, ...
|
||||
pp,mm,smpl,mf);
|
||||
|
||||
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
%max(max(abs(aK1-aK2)))
|
||||
|
||||
|
||||
H = zeros(size(H));
|
||||
[alphahat1,etahat1,a11, aK1] = DiffuseKalmanSmoother1(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,epsilonhat2,etahat2,a12, aK2] = DiffuseKalmanSmootherH1(T,R,Q,H, ...
|
||||
Pinf1,Pstar1,Y,trend, ...
|
||||
pp,mm,smpl,mf);
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
%max(max(abs(aK1-aK2)))
|
||||
|
||||
|
||||
[alphahat1,etahat1,a11, aK1] = DiffuseKalmanSmoother3(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,epsilonhat2,etahat2,a12, aK2] = DiffuseKalmanSmootherH3(T,R,Q, H, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
%max(max(abs(aK1-aK2)))
|
||||
load test
|
||||
% $$$ Y = Y(1:2,:);
|
||||
% $$$ mf = mf(1:2);
|
||||
% $$$ H=H(1:2,1:2);
|
||||
% $$$ pp = pp-1;
|
||||
% $$$ trend =trend(1:2,:);
|
||||
Pinf1(1,1) = 1;
|
||||
Pstar1(1,1) = 0;
|
||||
Pstar1(4,1) = 0;
|
||||
Pstar1(1,4) = 0;
|
||||
[alphahat1,epsilonhat1,etahat1,a11, aK1] = DiffuseKalmanSmootherH1(T,R,Q,H, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,epsilonhat2,etahat2,a12, aK2] = DiffuseKalmanSmootherH3(T,R,Q,H, ...
|
||||
Pinf1,Pstar1,Y,trend, ...
|
||||
pp,mm,smpl,mf);
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(epsilonhat1-epsilonhat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
max(max(abs(aK1-aK2)))
|
||||
|
||||
return
|
||||
[alphahat1,etahat1,a11, aK1] = DiffuseKalmanSmoother1(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,etahat2,a12, aK2] = DiffuseKalmanSmoother3(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend, ...
|
||||
pp,mm,smpl,mf);
|
||||
|
||||
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
%max(max(abs(aK1-aK2)))
|
||||
|
||||
|
||||
H = zeros(size(H));
|
||||
[alphahat1,etahat1,a11, aK1] = DiffuseKalmanSmoother1(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,epsilonhat2,etahat2,a12, aK2] = DiffuseKalmanSmootherH1(T,R,Q,H, ...
|
||||
Pinf1,Pstar1,Y,trend, ...
|
||||
pp,mm,smpl,mf);
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
%max(max(abs(aK1-aK2)))
|
||||
|
||||
|
||||
[alphahat1,etahat1,a11, aK1] = DiffuseKalmanSmoother3(T,R,Q, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
[alphahat2,epsilonhat2,etahat2,a12, aK2] = DiffuseKalmanSmootherH3(T,R,Q, H, ...
|
||||
Pinf1,Pstar1,Y,trend,pp,mm,smpl,mf);
|
||||
|
||||
max(max(abs(alphahat1-alphahat2)))
|
||||
max(max(abs(etahat1-etahat2)))
|
||||
max(max(abs(a11-a12)))
|
||||
%max(max(abs(aK1-aK2)))
|
||||
|
|
|
|||
|
|
@ -1,100 +1,100 @@
|
|||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
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|
||||
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|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
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|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
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|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
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|
||||
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|
||||
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|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
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|
||||
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|
||||
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|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
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|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
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|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
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|
||||
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|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
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|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
|
|
|
|||
|
|
@ -1,100 +1,100 @@
|
|||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
1.68081431462 3.34729969129 10 1.41159342106 -1.59065680853 ...
|
||||
-0.343321601133 5.05563513564 12 1.75117366498 -2.40127764642 ...
|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
-0.562233624818 3.88598638237 9.75 -0.0505384765105 0.332826708151 ...
|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
0.842215068977 3.11164509647 12.25 -1.08290421696 0.014323281961 ...
|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
-0.418465249225 3.75861110232 14.75 -1.03131674824 0.188507675831 ...
|
||||
-0.644028342116 4.15104788154 13.75 -1.48911756546 0.204560913792 ...
|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
-0.00264276644799 3.07989972052 8.75 -2.56342461535 2.105998353 ...
|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
1.68081431462 3.34729969129 10 1.41159342106 -1.59065680853 ...
|
||||
-0.343321601133 5.05563513564 12 1.75117366498 -2.40127764642 ...
|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
-0.562233624818 3.88598638237 9.75 -0.0505384765105 0.332826708151 ...
|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
0.842215068977 3.11164509647 12.25 -1.08290421696 0.014323281961 ...
|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
-0.418465249225 3.75861110232 14.75 -1.03131674824 0.188507675831 ...
|
||||
-0.644028342116 4.15104788154 13.75 -1.48911756546 0.204560913792 ...
|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
-0.00264276644799 3.07989972052 8.75 -2.56342461535 2.105998353 ...
|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
|
|
|
|||
|
|
@ -1,228 +1,228 @@
|
|||
function [Ui,Vi,n0,np] = ftd_2s_caseall_upperchol3v(lags,nvar,nStates,indxEqnTv_m,nexo)
|
||||
% Case 2&3: Policy a0j and a+j have only time-varying structural variances -- Case 2.
|
||||
% All policy and nonpolicy a0j's and the corresponding constant terms are completely time-varying and only the scale
|
||||
% of each variable in d+j,1** (excluding the constant term) is time-varying -- Case 3.
|
||||
%
|
||||
% Variables: Pcom, M2, FFR, y, P, U. Equations: information, policy, money demand, y, P, U.
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions
|
||||
% (equation by equation) with time-varying A0 and D+** equations.
|
||||
% See Model II.3 on pp.71k-71r in TVBVAR NOTES (and Waggoner and Zha's Gibbs sampling paper and TVBVAR NOTES p.58).
|
||||
%
|
||||
% lags: Maximum length of lag.
|
||||
% nvar: Number of endogeous variables.
|
||||
% nStates: Number of states.
|
||||
% indxEqnTv_m: nvar-by-2. Stores equation characteristics.
|
||||
% 1st column: labels of equations [1:nvar]'.
|
||||
% 2nd column: labels of time-varying features with
|
||||
% 1: indxConst -- all coefficients are constant,
|
||||
% 2: indxStv -- only shocks are time-varying,
|
||||
% 3: indxTva0pv -- a0 are freely time-varying and each variable i for d+ is time-varying only by the scale lambda_i(s_t).
|
||||
% 4: indxTva0ps -- a0 are freely time-varying and only the scale for the whole of d+ is time-varying.
|
||||
% 5: indxTv -- time-varying for all coeffficients (a0 and a+) where the lag length for a+ may be shorter.
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant.
|
||||
% So far this function is written to handle one exogenous variable, which is a constant term.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar*nStates-by-qi*si orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters
|
||||
% within the state and si is the number of free states.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation in the order of [a_i for 1st state, ..., a_i for last state].
|
||||
% Vi: nvar-by-1 cell. In each cell, k*nStates-by-ri*si orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters within the state and si is the number of free states.
|
||||
% With this transformation, we have fi = Vi*gi or Vi'*fi = gi where fi is a vector of total original
|
||||
% parameters and gi is a vector of free parameters. The ith equation is in the order of [nvar variables
|
||||
% for 1st lag and 1st state, ..., nvar variables for last lag and 1st state, const for 1st state, nvar
|
||||
% variables for 1st lag and 2nd state, nvar variables for last lag and 2nd state, const for 2nd state, and so on].
|
||||
% n0: nvar-by-1, whose ith element represents the number of free A0 parameters in ith equation in *all states*.
|
||||
% np: nvar-by-1, whose ith element represents the number of free D+ parameters in ith equation in *all states*.
|
||||
%
|
||||
% Tao Zha, February 2003
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation in all states.
|
||||
np = zeros(nvar,1); % ith element represents the number of free D+ parameters in ith equation in all states.
|
||||
|
||||
if (nargin==3)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
end
|
||||
|
||||
|
||||
n = nvar*nStates;
|
||||
kvar=lags*nvar+nexo; % Maximum number of lagged and exogenous variables in each equation under each state.
|
||||
k = kvar*nStates; % Maximum number of lagged and exogenous variables in each equation in all states.
|
||||
|
||||
Qi = zeros(n,n,nvar); % 3rd dim: nvar contemporaneous equations.
|
||||
Ri = zeros(k,k,nvar); % 1st and 2nd dims: lagged and exogenous equations.
|
||||
% Row corresponds to equation with nvar variables for state 1, ..., nvar variables for state nState.
|
||||
% 0 means no restriction.
|
||||
% 1 and -1 or any other number means the linear combination of the corresponding parameters is restricted to 0.
|
||||
% 1 (only 1) means that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time for A0_s.
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
eqninx = 1;
|
||||
nreseqn = 2; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 -1 0 0
|
||||
0 1 0 0 -1 0
|
||||
0 0 1 0 0 -1
|
||||
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 1 0 0 0 0
|
||||
0 0 1 0 0 0
|
||||
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_*.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
eqninx = 2;
|
||||
nreseqn = 1; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 -1 0 0
|
||||
0 1 0 0 -1 0
|
||||
0 0 1 0 0 -1
|
||||
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 1 0 0 0
|
||||
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_3s_case3a.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
|
||||
%==== For freely time-varying A+ for only the first 6 lags.
|
||||
%==== Lagged restrictions: zeros on all lags except the first 6 lags in the MS equation.
|
||||
% nlagsno0 = 6; % Number of lags to be nonzero.
|
||||
% for si=1:nStates
|
||||
% for ki = 1:lags-nlagsno0
|
||||
% for kj=1:nvar
|
||||
% Ri(kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,2) = 1;
|
||||
% end
|
||||
% end
|
||||
% end
|
||||
%**** For constant D+_s except the first two lags and the constant term. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
% for si=1:nStates-1
|
||||
% for ki=[2*nvar+1:kvar-1]
|
||||
% Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
% end
|
||||
% end
|
||||
end
|
||||
|
||||
|
||||
%======== The third equation (money demand) ===========
|
||||
eqninx = 3;
|
||||
nreseqn = 0; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 -1 0 0
|
||||
0 1 0 0 -1 0
|
||||
0 0 1 0 0 -1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_*.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
for ki=1:nvar % initializing loop for each equation
|
||||
Ui{ki} = null(Qi(:,:,ki));
|
||||
Vi{ki} = null(Ri(:,:,ki));
|
||||
n0(ki) = size(Ui{ki},2);
|
||||
np(ki) = size(Vi{ki},2);
|
||||
end
|
||||
function [Ui,Vi,n0,np] = ftd_2s_caseall_upperchol3v(lags,nvar,nStates,indxEqnTv_m,nexo)
|
||||
% Case 2&3: Policy a0j and a+j have only time-varying structural variances -- Case 2.
|
||||
% All policy and nonpolicy a0j's and the corresponding constant terms are completely time-varying and only the scale
|
||||
% of each variable in d+j,1** (excluding the constant term) is time-varying -- Case 3.
|
||||
%
|
||||
% Variables: Pcom, M2, FFR, y, P, U. Equations: information, policy, money demand, y, P, U.
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions
|
||||
% (equation by equation) with time-varying A0 and D+** equations.
|
||||
% See Model II.3 on pp.71k-71r in TVBVAR NOTES (and Waggoner and Zha's Gibbs sampling paper and TVBVAR NOTES p.58).
|
||||
%
|
||||
% lags: Maximum length of lag.
|
||||
% nvar: Number of endogeous variables.
|
||||
% nStates: Number of states.
|
||||
% indxEqnTv_m: nvar-by-2. Stores equation characteristics.
|
||||
% 1st column: labels of equations [1:nvar]'.
|
||||
% 2nd column: labels of time-varying features with
|
||||
% 1: indxConst -- all coefficients are constant,
|
||||
% 2: indxStv -- only shocks are time-varying,
|
||||
% 3: indxTva0pv -- a0 are freely time-varying and each variable i for d+ is time-varying only by the scale lambda_i(s_t).
|
||||
% 4: indxTva0ps -- a0 are freely time-varying and only the scale for the whole of d+ is time-varying.
|
||||
% 5: indxTv -- time-varying for all coeffficients (a0 and a+) where the lag length for a+ may be shorter.
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant.
|
||||
% So far this function is written to handle one exogenous variable, which is a constant term.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar*nStates-by-qi*si orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters
|
||||
% within the state and si is the number of free states.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation in the order of [a_i for 1st state, ..., a_i for last state].
|
||||
% Vi: nvar-by-1 cell. In each cell, k*nStates-by-ri*si orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters within the state and si is the number of free states.
|
||||
% With this transformation, we have fi = Vi*gi or Vi'*fi = gi where fi is a vector of total original
|
||||
% parameters and gi is a vector of free parameters. The ith equation is in the order of [nvar variables
|
||||
% for 1st lag and 1st state, ..., nvar variables for last lag and 1st state, const for 1st state, nvar
|
||||
% variables for 1st lag and 2nd state, nvar variables for last lag and 2nd state, const for 2nd state, and so on].
|
||||
% n0: nvar-by-1, whose ith element represents the number of free A0 parameters in ith equation in *all states*.
|
||||
% np: nvar-by-1, whose ith element represents the number of free D+ parameters in ith equation in *all states*.
|
||||
%
|
||||
% Tao Zha, February 2003
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation in all states.
|
||||
np = zeros(nvar,1); % ith element represents the number of free D+ parameters in ith equation in all states.
|
||||
|
||||
if (nargin==3)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
end
|
||||
|
||||
|
||||
n = nvar*nStates;
|
||||
kvar=lags*nvar+nexo; % Maximum number of lagged and exogenous variables in each equation under each state.
|
||||
k = kvar*nStates; % Maximum number of lagged and exogenous variables in each equation in all states.
|
||||
|
||||
Qi = zeros(n,n,nvar); % 3rd dim: nvar contemporaneous equations.
|
||||
Ri = zeros(k,k,nvar); % 1st and 2nd dims: lagged and exogenous equations.
|
||||
% Row corresponds to equation with nvar variables for state 1, ..., nvar variables for state nState.
|
||||
% 0 means no restriction.
|
||||
% 1 and -1 or any other number means the linear combination of the corresponding parameters is restricted to 0.
|
||||
% 1 (only 1) means that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time for A0_s.
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
eqninx = 1;
|
||||
nreseqn = 2; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 -1 0 0
|
||||
0 1 0 0 -1 0
|
||||
0 0 1 0 0 -1
|
||||
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 1 0 0 0 0
|
||||
0 0 1 0 0 0
|
||||
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_*.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
eqninx = 2;
|
||||
nreseqn = 1; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 -1 0 0
|
||||
0 1 0 0 -1 0
|
||||
0 0 1 0 0 -1
|
||||
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 1 0 0 0
|
||||
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_3s_case3a.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
|
||||
%==== For freely time-varying A+ for only the first 6 lags.
|
||||
%==== Lagged restrictions: zeros on all lags except the first 6 lags in the MS equation.
|
||||
% nlagsno0 = 6; % Number of lags to be nonzero.
|
||||
% for si=1:nStates
|
||||
% for ki = 1:lags-nlagsno0
|
||||
% for kj=1:nvar
|
||||
% Ri(kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,2) = 1;
|
||||
% end
|
||||
% end
|
||||
% end
|
||||
%**** For constant D+_s except the first two lags and the constant term. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
% for si=1:nStates-1
|
||||
% for ki=[2*nvar+1:kvar-1]
|
||||
% Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
% end
|
||||
% end
|
||||
end
|
||||
|
||||
|
||||
%======== The third equation (money demand) ===========
|
||||
eqninx = 3;
|
||||
nreseqn = 0; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 -1 0 0
|
||||
0 1 0 0 -1 0
|
||||
0 0 1 0 0 -1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_*.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
for ki=1:nvar % initializing loop for each equation
|
||||
Ui{ki} = null(Qi(:,:,ki));
|
||||
Vi{ki} = null(Ri(:,:,ki));
|
||||
n0(ki) = size(Ui{ki},2);
|
||||
np(ki) = size(Vi{ki},2);
|
||||
end
|
||||
|
|
|
|||
|
|
@ -1,331 +1,331 @@
|
|||
function [Ui,Vi,n0,np] = ftd_2s_caseall_upperchol4v(lags,nvar,nStates,indxEqnTv_m,nexo)
|
||||
% Case 2&3: Policy a0j and a+j have only time-varying structural variances -- Case 2.
|
||||
% All policy and nonpolicy a0j's and the corresponding constant terms are completely time-varying and only the scale
|
||||
% of each variable in d+j,1** (excluding the constant term) is time-varying -- Case 3.
|
||||
%
|
||||
% Variables: Pcom, M2, FFR, y, P, U. Equations: information, policy, money demand, y, P, U.
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions
|
||||
% (equation by equation) with time-varying A0 and D+** equations.
|
||||
% See Model II.3 on pp.71k-71r in TVBVAR NOTES (and Waggoner and Zha's Gibbs sampling paper and TVBVAR NOTES p.58).
|
||||
%
|
||||
% lags: Maximum length of lag.
|
||||
% nvar: Number of endogeous variables.
|
||||
% nStates: Number of states.
|
||||
% indxEqnTv_m: nvar-by-2. Stores equation characteristics.
|
||||
% 1st column: labels of equations [1:nvar]'.
|
||||
% 2nd column: labels of time-varying features with
|
||||
% 1: indxConst -- all coefficients are constant,
|
||||
% 2: indxStv -- only shocks are time-varying,
|
||||
% 3: indxTva0pv -- a0 are freely time-varying and each variable i for d+ is time-varying only by the scale lambda_i(s_t).
|
||||
% 4: indxTva0ps -- a0 are freely time-varying and only the scale for the whole of d+ is time-varying.
|
||||
% 5: indxTv -- time-varying for all coeffficients (a0 and a+) where the lag length for a+ may be shorter.
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant.
|
||||
% So far this function is written to handle one exogenous variable, which is a constant term.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar*nStates-by-qi*si orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters
|
||||
% within the state and si is the number of free states.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation in the order of [a_i for 1st state, ..., a_i for last state].
|
||||
% Vi: nvar-by-1 cell. In each cell, k*nStates-by-ri*si orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters within the state and si is the number of free states.
|
||||
% With this transformation, we have fi = Vi*gi or Vi'*fi = gi where fi is a vector of total original
|
||||
% parameters and gi is a vector of free parameters. The ith equation is in the order of [nvar variables
|
||||
% for 1st lag and 1st state, ..., nvar variables for last lag and 1st state, const for 1st state, nvar
|
||||
% variables for 1st lag and 2nd state, nvar variables for last lag and 2nd state, const for 2nd state, and so on].
|
||||
% n0: nvar-by-1, whose ith element represents the number of free A0 parameters in ith equation in *all states*.
|
||||
% np: nvar-by-1, whose ith element represents the number of free D+ parameters in ith equation in *all states*.
|
||||
%
|
||||
% Tao Zha, February 2003
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation in all states.
|
||||
np = zeros(nvar,1); % ith element represents the number of free D+ parameters in ith equation in all states.
|
||||
|
||||
if (nargin==3)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
end
|
||||
|
||||
|
||||
n = nvar*nStates;
|
||||
kvar=lags*nvar+nexo; % Maximum number of lagged and exogenous variables in each equation under each state.
|
||||
k = kvar*nStates; % Maximum number of lagged and exogenous variables in each equation in all states.
|
||||
|
||||
Qi = zeros(n,n,nvar); % 3rd dim: nvar contemporaneous equations.
|
||||
Ri = zeros(k,k,nvar); % 1st and 2nd dims: lagged and exogenous equations.
|
||||
% Row corresponds to equation with nvar variables for state 1, ..., nvar variables for state nState.
|
||||
% 0 means no restriction.
|
||||
% 1 and -1 or any other number means the linear combination of the corresponding parameters is restricted to 0.
|
||||
% 1 (only 1) means that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time for A0_s.
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
eqninx = 1;
|
||||
nreseqn = 3; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 1 0 0 0 0 0 0
|
||||
0 0 1 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0
|
||||
|
||||
0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
eqninx = 2;
|
||||
nreseqn = 2; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 1 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_3s_case3a.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
|
||||
%==== For freely time-varying A+ for only the first 6 lags.
|
||||
%==== Lagged restrictions: zeros on all lags except the first 6 lags in the MS equation.
|
||||
% nlagsno0 = 6; % Number of lags to be nonzero.
|
||||
% for si=1:nStates
|
||||
% for ki = 1:lags-nlagsno0
|
||||
% for kj=1:nvar
|
||||
% Ri(kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,2) = 1;
|
||||
% end
|
||||
% end
|
||||
% end
|
||||
%**** For constant D+_s except the first two lags and the constant term. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
% for si=1:nStates-1
|
||||
% for ki=[2*nvar+1:kvar-1]
|
||||
% Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
% end
|
||||
% end
|
||||
end
|
||||
|
||||
|
||||
%======== The third equation ===========
|
||||
eqninx = 3;
|
||||
nreseqn = 1; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 1 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
eqninx = 4;
|
||||
nreseqn = 0; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
|
||||
for ki=1:nvar % initializing loop for each equation
|
||||
Ui{ki} = null(Qi(:,:,ki));
|
||||
Vi{ki} = null(Ri(:,:,ki));
|
||||
n0(ki) = size(Ui{ki},2);
|
||||
np(ki) = size(Vi{ki},2);
|
||||
end
|
||||
function [Ui,Vi,n0,np] = ftd_2s_caseall_upperchol4v(lags,nvar,nStates,indxEqnTv_m,nexo)
|
||||
% Case 2&3: Policy a0j and a+j have only time-varying structural variances -- Case 2.
|
||||
% All policy and nonpolicy a0j's and the corresponding constant terms are completely time-varying and only the scale
|
||||
% of each variable in d+j,1** (excluding the constant term) is time-varying -- Case 3.
|
||||
%
|
||||
% Variables: Pcom, M2, FFR, y, P, U. Equations: information, policy, money demand, y, P, U.
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions
|
||||
% (equation by equation) with time-varying A0 and D+** equations.
|
||||
% See Model II.3 on pp.71k-71r in TVBVAR NOTES (and Waggoner and Zha's Gibbs sampling paper and TVBVAR NOTES p.58).
|
||||
%
|
||||
% lags: Maximum length of lag.
|
||||
% nvar: Number of endogeous variables.
|
||||
% nStates: Number of states.
|
||||
% indxEqnTv_m: nvar-by-2. Stores equation characteristics.
|
||||
% 1st column: labels of equations [1:nvar]'.
|
||||
% 2nd column: labels of time-varying features with
|
||||
% 1: indxConst -- all coefficients are constant,
|
||||
% 2: indxStv -- only shocks are time-varying,
|
||||
% 3: indxTva0pv -- a0 are freely time-varying and each variable i for d+ is time-varying only by the scale lambda_i(s_t).
|
||||
% 4: indxTva0ps -- a0 are freely time-varying and only the scale for the whole of d+ is time-varying.
|
||||
% 5: indxTv -- time-varying for all coeffficients (a0 and a+) where the lag length for a+ may be shorter.
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant.
|
||||
% So far this function is written to handle one exogenous variable, which is a constant term.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar*nStates-by-qi*si orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters
|
||||
% within the state and si is the number of free states.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation in the order of [a_i for 1st state, ..., a_i for last state].
|
||||
% Vi: nvar-by-1 cell. In each cell, k*nStates-by-ri*si orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters within the state and si is the number of free states.
|
||||
% With this transformation, we have fi = Vi*gi or Vi'*fi = gi where fi is a vector of total original
|
||||
% parameters and gi is a vector of free parameters. The ith equation is in the order of [nvar variables
|
||||
% for 1st lag and 1st state, ..., nvar variables for last lag and 1st state, const for 1st state, nvar
|
||||
% variables for 1st lag and 2nd state, nvar variables for last lag and 2nd state, const for 2nd state, and so on].
|
||||
% n0: nvar-by-1, whose ith element represents the number of free A0 parameters in ith equation in *all states*.
|
||||
% np: nvar-by-1, whose ith element represents the number of free D+ parameters in ith equation in *all states*.
|
||||
%
|
||||
% Tao Zha, February 2003
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation in all states.
|
||||
np = zeros(nvar,1); % ith element represents the number of free D+ parameters in ith equation in all states.
|
||||
|
||||
if (nargin==3)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
end
|
||||
|
||||
|
||||
n = nvar*nStates;
|
||||
kvar=lags*nvar+nexo; % Maximum number of lagged and exogenous variables in each equation under each state.
|
||||
k = kvar*nStates; % Maximum number of lagged and exogenous variables in each equation in all states.
|
||||
|
||||
Qi = zeros(n,n,nvar); % 3rd dim: nvar contemporaneous equations.
|
||||
Ri = zeros(k,k,nvar); % 1st and 2nd dims: lagged and exogenous equations.
|
||||
% Row corresponds to equation with nvar variables for state 1, ..., nvar variables for state nState.
|
||||
% 0 means no restriction.
|
||||
% 1 and -1 or any other number means the linear combination of the corresponding parameters is restricted to 0.
|
||||
% 1 (only 1) means that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time for A0_s.
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
eqninx = 1;
|
||||
nreseqn = 3; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 1 0 0 0 0 0 0
|
||||
0 0 1 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0
|
||||
|
||||
0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
eqninx = 2;
|
||||
nreseqn = 2; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 1 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_3s_case3a.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
|
||||
%==== For freely time-varying A+ for only the first 6 lags.
|
||||
%==== Lagged restrictions: zeros on all lags except the first 6 lags in the MS equation.
|
||||
% nlagsno0 = 6; % Number of lags to be nonzero.
|
||||
% for si=1:nStates
|
||||
% for ki = 1:lags-nlagsno0
|
||||
% for kj=1:nvar
|
||||
% Ri(kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,2) = 1;
|
||||
% end
|
||||
% end
|
||||
% end
|
||||
%**** For constant D+_s except the first two lags and the constant term. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
% for si=1:nStates-1
|
||||
% for ki=[2*nvar+1:kvar-1]
|
||||
% Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
% end
|
||||
% end
|
||||
end
|
||||
|
||||
|
||||
%======== The third equation ===========
|
||||
eqninx = 3;
|
||||
nreseqn = 1; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 1 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
eqninx = 4;
|
||||
nreseqn = 0; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 -1 0 0 0
|
||||
0 1 0 0 0 -1 0 0
|
||||
0 0 1 0 0 0 -1 0
|
||||
0 0 0 1 0 0 0 -1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
|
||||
for ki=1:nvar % initializing loop for each equation
|
||||
Ui{ki} = null(Qi(:,:,ki));
|
||||
Vi{ki} = null(Ri(:,:,ki));
|
||||
n0(ki) = size(Ui{ki},2);
|
||||
np(ki) = size(Vi{ki},2);
|
||||
end
|
||||
|
|
|
|||
|
|
@ -1,455 +1,455 @@
|
|||
function [Ui,Vi,n0,np] = ftd_2s_caseall_upperchol6v(lags,nvar,nStates,indxEqnTv_m,nexo)
|
||||
% Case 2&3: Policy a0j and a+j have only time-varying structural variances -- Case 2.
|
||||
% All policy and nonpolicy a0j's and the corresponding constant terms are completely time-varying and only the scale
|
||||
% of each variable in d+j,1** (excluding the constant term) is time-varying -- Case 3.
|
||||
%
|
||||
% Variables: Pcom, M2, FFR, y, P, U. Equations: information, policy, money demand, y, P, U.
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions
|
||||
% (equation by equation) with time-varying A0 and D+** equations.
|
||||
% See Model II.3 on pp.71k-71r in TVBVAR NOTES (and Waggoner and Zha's Gibbs sampling paper and TVBVAR NOTES p.58).
|
||||
%
|
||||
% lags: Maximum length of lag.
|
||||
% nvar: Number of endogeous variables.
|
||||
% nStates: Number of states.
|
||||
% indxEqnTv_m: nvar-by-2. Stores equation characteristics.
|
||||
% 1st column: labels of equations [1:nvar]'.
|
||||
% 2nd column: labels of time-varying features with
|
||||
% 1: indxConst -- all coefficients are constant,
|
||||
% 2: indxStv -- only shocks are time-varying,
|
||||
% 3: indxTva0pv -- a0 are freely time-varying and each variable i for d+ is time-varying only by the scale lambda_i(s_t).
|
||||
% 4: indxTva0ps -- a0 are freely time-varying and only the scale for the whole of d+ is time-varying.
|
||||
% 5: indxTv -- time-varying for all coeffficients (a0 and a+) where the lag length for a+ may be shorter.
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant.
|
||||
% So far this function is written to handle one exogenous variable, which is a constant term.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar*nStates-by-qi*si orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters
|
||||
% within the state and si is the number of free states.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation in the order of [a_i for 1st state, ..., a_i for last state].
|
||||
% Vi: nvar-by-1 cell. In each cell, k*nStates-by-ri*si orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters within the state and si is the number of free states.
|
||||
% With this transformation, we have fi = Vi*gi or Vi'*fi = gi where fi is a vector of total original
|
||||
% parameters and gi is a vector of free parameters. The ith equation is in the order of [nvar variables
|
||||
% for 1st lag and 1st state, ..., nvar variables for last lag and 1st state, const for 1st state, nvar
|
||||
% variables for 1st lag and 2nd state, nvar variables for last lag and 2nd state, const for 2nd state, and so on].
|
||||
% n0: nvar-by-1, whose ith element represents the number of free A0 parameters in ith equation in *all states*.
|
||||
% np: nvar-by-1, whose ith element represents the number of free D+ parameters in ith equation in *all states*.
|
||||
%
|
||||
% Tao Zha, February 2003
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation in all states.
|
||||
np = zeros(nvar,1); % ith element represents the number of free D+ parameters in ith equation in all states.
|
||||
|
||||
if (nargin==3)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
end
|
||||
|
||||
|
||||
n = nvar*nStates;
|
||||
kvar=lags*nvar+nexo; % Maximum number of lagged and exogenous variables in each equation under each state.
|
||||
k = kvar*nStates; % Maximum number of lagged and exogenous variables in each equation in all states.
|
||||
|
||||
Qi = zeros(n,n,nvar); % 3rd dim: nvar contemporaneous equations.
|
||||
Ri = zeros(k,k,nvar); % 1st and 2nd dims: lagged and exogenous equations.
|
||||
% Row corresponds to equation with nvar variables for state 1, ..., nvar variables for state nState.
|
||||
% 0 means no restriction.
|
||||
% 1 and -1 or any other number means the linear combination of the corresponding parameters is restricted to 0.
|
||||
% 1 (only 1) means that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time for A0_s.
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
eqninx = 1;
|
||||
nreseqn = 5; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 1 0 0 0 0
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 1 0 0 0 0 0 0 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 0 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 1 0 0 0 0
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
eqninx = 2;
|
||||
nreseqn = 4; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 1 0 0 0 0 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 0 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The third equation ===========
|
||||
eqninx = 3;
|
||||
nreseqn = 3; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 1 0 0 0 0 0 0 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_3s_case3a.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
|
||||
%==== For freely time-varying A+ for only the first 6 lags.
|
||||
%==== Lagged restrictions: zeros on all lags except the first 6 lags in the MS equation.
|
||||
% nlagsno0 = 6; % Number of lags to be nonzero.
|
||||
% for si=1:nStates
|
||||
% for ki = 1:lags-nlagsno0
|
||||
% for kj=1:nvar
|
||||
% Ri(kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,2) = 1;
|
||||
% end
|
||||
% end
|
||||
% end
|
||||
%**** For constant D+_s except the first two lags and the constant term. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
% for si=1:nStates-1
|
||||
% for ki=[2*nvar+1:kvar-1]
|
||||
% Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
% end
|
||||
% end
|
||||
end
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
eqninx = 4;
|
||||
nreseqn = 2; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
eqninx = 5;
|
||||
nreseqn = 1; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The sixth equation ===========
|
||||
eqninx = 6;
|
||||
nreseqn = 0; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
|
||||
for ki=1:nvar % initializing loop for each equation
|
||||
Ui{ki} = null(Qi(:,:,ki));
|
||||
Vi{ki} = null(Ri(:,:,ki));
|
||||
n0(ki) = size(Ui{ki},2);
|
||||
np(ki) = size(Vi{ki},2);
|
||||
end
|
||||
function [Ui,Vi,n0,np] = ftd_2s_caseall_upperchol6v(lags,nvar,nStates,indxEqnTv_m,nexo)
|
||||
% Case 2&3: Policy a0j and a+j have only time-varying structural variances -- Case 2.
|
||||
% All policy and nonpolicy a0j's and the corresponding constant terms are completely time-varying and only the scale
|
||||
% of each variable in d+j,1** (excluding the constant term) is time-varying -- Case 3.
|
||||
%
|
||||
% Variables: Pcom, M2, FFR, y, P, U. Equations: information, policy, money demand, y, P, U.
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions
|
||||
% (equation by equation) with time-varying A0 and D+** equations.
|
||||
% See Model II.3 on pp.71k-71r in TVBVAR NOTES (and Waggoner and Zha's Gibbs sampling paper and TVBVAR NOTES p.58).
|
||||
%
|
||||
% lags: Maximum length of lag.
|
||||
% nvar: Number of endogeous variables.
|
||||
% nStates: Number of states.
|
||||
% indxEqnTv_m: nvar-by-2. Stores equation characteristics.
|
||||
% 1st column: labels of equations [1:nvar]'.
|
||||
% 2nd column: labels of time-varying features with
|
||||
% 1: indxConst -- all coefficients are constant,
|
||||
% 2: indxStv -- only shocks are time-varying,
|
||||
% 3: indxTva0pv -- a0 are freely time-varying and each variable i for d+ is time-varying only by the scale lambda_i(s_t).
|
||||
% 4: indxTva0ps -- a0 are freely time-varying and only the scale for the whole of d+ is time-varying.
|
||||
% 5: indxTv -- time-varying for all coeffficients (a0 and a+) where the lag length for a+ may be shorter.
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant.
|
||||
% So far this function is written to handle one exogenous variable, which is a constant term.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar*nStates-by-qi*si orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters
|
||||
% within the state and si is the number of free states.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation in the order of [a_i for 1st state, ..., a_i for last state].
|
||||
% Vi: nvar-by-1 cell. In each cell, k*nStates-by-ri*si orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters within the state and si is the number of free states.
|
||||
% With this transformation, we have fi = Vi*gi or Vi'*fi = gi where fi is a vector of total original
|
||||
% parameters and gi is a vector of free parameters. The ith equation is in the order of [nvar variables
|
||||
% for 1st lag and 1st state, ..., nvar variables for last lag and 1st state, const for 1st state, nvar
|
||||
% variables for 1st lag and 2nd state, nvar variables for last lag and 2nd state, const for 2nd state, and so on].
|
||||
% n0: nvar-by-1, whose ith element represents the number of free A0 parameters in ith equation in *all states*.
|
||||
% np: nvar-by-1, whose ith element represents the number of free D+ parameters in ith equation in *all states*.
|
||||
%
|
||||
% Tao Zha, February 2003
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation in all states.
|
||||
np = zeros(nvar,1); % ith element represents the number of free D+ parameters in ith equation in all states.
|
||||
|
||||
if (nargin==3)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
end
|
||||
|
||||
|
||||
n = nvar*nStates;
|
||||
kvar=lags*nvar+nexo; % Maximum number of lagged and exogenous variables in each equation under each state.
|
||||
k = kvar*nStates; % Maximum number of lagged and exogenous variables in each equation in all states.
|
||||
|
||||
Qi = zeros(n,n,nvar); % 3rd dim: nvar contemporaneous equations.
|
||||
Ri = zeros(k,k,nvar); % 1st and 2nd dims: lagged and exogenous equations.
|
||||
% Row corresponds to equation with nvar variables for state 1, ..., nvar variables for state nState.
|
||||
% 0 means no restriction.
|
||||
% 1 and -1 or any other number means the linear combination of the corresponding parameters is restricted to 0.
|
||||
% 1 (only 1) means that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time for A0_s.
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
eqninx = 1;
|
||||
nreseqn = 5; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 1 0 0 0 0
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 1 0 0 0 0 0 0 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 0 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 1 0 0 0 0
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
eqninx = 2;
|
||||
nreseqn = 4; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 1 0 0 0 0 0 0 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 0 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 1 0 0 0
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The third equation ===========
|
||||
eqninx = 3;
|
||||
nreseqn = 3; % Number of linear restrictions for A0(:,eqninx) for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 1 0 0 0 0 0 0 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 0 1 0 0
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_3s_case3a.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
|
||||
%==== For freely time-varying A+ for only the first 6 lags.
|
||||
%==== Lagged restrictions: zeros on all lags except the first 6 lags in the MS equation.
|
||||
% nlagsno0 = 6; % Number of lags to be nonzero.
|
||||
% for si=1:nStates
|
||||
% for ki = 1:lags-nlagsno0
|
||||
% for kj=1:nvar
|
||||
% Ri(kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,kvar*(si-1)+nlagsno0*nvar+nvar*(ki-1)+kj,2) = 1;
|
||||
% end
|
||||
% end
|
||||
% end
|
||||
%**** For constant D+_s except the first two lags and the constant term. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
% for si=1:nStates-1
|
||||
% for ki=[2*nvar+1:kvar-1]
|
||||
% Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
% end
|
||||
% end
|
||||
end
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
eqninx = 4;
|
||||
nreseqn = 2; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 0 1 0 0 0 0 0 0 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
eqninx = 5;
|
||||
nreseqn = 1; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For time-varying A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:nreseqn*nStates,:,eqninx) = [
|
||||
0 0 0 0 0 1 0 0 0 0 0 0
|
||||
|
||||
0 0 0 0 0 0 0 0 0 0 0 1
|
||||
];
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
%======== The sixth equation ===========
|
||||
eqninx = 6;
|
||||
nreseqn = 0; % Number of linear restrictions for the equation for each state.
|
||||
if (indxEqnTv_m(eqninx, 2)<=2)
|
||||
%**** For constant A0_s. In the order of [a0j(1),...,a0j(nStates)] for the 2nd dim of Qi.
|
||||
Qi(1:(nStates-1)*nvar+nreseqn,:,eqninx) = [
|
||||
1 0 0 0 0 0 -1 0 0 0 0 0
|
||||
0 1 0 0 0 0 0 -1 0 0 0 0
|
||||
0 0 1 0 0 0 0 0 -1 0 0 0
|
||||
0 0 0 1 0 0 0 0 0 -1 0 0
|
||||
0 0 0 0 1 0 0 0 0 0 -1 0
|
||||
0 0 0 0 0 1 0 0 0 0 0 -1
|
||||
];
|
||||
%**** For constant D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else % Time-varying equations at least for A0_s. For D+_s, constant-parameter equations in general.
|
||||
%**** For D+_s. In the order of [aj+(1),...,aj+(nStates)] for the 2nd dim of Ri.
|
||||
if (indxEqnTv_m(eqninx, 2)==3) % For constant D+** except the constant term. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar-1 % -1: no restrictions on the constant term, which is freely time-varying.
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
elseif (indxEqnTv_m(eqninx, 2)==4) % For constant D+**. In the order of [dj**(1),...,dj**(nStates)] for the 2nd dim of Ri.
|
||||
for si=1:nStates-1
|
||||
for ki=1:kvar
|
||||
Ri(kvar*(si-1)+ki,[kvar*(si-1)+ki si*kvar+ki],eqninx) = [1 -1];
|
||||
end
|
||||
end
|
||||
else
|
||||
error('.../ftd_2s_caseall_simszha5v.m: Have not got time to deal with the simple case indxEqnTv_m(eqninx, 2)=5.')
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
|
||||
for ki=1:nvar % initializing loop for each equation
|
||||
Ui{ki} = null(Qi(:,:,ki));
|
||||
Vi{ki} = null(Ri(:,:,ki));
|
||||
n0(ki) = size(Ui{ki},2);
|
||||
np(ki) = size(Vi{ki},2);
|
||||
end
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,188 +1,188 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_reac_function_4v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [ff+ch fh dpgdp ffr)
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% HERE FIRTS 3 EQUATIONS ARE AR2 AND THE LAST EQUATION IS AN UNRESTRICTED
|
||||
% REACTION FUNCTION 2 lags
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
% BN
|
||||
|
||||
nvar=4;
|
||||
lags=4;
|
||||
nexo=1;
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:3,:,1) = [
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:2,:,2) = [
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation =========== NOTE THAT WE FORBID A
|
||||
%CONTEMPORANEOUS IMPACT OF OUTPUTON PRICES TO AVOID A CONSTRAINT THAT
|
||||
%INVOLVE A0 and Aplus
|
||||
Qi(1:3,:,3) = [
|
||||
1 0 0 0
|
||||
0 1 0 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
|
||||
|
||||
% Restrictions on the A+ in order to focus strictly on the reaction fucntion
|
||||
|
||||
% indicates free parameterers X i
|
||||
% Ap = [
|
||||
% X X X X
|
||||
% X X X X
|
||||
% -a1 -b1 X X
|
||||
% a1 b1 0 X (1st lag)
|
||||
% X X X X
|
||||
% X X X X
|
||||
% -a2 -b2 X X
|
||||
% b2 b2 0 X (2nd lag)
|
||||
% X 0 X X
|
||||
% X X X X
|
||||
% -a3 -b3 X X
|
||||
% a3 a3 0 X (3rd lag)
|
||||
% X X X X
|
||||
% X X X X
|
||||
% -a4 -b4 X X
|
||||
% a4 b4 0 X (4th lag)
|
||||
% X X X X (constant terms)
|
||||
% ];
|
||||
|
||||
k=nvar*lags+nexo;
|
||||
Ri = zeros(k,k,nvar);
|
||||
% constraints on IS curve /conso+corporate investment
|
||||
for nv=1:2
|
||||
for ll=1:lags
|
||||
Ri(ll,3+lags*(ll-1),nv)=1;
|
||||
Ri(ll,4+lags*(ll-1),nv)=1;
|
||||
end
|
||||
end
|
||||
|
||||
% constraints on IS curve /conso+corporate investment only on the long run
|
||||
% impact
|
||||
% for nv=1:2
|
||||
% for ll=1:lags
|
||||
% Ri(1,3+lags*(ll-1),nv)=1;
|
||||
% Ri(1,4+lags*(ll-1),nv)=1;
|
||||
% end
|
||||
% end
|
||||
|
||||
|
||||
% constraints on Ph curve / inflation does not react to interest rates
|
||||
for ll=1:lags
|
||||
Ri(ll,4+lags*(ll-1),3)=1;
|
||||
end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_reac_function_4v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [ff+ch fh dpgdp ffr)
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% HERE FIRTS 3 EQUATIONS ARE AR2 AND THE LAST EQUATION IS AN UNRESTRICTED
|
||||
% REACTION FUNCTION 2 lags
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
% BN
|
||||
|
||||
nvar=4;
|
||||
lags=4;
|
||||
nexo=1;
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:3,:,1) = [
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:2,:,2) = [
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation =========== NOTE THAT WE FORBID A
|
||||
%CONTEMPORANEOUS IMPACT OF OUTPUTON PRICES TO AVOID A CONSTRAINT THAT
|
||||
%INVOLVE A0 and Aplus
|
||||
Qi(1:3,:,3) = [
|
||||
1 0 0 0
|
||||
0 1 0 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
|
||||
|
||||
% Restrictions on the A+ in order to focus strictly on the reaction fucntion
|
||||
|
||||
% indicates free parameterers X i
|
||||
% Ap = [
|
||||
% X X X X
|
||||
% X X X X
|
||||
% -a1 -b1 X X
|
||||
% a1 b1 0 X (1st lag)
|
||||
% X X X X
|
||||
% X X X X
|
||||
% -a2 -b2 X X
|
||||
% b2 b2 0 X (2nd lag)
|
||||
% X 0 X X
|
||||
% X X X X
|
||||
% -a3 -b3 X X
|
||||
% a3 a3 0 X (3rd lag)
|
||||
% X X X X
|
||||
% X X X X
|
||||
% -a4 -b4 X X
|
||||
% a4 b4 0 X (4th lag)
|
||||
% X X X X (constant terms)
|
||||
% ];
|
||||
|
||||
k=nvar*lags+nexo;
|
||||
Ri = zeros(k,k,nvar);
|
||||
% constraints on IS curve /conso+corporate investment
|
||||
for nv=1:2
|
||||
for ll=1:lags
|
||||
Ri(ll,3+lags*(ll-1),nv)=1;
|
||||
Ri(ll,4+lags*(ll-1),nv)=1;
|
||||
end
|
||||
end
|
||||
|
||||
% constraints on IS curve /conso+corporate investment only on the long run
|
||||
% impact
|
||||
% for nv=1:2
|
||||
% for ll=1:lags
|
||||
% Ri(1,3+lags*(ll-1),nv)=1;
|
||||
% Ri(1,4+lags*(ll-1),nv)=1;
|
||||
% end
|
||||
% end
|
||||
|
||||
|
||||
% constraints on Ph curve / inflation does not react to interest rates
|
||||
for ll=1:lags
|
||||
Ri(ll,4+lags*(ll-1),3)=1;
|
||||
end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,251 +1,251 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_cholesky(lags,nvar,nexo,indxC0Pres)
|
||||
%vlist = [1:4]; % regarding "xdd", % 1: p; 2: id; 3: ik; 4: y.
|
||||
%For restricted VARs in the form: y_t'*A0 = x_t'*Ap + e_t', where y_t is a vector of endogenous variables
|
||||
% and x_t is a vector of lagged endogenous variables and the constant term (last term).
|
||||
% Note that the columns of A0 and Ap correspnd to equations.
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%The restrictions considered here are in the following form where X means unrestricted:
|
||||
% A0 = [
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 0 X
|
||||
% ];
|
||||
% Ap = [
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (1st lag)
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (2nd lag)
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (3rd lag)
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (4th lag)
|
||||
% 0 X 0 0 (constant terms)
|
||||
% ];
|
||||
|
||||
if (0)
|
||||
%------------------------ Lower triangular A0 ------------------------------
|
||||
%======== The first equation ===========
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:1,:,2) = [
|
||||
1 0 0 0
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:2,:,3) = [
|
||||
1 0 0 0
|
||||
0 1 0 0
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:3,:,4) = [
|
||||
1 0 0 0
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
];
|
||||
else
|
||||
%------------------------ Upper triangular A0 ------------------------------
|
||||
%======== The first equation ===========
|
||||
Qi(2:4,:,1) = [
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi([1 3:4],:,2) = [
|
||||
1 0 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(4:4,:,3) = [
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
end
|
||||
|
||||
|
||||
%-------------------------- Lag restrictions. ------------------------------------------
|
||||
if (1)
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 1; %Which equation.
|
||||
nrestrs = (nvar-1)*lags+1; %Number of restrictions.
|
||||
vars_restr = [2:nvar]; %Variables that are restricted: id, ik, and y.
|
||||
blags = zeros(nrestrs,k); %k=nvar*lags+1
|
||||
cnt = 0;
|
||||
for ki = 1:lags
|
||||
for kj=vars_restr
|
||||
cnt = cnt+1;
|
||||
blags(cnt,nvar*(ki-1)+kj) = 1;
|
||||
end
|
||||
end
|
||||
%--- Keep constant zero.
|
||||
cnt = cnt+1;
|
||||
blags(cnt,end) = 1; %Constant = 0.
|
||||
if cnt~=nrestrs
|
||||
error('Check lagged restrictions in 1st equation!')
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 2; %Which equation.
|
||||
nrestrs = (nvar-1)*lags; %Number of restrictions.
|
||||
vars_restr = [1 3:nvar]; %Variables that are restricted: id, ik, and y.
|
||||
blags = zeros(nrestrs,k); %k=nvar*lags+1
|
||||
cnt = 0;
|
||||
for ki = 1:lags
|
||||
for kj=vars_restr
|
||||
cnt = cnt+1;
|
||||
blags(cnt,nvar*(ki-1)+kj) = 1;
|
||||
end
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 3; %Which equation.
|
||||
nrestrs = 1; %Number of restrictions.
|
||||
blags = zeros(nrestrs,k);
|
||||
cnt = 0;
|
||||
%--- Keep constant zero.
|
||||
cnt = cnt+1;
|
||||
blags(cnt,end) = 1; %Constant = 0.
|
||||
if cnt~=nrestrs
|
||||
error('Check lagged restrictions in 1st equation!')
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 4; %Which equation.
|
||||
nrestrs = 1; %Number of restrictions.
|
||||
blags = zeros(nrestrs,k);
|
||||
cnt = 0;
|
||||
%--- Keep constant zero.
|
||||
cnt = cnt+1;
|
||||
blags(cnt,end) = 1; %Constant = 0.
|
||||
if cnt~=nrestrs
|
||||
error('Check lagged restrictions in 1st equation!')
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
% This type of restriction is used for the New-Keysian model studied by Leeper and Zha
|
||||
% "Assessing Simple Policy Rules: A View from a Complete Macroeconomic Model" published
|
||||
% by St. Louis Fed Review.
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_cholesky(lags,nvar,nexo,indxC0Pres)
|
||||
%vlist = [1:4]; % regarding "xdd", % 1: p; 2: id; 3: ik; 4: y.
|
||||
%For restricted VARs in the form: y_t'*A0 = x_t'*Ap + e_t', where y_t is a vector of endogenous variables
|
||||
% and x_t is a vector of lagged endogenous variables and the constant term (last term).
|
||||
% Note that the columns of A0 and Ap correspnd to equations.
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%The restrictions considered here are in the following form where X means unrestricted:
|
||||
% A0 = [
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 0 X
|
||||
% ];
|
||||
% Ap = [
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (1st lag)
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (2nd lag)
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (3rd lag)
|
||||
% X 0 X X
|
||||
% 0 X X X
|
||||
% 0 0 X X
|
||||
% 0 0 X X (4th lag)
|
||||
% 0 X 0 0 (constant terms)
|
||||
% ];
|
||||
|
||||
if (0)
|
||||
%------------------------ Lower triangular A0 ------------------------------
|
||||
%======== The first equation ===========
|
||||
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:1,:,2) = [
|
||||
1 0 0 0
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:2,:,3) = [
|
||||
1 0 0 0
|
||||
0 1 0 0
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:3,:,4) = [
|
||||
1 0 0 0
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
];
|
||||
else
|
||||
%------------------------ Upper triangular A0 ------------------------------
|
||||
%======== The first equation ===========
|
||||
Qi(2:4,:,1) = [
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi([1 3:4],:,2) = [
|
||||
1 0 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(4:4,:,3) = [
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
end
|
||||
|
||||
|
||||
%-------------------------- Lag restrictions. ------------------------------------------
|
||||
if (1)
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 1; %Which equation.
|
||||
nrestrs = (nvar-1)*lags+1; %Number of restrictions.
|
||||
vars_restr = [2:nvar]; %Variables that are restricted: id, ik, and y.
|
||||
blags = zeros(nrestrs,k); %k=nvar*lags+1
|
||||
cnt = 0;
|
||||
for ki = 1:lags
|
||||
for kj=vars_restr
|
||||
cnt = cnt+1;
|
||||
blags(cnt,nvar*(ki-1)+kj) = 1;
|
||||
end
|
||||
end
|
||||
%--- Keep constant zero.
|
||||
cnt = cnt+1;
|
||||
blags(cnt,end) = 1; %Constant = 0.
|
||||
if cnt~=nrestrs
|
||||
error('Check lagged restrictions in 1st equation!')
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 2; %Which equation.
|
||||
nrestrs = (nvar-1)*lags; %Number of restrictions.
|
||||
vars_restr = [1 3:nvar]; %Variables that are restricted: id, ik, and y.
|
||||
blags = zeros(nrestrs,k); %k=nvar*lags+1
|
||||
cnt = 0;
|
||||
for ki = 1:lags
|
||||
for kj=vars_restr
|
||||
cnt = cnt+1;
|
||||
blags(cnt,nvar*(ki-1)+kj) = 1;
|
||||
end
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 3; %Which equation.
|
||||
nrestrs = 1; %Number of restrictions.
|
||||
blags = zeros(nrestrs,k);
|
||||
cnt = 0;
|
||||
%--- Keep constant zero.
|
||||
cnt = cnt+1;
|
||||
blags(cnt,end) = 1; %Constant = 0.
|
||||
if cnt~=nrestrs
|
||||
error('Check lagged restrictions in 1st equation!')
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
|
||||
%--- Lag restrictions.
|
||||
indxeqn = 4; %Which equation.
|
||||
nrestrs = 1; %Number of restrictions.
|
||||
blags = zeros(nrestrs,k);
|
||||
cnt = 0;
|
||||
%--- Keep constant zero.
|
||||
cnt = cnt+1;
|
||||
blags(cnt,end) = 1; %Constant = 0.
|
||||
if cnt~=nrestrs
|
||||
error('Check lagged restrictions in 1st equation!')
|
||||
end
|
||||
Ri(1:nrestrs,:,indxeqn) = blags;
|
||||
end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
% This type of restriction is used for the New-Keysian model studied by Leeper and Zha
|
||||
% "Assessing Simple Policy Rules: A View from a Complete Macroeconomic Model" published
|
||||
% by St. Louis Fed Review.
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,192 +1,192 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol5v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 93 141 21]; % 1: GDP; 2: GDP deflator 124 (consumption deflator 79); 3: R; 4: M3 141 (M2 140); 5: exchange rate 21.
|
||||
% varlist={'y', 'P', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:4,:,1) = [
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:3,:,2) = [
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:2,:,3) = [
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
%Qi(1:1,:,4) = [
|
||||
% 0 0 0 0 1
|
||||
% ];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
|
||||
Qi(1:3,:,5) = [
|
||||
1 0 0 0 0
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
];
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol5v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 93 141 21]; % 1: GDP; 2: GDP deflator 124 (consumption deflator 79); 3: R; 4: M3 141 (M2 140); 5: exchange rate 21.
|
||||
% varlist={'y', 'P', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:4,:,1) = [
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:3,:,2) = [
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:2,:,3) = [
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
%Qi(1:1,:,4) = [
|
||||
% 0 0 0 0 1
|
||||
% ];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
|
||||
Qi(1:3,:,5) = [
|
||||
1 0 0 0 0
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
];
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,190 +1,190 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_simszha5v(lags,nvar,nexo,indxC0Pres)
|
||||
%vlist = [21 141 93 127 124]; % 1: Pcom 2 (exchange rate 21); 2: M3 141 (M2 140); 3: R; 4: GDP; 5: GDP deflator 124 (consumption deflator 79).
|
||||
%varlist={'Ex', 'M3', 'R', 'y','P'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation: information sector ===========
|
||||
|
||||
|
||||
%======== The second equation: monetary policy ===========
|
||||
%Qi(1:2,:,2) = [
|
||||
% 0 0 0 1 0
|
||||
% 0 0 0 0 1
|
||||
% ]; % Respond to Pcom.
|
||||
Qi(1:3,:,2) = [
|
||||
1 0 0 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
]; % Not respond to Pcom.
|
||||
|
||||
%======== The third equation: money demand ===========
|
||||
Qi(1,:,3) = [
|
||||
1 0 0 0 0
|
||||
];
|
||||
|
||||
%======== The fourth equation: y equation ===========
|
||||
Qi(1:4,:,4) = [
|
||||
1 0 0 0 0
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fifth equation: p equation ===========
|
||||
Qi(1:3,:,5) = [
|
||||
1 0 0 0 0
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
];
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_simszha5v(lags,nvar,nexo,indxC0Pres)
|
||||
%vlist = [21 141 93 127 124]; % 1: Pcom 2 (exchange rate 21); 2: M3 141 (M2 140); 3: R; 4: GDP; 5: GDP deflator 124 (consumption deflator 79).
|
||||
%varlist={'Ex', 'M3', 'R', 'y','P'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation: information sector ===========
|
||||
|
||||
|
||||
%======== The second equation: monetary policy ===========
|
||||
%Qi(1:2,:,2) = [
|
||||
% 0 0 0 1 0
|
||||
% 0 0 0 0 1
|
||||
% ]; % Respond to Pcom.
|
||||
Qi(1:3,:,2) = [
|
||||
1 0 0 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
]; % Not respond to Pcom.
|
||||
|
||||
%======== The third equation: money demand ===========
|
||||
Qi(1,:,3) = [
|
||||
1 0 0 0 0
|
||||
];
|
||||
|
||||
%======== The fourth equation: y equation ===========
|
||||
Qi(1:4,:,4) = [
|
||||
1 0 0 0 0
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fifth equation: p equation ===========
|
||||
Qi(1:3,:,5) = [
|
||||
1 0 0 0 0
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
];
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,170 +1,170 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol3v(lags,nvar,nexo,indxC0Pres)
|
||||
%vlist = [20 6 3 44 1 10]; % regarding "xdd", Pcom (Poil or imfcom), M2, FFR, GDP, CPI (or PCE), and U.
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
Qi(1:2,:,1) = [
|
||||
0 1 0
|
||||
0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:1,:,2) = [
|
||||
0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The third equation ===========
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol3v(lags,nvar,nexo,indxC0Pres)
|
||||
%vlist = [20 6 3 44 1 10]; % regarding "xdd", Pcom (Poil or imfcom), M2, FFR, GDP, CPI (or PCE), and U.
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
|
||||
%======== The first equation ===========
|
||||
Qi(1:2,:,1) = [
|
||||
0 1 0
|
||||
0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:1,:,2) = [
|
||||
0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The third equation ===========
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,178 +1,178 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol4v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 93 141 21]; % 1: GDP; 2: GDP deflator 124 (consumption deflator 79); 3: R; 4: M3 141 (M2 140); 5: exchange rate 21.
|
||||
% varlist={'y', 'P', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:3,:,1) = [
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:2,:,2) = [
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:1,:,3) = [
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol4v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 93 141 21]; % 1: GDP; 2: GDP deflator 124 (consumption deflator 79); 3: R; 4: M3 141 (M2 140); 5: exchange rate 21.
|
||||
% varlist={'y', 'P', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:3,:,1) = [
|
||||
0 1 0 0
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:2,:,2) = [
|
||||
0 0 1 0
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:1,:,3) = [
|
||||
0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,187 +1,187 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol5v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 93 141 21]; % 1: GDP; 2: GDP deflator 124 (consumption deflator 79); 3: R; 4: M3 141 (M2 140); 5: exchange rate 21.
|
||||
% varlist={'y', 'P', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:4,:,1) = [
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:3,:,2) = [
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:2,:,3) = [
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:1,:,4) = [
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol5v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 93 141 21]; % 1: GDP; 2: GDP deflator 124 (consumption deflator 79); 3: R; 4: M3 141 (M2 140); 5: exchange rate 21.
|
||||
% varlist={'y', 'P', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:4,:,1) = [
|
||||
0 1 0 0 0
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:3,:,2) = [
|
||||
0 0 1 0 0
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:2,:,3) = [
|
||||
0 0 0 1 0
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:1,:,4) = [
|
||||
0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
|
||||
|
||||
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,194 +1,194 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol6v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 2 93 141 21]; % 1: Pcom 2 (exchange rate 21); 2: M3 141 (M2 140); 3: R; 4: GDP; 5: GDP deflator 124 (consumption deflator 79).
|
||||
% varlist={'y', 'P', 'Pcom', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:5,:,1) = [
|
||||
0 1 0 0 0 0
|
||||
0 0 1 0 0 0
|
||||
0 0 0 1 0 0
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:4,:,2) = [
|
||||
0 0 1 0 0 0
|
||||
0 0 0 1 0 0
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:3,:,3) = [
|
||||
0 0 0 1 0 0
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:2,:,4) = [
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
Qi(1:1,:,5) = [
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The sixth equation ===========
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol6v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 2 93 141 21]; % 1: Pcom 2 (exchange rate 21); 2: M3 141 (M2 140); 3: R; 4: GDP; 5: GDP deflator 124 (consumption deflator 79).
|
||||
% varlist={'y', 'P', 'Pcom', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:5,:,1) = [
|
||||
0 1 0 0 0 0
|
||||
0 0 1 0 0 0
|
||||
0 0 0 1 0 0
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:4,:,2) = [
|
||||
0 0 1 0 0 0
|
||||
0 0 0 1 0 0
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:3,:,3) = [
|
||||
0 0 0 1 0 0
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:2,:,4) = [
|
||||
0 0 0 0 1 0
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
Qi(1:1,:,5) = [
|
||||
0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The sixth equation ===========
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,204 +1,204 @@
|
|||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol7v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 2 93 141 21]; % 1: Pcom 2 (exchange rate 21); 2: M3 141 (M2 140); 3: R; 4: GDP; 5: GDP deflator 124 (consumption deflator 79).
|
||||
% varlist={'y', 'P', 'Pcom', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:6,:,1) = [
|
||||
0 1 0 0 0 0 0
|
||||
0 0 1 0 0 0 0
|
||||
0 0 0 1 0 0 0
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:5,:,2) = [
|
||||
0 0 1 0 0 0 0
|
||||
0 0 0 1 0 0 0
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:4,:,3) = [
|
||||
0 0 0 1 0 0 0
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:3,:,4) = [
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
Qi(1:2,:,5) = [
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The sixth equation ===========
|
||||
Qi(1:1,:,6) = [
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The seventh equation ===========
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
function [Ui,Vi,n0,np,ixmC0Pres] = ftd_upperchol7v(lags,nvar,nexo,indxC0Pres)
|
||||
% vlist = [127 124 2 93 141 21]; % 1: Pcom 2 (exchange rate 21); 2: M3 141 (M2 140); 3: R; 4: GDP; 5: GDP deflator 124 (consumption deflator 79).
|
||||
% varlist={'y', 'P', 'Pcom', 'R', 'M3', 'Ex'};
|
||||
%
|
||||
% Exporting orthonormal matrices for the deterministic linear restrictions (equation by equation)
|
||||
% See Waggoner and Zha's Gibbs sampling paper.
|
||||
%
|
||||
% q_m: quarter or month
|
||||
% lags: the maximum length of lag
|
||||
% nvar: number of endogeous variables
|
||||
% nexo: number of exogenous variables. If nexo is not supplied, nexo=1 as default for a constant
|
||||
% indxC0Pres: index for cross-A0-A+ restrictions. if 1: cross-A0-and-A+ restrictions; 0: idfile is all we have
|
||||
% Example for indxOres==1: restrictions of the form P(t) = P(t-1).
|
||||
% These restrictions have to be manually and carefully keyed in.
|
||||
%-----------------
|
||||
% Ui: nvar-by-1 cell. In each cell, nvar-by-qi orthonormal basis for the null of the ith
|
||||
% equation contemporaneous restriction matrix where qi is the number of free parameters.
|
||||
% With this transformation, we have ai = Ui*bi or Ui'*ai = bi where ai is a vector
|
||||
% of total original parameters and bi is a vector of free parameters. When no
|
||||
% restrictions are imposed, we have Ui = I. There must be at least one free
|
||||
% parameter left for the ith equation.
|
||||
% Vi: nvar-by-1 cell. In each cell, k-by-ri orthonormal basis for the null of the ith
|
||||
% equation lagged restriction matrix where k is a total of exogenous variables and
|
||||
% ri is the number of free parameters. With this transformation, we have fi = Vi*gi
|
||||
% or Vi'*fi = gi where fi is a vector of total original parameters and gi is a
|
||||
% vector of free parameters. There must be at least one free parameter left for
|
||||
% the ith equation.
|
||||
% n0: nvar-by-1, ith element represents the number of free A0 parameters in ith equation
|
||||
% np: nvar-by-1, ith element represents the number of free A+ parameters in ith equation
|
||||
% ixmC0Pres: neq_cres-by-1 cell. Effective only if indxC0Pres=1, otherwise equals NaN.
|
||||
% neq_cres is the number of equations in which cross-A0-A+ restrictions occur.
|
||||
% In the jth cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%
|
||||
% Tao Zha, May 2000
|
||||
|
||||
|
||||
|
||||
Ui = cell(nvar,1); % initializing for contemporaneous endogenous variables
|
||||
Vi = cell(nvar,1); % initializing for lagged and exogenous variables
|
||||
n0 = zeros(nvar,1); % ith element represents the number of free A0 parameters in ith equation
|
||||
np = zeros(nvar,1); % ith element represents the number of free A+ parameters in ith equation
|
||||
|
||||
if (nargin==2)
|
||||
nexo = 1; % 1: constant as default where nexo must be a nonnegative integer
|
||||
elseif (nargin==3)
|
||||
indxC0Pres = 0; % default is no cross-A0-and-A+ restrictions.
|
||||
end
|
||||
|
||||
k = lags*nvar+nexo; % maximum number of lagged and exogenous variables in each equation
|
||||
|
||||
Qi = zeros(nvar,nvar,nvar); % for nvar contemporaneous equations
|
||||
Ri = zeros(k,k,nvar); % for nvar lagged and exogenous equations
|
||||
% Row corresponds to equation. 0 means no restriction.
|
||||
% 1 means exclusion restriction such that the corresponding parameter is restricted to 0.
|
||||
|
||||
%nfvar = 6; % number of foreign (Granger causing) variables
|
||||
%nhvar = nvar-nfvar; % number of home (affected) variables.
|
||||
|
||||
|
||||
%-------------------------------------------------------------
|
||||
% Beginning the manual input of the restrictions one quation at a time
|
||||
%-------------------------------------------------------------
|
||||
%
|
||||
%======== The first equation ===========
|
||||
Qi(1:6,:,1) = [
|
||||
0 1 0 0 0 0 0
|
||||
0 0 1 0 0 0 0
|
||||
0 0 0 1 0 0 0
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The second equation ===========
|
||||
Qi(1:5,:,2) = [
|
||||
0 0 1 0 0 0 0
|
||||
0 0 0 1 0 0 0
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The third equation ===========
|
||||
Qi(1:4,:,3) = [
|
||||
0 0 0 1 0 0 0
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
%======== The fourth equation ===========
|
||||
Qi(1:3,:,4) = [
|
||||
0 0 0 0 1 0 0
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The fifth equation ===========
|
||||
Qi(1:2,:,5) = [
|
||||
0 0 0 0 0 1 0
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The sixth equation ===========
|
||||
Qi(1:1,:,6) = [
|
||||
0 0 0 0 0 0 1
|
||||
];
|
||||
|
||||
|
||||
%======== The seventh equation ===========
|
||||
|
||||
%===== Lagged restrictions in foreign (Granger causing) block
|
||||
%nfbres = lags*(nvar-nfvar); % number of block restrictions in each foreign equation
|
||||
%bfor = zeros(nfbres,k); % each foreign equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:nvar-nfvar
|
||||
% cnt=cnt+1;
|
||||
% bfor(cnt,nvar*(ki-1)+nfvar+kj) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nfbres
|
||||
% error('Check lagged restrictions in foreign equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=1:nfvar
|
||||
% Ri(1:nfbres,:,kj) = bfor;
|
||||
%end
|
||||
|
||||
|
||||
%===== Lagged restrictions in home (affected) block
|
||||
%
|
||||
%~~~~~ selected domestic equations
|
||||
%dlrindx = nfvar+1; %[nfvar+1 nfvar+2]; % index for relevant home equations
|
||||
%rfvindx = []; %[6]; %[1 2 3 5]; % index for restricted foreign variables (e.g., Poil, M2, FFR, P).
|
||||
%%nf2hvar = nfvar-length(rfvindx); % number of free parameters -- foreign variables entering the home sector
|
||||
%nhbres = lags*length(rfvindx); % number of block restrictions in each home equation
|
||||
%bhom = zeros(nhbres,k); % each home equation
|
||||
%cnt=0;
|
||||
%for ki = 1:lags
|
||||
% for kj=1:length(rfvindx)
|
||||
% cnt=cnt+1;
|
||||
% bhom(cnt,nvar*(ki-1)+rfvindx(kj)) = 1;
|
||||
% end
|
||||
%end
|
||||
%%
|
||||
%if cnt~=nhbres
|
||||
% error('Check lagged restrictions in domestic equations!')
|
||||
%end
|
||||
%%
|
||||
%for kj=dlrindx
|
||||
% Ri(1:nhbres,:,kj) = bhom;
|
||||
%end
|
||||
|
||||
|
||||
for n=1:nvar % initializing loop for each equation
|
||||
Ui{n} = null(Qi(:,:,n));
|
||||
Vi{n} = null(Ri(:,:,n));
|
||||
n0(n) = size(Ui{n},2);
|
||||
np(n) = size(Vi{n},2);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%(2)-------------------------------------------------------------
|
||||
% Cross-A0-and-A+ rerestrictions one quation at a time
|
||||
% i.e., the first, second, ..., kjth, ..., equation
|
||||
%(2)-------------------------------------------------------------
|
||||
%
|
||||
if indxC0Pres
|
||||
neq_cres = 3; % the number of equations in which cross-A0-A+ restrictions occur.
|
||||
ixmC0Pres = cell(neq_cres,1); % in each cell representing equation, we have 4 columns:
|
||||
% 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
%** 1st equation
|
||||
ixmC0Pres{1} = [1 2 2 1
|
||||
1 7 1 1];
|
||||
%** 2nd equation
|
||||
ixmC0Pres{2} = [2 2 2 2];
|
||||
%** 3rd equation
|
||||
ixmC0Pres{3} = [3 7 1 1
|
||||
3 2 2 1];
|
||||
|
||||
|
||||
% % 4 columns.
|
||||
% ncres = 5; % manually key in the number of cross-A0-A+ restrictions
|
||||
|
||||
% % 1st: the jth column (equation) of A+ or A0: f_j or a_j
|
||||
% % 2nd: the ith element f_j(i) -- the ith element in the jth column of A+
|
||||
% % 3rd: the hth element a_j(h) -- the hth element in the jth column of A0
|
||||
% % 4th: the number s such that f_j(i) = s * a_j(h) holds.
|
||||
else
|
||||
ixmC0Pres = NaN;
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,90 +1,90 @@
|
|||
//MODEL:
|
||||
//test on Dynare to find the lagrangean multipliers.
|
||||
//We consider a standard NK model. We use the FOCS of the competitive economy and we aim at calculating the Ramsey optimal problem.
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
//1. Variable declaration
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
var pai, c, n, r, a;
|
||||
|
||||
//4 variables + 1 shock
|
||||
|
||||
varexo u;
|
||||
|
||||
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
// 2. Parameter declaration and calibration
|
||||
//-------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
parameters beta, rho, epsilon, omega, phi, gamma;
|
||||
|
||||
beta=0.99;
|
||||
gamma=3; //Frish elasticity
|
||||
omega=17; //price stickyness
|
||||
epsilon=8; //elasticity for each variety of consumption
|
||||
phi=1; //coefficient associated to labor effort disutility
|
||||
|
||||
rho=0.95; //coefficient associated to productivity shock
|
||||
|
||||
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
// 3. The model
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
|
||||
model;
|
||||
|
||||
|
||||
a=rho*(a(-1))+u;
|
||||
|
||||
1/c=beta*(1/(c(+1)))*(r/(pai(+1))); //euler
|
||||
|
||||
|
||||
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
|
||||
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
|
||||
|
||||
(exp(a))*n=c+(omega/2)*((pai-1)^2);
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 4. Steady state
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
initval;
|
||||
|
||||
pai=1;
|
||||
r=1/beta;
|
||||
c=0.9671684882;
|
||||
n=0.9671684882;
|
||||
a=0;
|
||||
|
||||
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
// 5. shocks
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
shocks;
|
||||
var u; stderr 0.008;
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 6. Ramsey problem
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
|
||||
|
||||
write_latex_static_model;
|
||||
|
||||
ramsey_policy(planner_discount=0.99);
|
||||
|
||||
|
||||
|
||||
//MODEL:
|
||||
//test on Dynare to find the lagrangean multipliers.
|
||||
//We consider a standard NK model. We use the FOCS of the competitive economy and we aim at calculating the Ramsey optimal problem.
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
//1. Variable declaration
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
var pai, c, n, r, a;
|
||||
|
||||
//4 variables + 1 shock
|
||||
|
||||
varexo u;
|
||||
|
||||
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
// 2. Parameter declaration and calibration
|
||||
//-------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
parameters beta, rho, epsilon, omega, phi, gamma;
|
||||
|
||||
beta=0.99;
|
||||
gamma=3; //Frish elasticity
|
||||
omega=17; //price stickyness
|
||||
epsilon=8; //elasticity for each variety of consumption
|
||||
phi=1; //coefficient associated to labor effort disutility
|
||||
|
||||
rho=0.95; //coefficient associated to productivity shock
|
||||
|
||||
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
// 3. The model
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
|
||||
model;
|
||||
|
||||
|
||||
a=rho*(a(-1))+u;
|
||||
|
||||
1/c=beta*(1/(c(+1)))*(r/(pai(+1))); //euler
|
||||
|
||||
|
||||
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
|
||||
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
|
||||
|
||||
(exp(a))*n=c+(omega/2)*((pai-1)^2);
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 4. Steady state
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
initval;
|
||||
|
||||
pai=1;
|
||||
r=1/beta;
|
||||
c=0.9671684882;
|
||||
n=0.9671684882;
|
||||
a=0;
|
||||
|
||||
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
// 5. shocks
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
shocks;
|
||||
var u; stderr 0.008;
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 6. Ramsey problem
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
|
||||
|
||||
write_latex_static_model;
|
||||
|
||||
ramsey_policy(planner_discount=0.99);
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -1,96 +1,96 @@
|
|||
//MODEL:
|
||||
// test for using expectation operator with Ramsey policy
|
||||
// The results is validated by comparing with replacing manually the expectation with an
|
||||
// auxiliary variable in nk_ramsey_expectation_a.mod
|
||||
// Note that the example doesn't make any sense from an economic point of view.
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
//1. Variable declaration
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
var pai, c, n, r, a;
|
||||
|
||||
//4 variables + 1 shock
|
||||
|
||||
varexo u;
|
||||
|
||||
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
// 2. Parameter declaration and calibration
|
||||
//-------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
parameters beta, rho, epsilon, omega, phi, gamma;
|
||||
|
||||
beta=0.99;
|
||||
gamma=3; //Frish elasticity
|
||||
omega=17; //price stickyness
|
||||
epsilon=8; //elasticity for each variety of consumption
|
||||
phi=1; //coefficient associated to labor effort disutility
|
||||
|
||||
rho=0.95; //coefficient associated to productivity shock
|
||||
|
||||
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
// 3. The model
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
|
||||
model;
|
||||
|
||||
|
||||
a=rho*(a(-1))+u;
|
||||
|
||||
1/c=beta*(1/(c(+1)))*(r/expectation(0)(pai(+1))); //euler
|
||||
|
||||
|
||||
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
|
||||
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
|
||||
|
||||
(exp(a))*n=c+(omega/2)*((pai-1)^2);
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 4. Steady state
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
initval;
|
||||
% this is the exact steady state under optimal policy
|
||||
%important for the comparison
|
||||
|
||||
pai=1;
|
||||
r=1/beta;
|
||||
c=((epsilon-1)/(epsilon*phi))^(1/(1+gamma));
|
||||
n=c;
|
||||
a=0;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
// 5. shocks
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
shocks;
|
||||
var u; stderr 0.008;
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 6. Ramsey problem
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
|
||||
|
||||
write_latex_static_model;
|
||||
write_latex_dynamic_model;
|
||||
|
||||
options_.solve_tolf=1e-12;
|
||||
ramsey_policy(planner_discount=0.99);
|
||||
|
||||
|
||||
|
||||
//MODEL:
|
||||
// test for using expectation operator with Ramsey policy
|
||||
// The results is validated by comparing with replacing manually the expectation with an
|
||||
// auxiliary variable in nk_ramsey_expectation_a.mod
|
||||
// Note that the example doesn't make any sense from an economic point of view.
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
//1. Variable declaration
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
var pai, c, n, r, a;
|
||||
|
||||
//4 variables + 1 shock
|
||||
|
||||
varexo u;
|
||||
|
||||
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
// 2. Parameter declaration and calibration
|
||||
//-------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
parameters beta, rho, epsilon, omega, phi, gamma;
|
||||
|
||||
beta=0.99;
|
||||
gamma=3; //Frish elasticity
|
||||
omega=17; //price stickyness
|
||||
epsilon=8; //elasticity for each variety of consumption
|
||||
phi=1; //coefficient associated to labor effort disutility
|
||||
|
||||
rho=0.95; //coefficient associated to productivity shock
|
||||
|
||||
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
// 3. The model
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
|
||||
model;
|
||||
|
||||
|
||||
a=rho*(a(-1))+u;
|
||||
|
||||
1/c=beta*(1/(c(+1)))*(r/expectation(0)(pai(+1))); //euler
|
||||
|
||||
|
||||
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
|
||||
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
|
||||
|
||||
(exp(a))*n=c+(omega/2)*((pai-1)^2);
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 4. Steady state
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
initval;
|
||||
% this is the exact steady state under optimal policy
|
||||
%important for the comparison
|
||||
|
||||
pai=1;
|
||||
r=1/beta;
|
||||
c=((epsilon-1)/(epsilon*phi))^(1/(1+gamma));
|
||||
n=c;
|
||||
a=0;
|
||||
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
// 5. shocks
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
shocks;
|
||||
var u; stderr 0.008;
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 6. Ramsey problem
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
|
||||
|
||||
write_latex_static_model;
|
||||
write_latex_dynamic_model;
|
||||
|
||||
options_.solve_tolf=1e-12;
|
||||
ramsey_policy(planner_discount=0.99);
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -1,104 +1,104 @@
|
|||
//MODEL:
|
||||
// test for using expectation operator with Ramsey policy
|
||||
// Here, the expected variable is replaced manually with an auxiliary variable (epai)
|
||||
// We check that the result is the same as with an explicit expectation operator in nk_ramsey_expectation.mod
|
||||
// Note that the example doesn't make any sense from an economic point of view.
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
//1. Variable declaration
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
var pai, c, n, r, a, epai;
|
||||
|
||||
//4 variables + 1 shock
|
||||
|
||||
varexo u;
|
||||
|
||||
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
// 2. Parameter declaration and calibration
|
||||
//-------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
parameters beta, rho, epsilon, omega, phi, gamma;
|
||||
|
||||
beta=0.99;
|
||||
gamma=3; //Frish elasticity
|
||||
omega=17; //price stickyness
|
||||
epsilon=8; //elasticity for each variety of consumption
|
||||
phi=1; //coefficient associated to labor effort disutility
|
||||
|
||||
rho=0.95; //coefficient associated to productivity shock
|
||||
|
||||
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
// 3. The model
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
|
||||
model;
|
||||
|
||||
|
||||
a=rho*(a(-1))+u;
|
||||
|
||||
1/c=beta*(1/(c(+1)))*(r/epai); //euler
|
||||
|
||||
|
||||
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
|
||||
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
|
||||
|
||||
(exp(a))*n=c+(omega/2)*((pai-1)^2);
|
||||
|
||||
epai = pai(+1);
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 4. Steady state
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
initval;
|
||||
% this is the exact steady state under optimal policy
|
||||
%important for the comparison
|
||||
|
||||
pai=1;
|
||||
epai=1;
|
||||
r=1/beta;
|
||||
c=((epsilon-1)/(epsilon*phi))^(1/(1+gamma));
|
||||
n=c;
|
||||
a=0;
|
||||
|
||||
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
// 5. shocks
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
shocks;
|
||||
var u; stderr 0.008;
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 6. Ramsey problem
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
|
||||
|
||||
options_.solve_tolf=1e-12;
|
||||
ramsey_policy(planner_discount=0.99);
|
||||
|
||||
o1=load('nk_ramsey_expectation_results');
|
||||
if (norm(o1.oo_.dr.ghx-oo_.dr.ghx,inf) > 1e-12)
|
||||
error('ghx doesn''t match')
|
||||
end
|
||||
if (norm(o1.oo_.dr.ghu-oo_.dr.ghu,inf) > 1e-12)
|
||||
error('ghu doesn''t match')
|
||||
end
|
||||
if (abs(o1.oo_.planner_objective_value(1)-oo_.planner_objective_value(1)) > 1e-12)
|
||||
error('planner objective value doesn''t match')
|
||||
end
|
||||
|
||||
//MODEL:
|
||||
// test for using expectation operator with Ramsey policy
|
||||
// Here, the expected variable is replaced manually with an auxiliary variable (epai)
|
||||
// We check that the result is the same as with an explicit expectation operator in nk_ramsey_expectation.mod
|
||||
// Note that the example doesn't make any sense from an economic point of view.
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
//1. Variable declaration
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
var pai, c, n, r, a, epai;
|
||||
|
||||
//4 variables + 1 shock
|
||||
|
||||
varexo u;
|
||||
|
||||
|
||||
|
||||
|
||||
//------------------------------------------------------------------------------------------------------------------------
|
||||
// 2. Parameter declaration and calibration
|
||||
//-------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
parameters beta, rho, epsilon, omega, phi, gamma;
|
||||
|
||||
beta=0.99;
|
||||
gamma=3; //Frish elasticity
|
||||
omega=17; //price stickyness
|
||||
epsilon=8; //elasticity for each variety of consumption
|
||||
phi=1; //coefficient associated to labor effort disutility
|
||||
|
||||
rho=0.95; //coefficient associated to productivity shock
|
||||
|
||||
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
// 3. The model
|
||||
//-----------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
|
||||
model;
|
||||
|
||||
|
||||
a=rho*(a(-1))+u;
|
||||
|
||||
1/c=beta*(1/(c(+1)))*(r/epai); //euler
|
||||
|
||||
|
||||
omega*pai*(pai-1)=beta*omega*(c/(c(+1)))*(pai(+1))*(pai(+1)-1)+epsilon*exp(a)*n*(c/exp(a)*phi*n^gamma-(epsilon-1)/epsilon); //NK pc
|
||||
//pai*(pai-1)/c = beta*pai(+1)*(pai(+1)-1)/c(+1)+epsilon*phi*n^(gamma+1)/omega-exp(a)*n*(epsilon-1)/(omega*c); //NK pc
|
||||
|
||||
(exp(a))*n=c+(omega/2)*((pai-1)^2);
|
||||
|
||||
epai = pai(+1);
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 4. Steady state
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
initval;
|
||||
% this is the exact steady state under optimal policy
|
||||
%important for the comparison
|
||||
|
||||
pai=1;
|
||||
epai=1;
|
||||
r=1/beta;
|
||||
c=((epsilon-1)/(epsilon*phi))^(1/(1+gamma));
|
||||
n=c;
|
||||
a=0;
|
||||
|
||||
|
||||
end;
|
||||
|
||||
|
||||
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
// 5. shocks
|
||||
//---------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
shocks;
|
||||
var u; stderr 0.008;
|
||||
|
||||
end;
|
||||
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
// 6. Ramsey problem
|
||||
//--------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
planner_objective(ln(c)-phi*((n^(1+gamma))/(1+gamma)));
|
||||
|
||||
options_.solve_tolf=1e-12;
|
||||
ramsey_policy(planner_discount=0.99);
|
||||
|
||||
o1=load('nk_ramsey_expectation_results');
|
||||
if (norm(o1.oo_.dr.ghx-oo_.dr.ghx,inf) > 1e-12)
|
||||
error('ghx doesn''t match')
|
||||
end
|
||||
if (norm(o1.oo_.dr.ghu-oo_.dr.ghu,inf) > 1e-12)
|
||||
error('ghu doesn''t match')
|
||||
end
|
||||
if (abs(o1.oo_.planner_objective_value(1)-oo_.planner_objective_value(1)) > 1e-12)
|
||||
error('planner objective value doesn''t match')
|
||||
end
|
||||
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
load ych.dat;
|
||||
data = log(ych);
|
||||
oy = data(:,1);
|
||||
oc = data(:,2);
|
||||
load ych.dat;
|
||||
data = log(ych);
|
||||
oy = data(:,1);
|
||||
oc = data(:,2);
|
||||
oh = data(:,3);
|
||||
|
|
@ -1,58 +1,58 @@
|
|||
function datasaver (s,var_list)
|
||||
% datasaver saves variables simulated by Dynare
|
||||
% INPUT
|
||||
% s: a string containing the name of the destination *.m file
|
||||
% var_list: a character matrix containting the name of the variables
|
||||
% to be saved (optional, default: all endogenous variables)
|
||||
% OUTPUT
|
||||
% none
|
||||
% This is part of the examples included in F. Barillas, R. Colacito,
|
||||
% S. Kitao, C. Matthes, T. Sargent and Y. Shin (2007) "Practicing
|
||||
% Dynare".
|
||||
|
||||
% Modified by M. Juillard to make it also compatible with Dynare
|
||||
% version 4 (12/4/07)
|
||||
|
||||
|
||||
global lgy_ lgx_ y_ endo_nbr M_ oo_
|
||||
|
||||
% test and adapt for Dynare version 4
|
||||
if isempty(lgy_)
|
||||
lgy_ = M_.endo_names;
|
||||
lgx_ + M_.exo_names;
|
||||
y_ = oo_.endo_simul;
|
||||
endo_nbr = M_.endo_nbr;
|
||||
end
|
||||
|
||||
sm=[s,'.m'];
|
||||
fid=fopen(sm,'w') ;
|
||||
|
||||
n = size(var_list,1);
|
||||
if n == 0
|
||||
n = endo_nbr;
|
||||
ivar = [1:n]';
|
||||
var_list = lgy_;
|
||||
else
|
||||
ivar=zeros(n,1);
|
||||
for i=1:n
|
||||
i_tmp = strmatch(var_list(i,:),lgy_,'exact');
|
||||
if isempty(i_tmp)
|
||||
error (['One of the specified variables does not exist']) ;
|
||||
else
|
||||
ivar(i) = i_tmp;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
for i = 1:n
|
||||
fprintf(fid,[lgy_(ivar(i),:), '=['],'\n') ;
|
||||
fprintf(fid,'\n') ;
|
||||
fprintf(fid,'%15.8g\n',y_(ivar(i),:)') ;
|
||||
fprintf(fid,'\n') ;
|
||||
fprintf(fid,'];\n') ;
|
||||
fprintf(fid,'\n') ;
|
||||
end
|
||||
fclose(fid) ;
|
||||
|
||||
return ;
|
||||
function datasaver (s,var_list)
|
||||
% datasaver saves variables simulated by Dynare
|
||||
% INPUT
|
||||
% s: a string containing the name of the destination *.m file
|
||||
% var_list: a character matrix containting the name of the variables
|
||||
% to be saved (optional, default: all endogenous variables)
|
||||
% OUTPUT
|
||||
% none
|
||||
% This is part of the examples included in F. Barillas, R. Colacito,
|
||||
% S. Kitao, C. Matthes, T. Sargent and Y. Shin (2007) "Practicing
|
||||
% Dynare".
|
||||
|
||||
% Modified by M. Juillard to make it also compatible with Dynare
|
||||
% version 4 (12/4/07)
|
||||
|
||||
|
||||
global lgy_ lgx_ y_ endo_nbr M_ oo_
|
||||
|
||||
% test and adapt for Dynare version 4
|
||||
if isempty(lgy_)
|
||||
lgy_ = M_.endo_names;
|
||||
lgx_ + M_.exo_names;
|
||||
y_ = oo_.endo_simul;
|
||||
endo_nbr = M_.endo_nbr;
|
||||
end
|
||||
|
||||
sm=[s,'.m'];
|
||||
fid=fopen(sm,'w') ;
|
||||
|
||||
n = size(var_list,1);
|
||||
if n == 0
|
||||
n = endo_nbr;
|
||||
ivar = [1:n]';
|
||||
var_list = lgy_;
|
||||
else
|
||||
ivar=zeros(n,1);
|
||||
for i=1:n
|
||||
i_tmp = strmatch(var_list(i,:),lgy_,'exact');
|
||||
if isempty(i_tmp)
|
||||
error (['One of the specified variables does not exist']) ;
|
||||
else
|
||||
ivar(i) = i_tmp;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
for i = 1:n
|
||||
fprintf(fid,[lgy_(ivar(i),:), '=['],'\n') ;
|
||||
fprintf(fid,'\n') ;
|
||||
fprintf(fid,'%15.8g\n',y_(ivar(i),:)') ;
|
||||
fprintf(fid,'\n') ;
|
||||
fprintf(fid,'];\n') ;
|
||||
fprintf(fid,'\n') ;
|
||||
end
|
||||
fclose(fid) ;
|
||||
|
||||
return ;
|
||||
|
|
|
|||
|
|
@ -1,100 +1,100 @@
|
|||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
1.68081431462 3.34729969129 10 1.41159342106 -1.59065680853 ...
|
||||
-0.343321601133 5.05563513564 12 1.75117366498 -2.40127764642 ...
|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
-0.562233624818 3.88598638237 9.75 -0.0505384765105 0.332826708151 ...
|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
0.842215068977 3.11164509647 12.25 -1.08290421696 0.014323281961 ...
|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
-0.418465249225 3.75861110232 14.75 -1.03131674824 0.188507675831 ...
|
||||
-0.644028342116 4.15104788154 13.75 -1.48911756546 0.204560913792 ...
|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
-0.00264276644799 3.07989972052 8.75 -2.56342461535 2.105998353 ...
|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
data = [0.928467646476 11.8716889412 20 0.418037507392 0.227382377518 ...
|
||||
-0.705994063083 11.7522582094 21.25 1.09254424511 -1.29488274994 ...
|
||||
-0.511895351926 9.68144025625 17.25 -1.66150408407 0.331508393098 ...
|
||||
-0.990955971267 10.0890781236 17 1.43016275252 -2.43589670141 ...
|
||||
-0.981233061806 12.1094840679 18.25 2.91293288733 -0.790246576864 ...
|
||||
-0.882182844512 8.54559460406 15 0.419579139481 0.358729719566 ...
|
||||
-0.930893002836 6.19238374422 12.5 -1.48847457959 0.739779938797 ...
|
||||
1.53158206947 2.76544271886 11.5 -0.336216769682 0.455559918769 ...
|
||||
2.2659052834 5.47418162513 11 0.306436789767 -0.0707985731221 ...
|
||||
1.05419803797 6.35698426189 11 0.140700250477 0.620401487202 ...
|
||||
1.20161076793 3.4253301593 11 0.461296492351 0.14354323987 ...
|
||||
1.73934077971 4.70926070322 11.5 1.35798282982 0.38564694435 ...
|
||||
1.71735262584 3.54232079749 12.5 2.9097529155 -0.804308583301 ...
|
||||
0.426343657844 3.32719108897 13 1.64214862652 -1.18214664701 ...
|
||||
1.67751812324 2.93444727338 11.25 0.344434910651 -1.6529373719 ...
|
||||
1.37013301099 4.72303361923 11.75 2.61511526582 0.327684243041 ...
|
||||
0.281231073781 4.4893853071 10.5 1.17043449257 1.12855106649 ...
|
||||
1.53638992834 3.7325309699 10.25 -0.683947046728 0.11943538737 ...
|
||||
1.68081431462 3.34729969129 10 1.41159342106 -1.59065680853 ...
|
||||
-0.343321601133 5.05563513564 12 1.75117366498 -2.40127764642 ...
|
||||
0.873415608666 3.2779996255 10.25 -1.39895866711 0.0971444398216 ...
|
||||
0.26399696544 4.78229419828 9.75 0.0914692438124 0.299310457612 ...
|
||||
-0.562233624818 3.88598638237 9.75 -0.0505384765105 0.332826708151 ...
|
||||
2.15161914936 3.84859710132 8.75 -3.44811080489 0.789138678784 ...
|
||||
1.2345093726 5.62225030942 9.5 -0.366945407434 2.32974981198 ...
|
||||
1.62554967459 4.24667132831 10 -0.800958371402 0.0293183770935 ...
|
||||
1.33035402527 2.75248979249 9.75 -0.855723113225 0.852493939813 ...
|
||||
1.52078814077 3.53415985826 9.75 -3.37963469203 -1.05133958119 ...
|
||||
1.16704983697 4.92754079464 10.75 -3.0142303324 0.459907431978 ...
|
||||
0.277213572101 4.55532133037 11.75 -0.851995599415 2.03242034852 ...
|
||||
0.842215068977 3.11164509647 12.25 -1.08290421696 0.014323281961 ...
|
||||
1.05325028606 4.92882647578 13.5 -1.1953883867 0.706764750654 ...
|
||||
0.453051253568 6.82998950103 13.5 0.111803656462 0.088462593153 ...
|
||||
0.199885995525 5.82643354662 13.5 -0.920501518421 -0.26504958666 ...
|
||||
0.137907999624 2.66076369132 13.5 -1.17122929812 -0.995642430514 ...
|
||||
0.721949686709 5.70497876823 14.25 1.19378169018 -1.10644839651 ...
|
||||
-0.418465249225 3.75861110232 14.75 -1.03131674824 0.188507675831 ...
|
||||
-0.644028342116 4.15104788154 13.75 -1.48911756546 0.204560913792 ...
|
||||
-0.848213852668 5.65580324027 12.75 0.677011703877 -0.849628054542 ...
|
||||
-1.51954076928 11.4866911266 11.25 -0.446024680774 -0.456342350765 ...
|
||||
0.265275055215 2.85472749592 9.75 -0.598778202436 -0.907311640831 ...
|
||||
0.356162529063 2.29614015658 9.5 -0.46820788432 -1.22130883441 ...
|
||||
0.368308864363 -0.539083504685 8 -0.781333991956 0.374007246518 ...
|
||||
-0.145751412732 1.61507621789 8.25 3.68291932628 1.32438399845 ...
|
||||
0.285457283664 2.14334055993 7 1.42819405379 -0.00818660844123 ...
|
||||
0.372390129412 1.60000213334 6.25 0.626106424052 -0.10136772765 ...
|
||||
0.382720203063 1.72614243263 7.25 4.89631941021 -1.10060711916 ...
|
||||
0.737957515573 2.90430582851 6 -0.0422721010314 0.4178952497 ...
|
||||
0.649532581668 0.657135682543 6 0.692066153971 0.422299120276 ...
|
||||
0.627159201987 1.70352689913 5.75 2.62066711305 -1.29237304034 ...
|
||||
0.905441299817 1.95663197267 5.5 1.5949697565 -0.27115830703 ...
|
||||
1.49322577898 -2.08741765309 6.25 1.23027694802 0.418336889527 ...
|
||||
1.48750731567 -1.57274121871 8 3.01660550994 -0.893958254365 ...
|
||||
1.39783858087 2.22623066426 7 -0.80842319214 1.47625453886 ...
|
||||
0.89274836317 1.30378081742 8 -0.249485058661 0.159871204185 ...
|
||||
0.920652246088 4.1437741965 9.75 2.8204453623 0.178149239655 ...
|
||||
-0.00264276644799 3.07989972052 8.75 -2.56342461535 2.105998353 ...
|
||||
0.0198190461681 0.766283759256 8 -1.15838865989 1.56888883418 ...
|
||||
0.440050515311 0.127570085801 7.5 0.0400753569995 0.028914333532 ...
|
||||
0.129536637901 1.78174141526 6.75 0.959943962785 0.307781224401 ...
|
||||
0.398549827172 3.03606770667 6.5 -0.340209794742 0.100979469478 ...
|
||||
1.17174775425 0.629625188037 5.75 0.403003686814 0.902394579377 ...
|
||||
0.991163981251 2.50862910684 4.75 -1.44963996982 1.16150986945 ...
|
||||
0.967603566096 2.12003739013 4.75 0.610846030775 -0.889994896068 ...
|
||||
1.14689383604 1.24185011459 4.75 2.01098091308 -1.73846431001 ...
|
||||
1.32593824054 0.990713820685 4.75 -0.0955142989332 -0.0369257308362 ...
|
||||
0.861135002644 -0.24744943605 6 1.72793107135 -0.691506789639 ...
|
||||
1.26870850151 2.09844764887 6.5 1.50720217572 -1.31399187077 ...
|
||||
0.260364987715 1.10650139716 6.5 1.13659047496 0.0720441664643 ...
|
||||
1.09731242214 0.490796381346 7.25 4.59123894147 -2.14073070763 ...
|
||||
1.63792841781 0.612652594286 6.75 1.79604605035 -0.644363995357 ...
|
||||
1.48465576034 0.978295808687 6.75 -2.00753620902 1.39437534964 ...
|
||||
1.0987608663 4.25212569087 6.25 -2.58901196498 2.56054320803 ...
|
||||
1.42592178132 2.76984518311 6.25 0.888195752358 1.03114549274 ...
|
||||
1.52958239462 1.31795955491 6.5 -0.902907564082 -0.0952198893776 ...
|
||||
1.0170168994 2.14733589918 7 -1.3054866978 2.68803738466 ...
|
||||
0.723253652257 3.43552889347 7.5 1.8213700853 0.592593586195 ...
|
||||
1.24720806008 3.87383806577 7.5 0.0522300654168 0.988871238698 ...
|
||||
0.482531471239 2.67793287032 7.5 2.9693944293 -0.108591166081 ...
|
||||
0.154056100439 0.927269031704 6.75 0.119222057561 3.30489209451 ...
|
||||
0.0694865769274 6.65916526788 6.25 0.889014476084 -2.83976849035 ...
|
||||
-0.121267434867 0.341442615696 5.25 0.323053239216 -3.49289229012 ...
|
||||
0.726473690375 -3.5423730964 4 2.19149290449 -3.20855054004 ...
|
||||
1.39271709108 2.63121085718 3.75 0.88406577736 0.75622580197 ...
|
||||
1.07502077727 5.88578836799 4.25 -2.55088273352 2.89018116374 ...
|
||||
0.759049251607 4.24703604223 4.5 0.575687665685 -0.388292506167 ...
|
||||
];
|
||||
|
||||
data = reshape(data,5,86)';
|
||||
y_obs = data(:,1);
|
||||
pie_obs = data(:,2);
|
||||
R_obs = data(:,3);
|
||||
de = data(:,4);
|
||||
dq = data(:,5);
|
||||
|
||||
%Country: Canada
|
||||
%Sample Range: 1981:2 to 2002:3
|
||||
%Observations: 86
|
||||
%Variables: Real GDP Growth [%], Inflation [annualized %], Nom Rate [%],
|
||||
% Exchange Rate Change [%], Terms of Trade Change [%]
|
||||
|
|
|
|||
|
|
@ -1,27 +1,27 @@
|
|||
@#define N = 4
|
||||
var A B;
|
||||
varexo eB;
|
||||
parameters Bss rho;
|
||||
|
||||
Bss=1;
|
||||
rho=0.9;
|
||||
|
||||
model;
|
||||
A = B(@{N});
|
||||
B = (1-rho)*Bss +rho*B(-1) +eB;
|
||||
end;
|
||||
|
||||
steady_state_model;
|
||||
A = Bss;
|
||||
B = Bss;
|
||||
end;
|
||||
|
||||
resid;
|
||||
steady;
|
||||
check;
|
||||
|
||||
shocks;
|
||||
var eB ; stderr 1 ;
|
||||
end;
|
||||
|
||||
stoch_simul(order=1,irf=0) ;
|
||||
@#define N = 4
|
||||
var A B;
|
||||
varexo eB;
|
||||
parameters Bss rho;
|
||||
|
||||
Bss=1;
|
||||
rho=0.9;
|
||||
|
||||
model;
|
||||
A = B(@{N});
|
||||
B = (1-rho)*Bss +rho*B(-1) +eB;
|
||||
end;
|
||||
|
||||
steady_state_model;
|
||||
A = Bss;
|
||||
B = Bss;
|
||||
end;
|
||||
|
||||
resid;
|
||||
steady;
|
||||
check;
|
||||
|
||||
shocks;
|
||||
var eB ; stderr 1 ;
|
||||
end;
|
||||
|
||||
stoch_simul(order=1,irf=0) ;
|
||||
|
|
|
|||
|
|
@ -1,68 +1,68 @@
|
|||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
change_type(var) Psi;
|
||||
change_type(parameters) n;
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
//Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model;
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
n=log(1/3);
|
||||
|
||||
initval;
|
||||
y = 0.2;
|
||||
c = 0.03;
|
||||
k = 2.7;
|
||||
m = 0.3;
|
||||
Psi = 1.5;
|
||||
R = 0.01;
|
||||
pi = 0.01;
|
||||
z = 0;
|
||||
u = 0;
|
||||
end;
|
||||
|
||||
|
||||
steady;
|
||||
|
||||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
change_type(var) Psi;
|
||||
change_type(parameters) n;
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
//Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model;
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
n=log(1/3);
|
||||
|
||||
initval;
|
||||
y = 0.2;
|
||||
c = 0.03;
|
||||
k = 2.7;
|
||||
m = 0.3;
|
||||
Psi = 1.5;
|
||||
R = 0.01;
|
||||
pi = 0.01;
|
||||
z = 0;
|
||||
u = 0;
|
||||
end;
|
||||
|
||||
|
||||
steady;
|
||||
|
||||
|
|
|
|||
|
|
@ -1,51 +1,51 @@
|
|||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model;
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
|
||||
steady;
|
||||
|
||||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model;
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
|
||||
steady;
|
||||
|
||||
|
|
|
|||
|
|
@ -1,72 +1,72 @@
|
|||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model;
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
steady_state_model;
|
||||
// solving in levels
|
||||
// calibrating n = 1/3 and recovering the value of Psi
|
||||
// adapting solution Walsh (2003) p. 84
|
||||
pi = thetass-1;
|
||||
en = 1/3;
|
||||
eR = 1/beta;
|
||||
y_k = (1/alpha)*(1/beta-1+delta);
|
||||
ek = en*y_k^(-1/(1-alpha));
|
||||
ec = ek*(y_k-delta);
|
||||
em = ec*(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^(-1/b);
|
||||
ey = ek*y_k;
|
||||
Xss = a*ec^(1-b)*(1+(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^((b-1)/b));
|
||||
Psi = (1-alpha)*(ey/en)*Xss^((b-phi1)/(1-b))*a*ec^(-b)*(1-en)^eta;
|
||||
n = log(en);
|
||||
k = log(ek);
|
||||
m = log(em);
|
||||
c = log(ec);
|
||||
y = log(ey);
|
||||
R = log(eR);
|
||||
end;
|
||||
|
||||
steady;
|
||||
|
||||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model;
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
steady_state_model;
|
||||
// solving in levels
|
||||
// calibrating n = 1/3 and recovering the value of Psi
|
||||
// adapting solution Walsh (2003) p. 84
|
||||
pi = thetass-1;
|
||||
en = 1/3;
|
||||
eR = 1/beta;
|
||||
y_k = (1/alpha)*(1/beta-1+delta);
|
||||
ek = en*y_k^(-1/(1-alpha));
|
||||
ec = ek*(y_k-delta);
|
||||
em = ec*(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^(-1/b);
|
||||
ey = ek*y_k;
|
||||
Xss = a*ec^(1-b)*(1+(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^((b-1)/b));
|
||||
Psi = (1-alpha)*(ey/en)*Xss^((b-phi1)/(1-b))*a*ec^(-b)*(1-en)^eta;
|
||||
n = log(en);
|
||||
k = log(ek);
|
||||
m = log(em);
|
||||
c = log(ec);
|
||||
y = log(ey);
|
||||
R = log(eR);
|
||||
end;
|
||||
|
||||
steady;
|
||||
|
||||
|
|
|
|||
|
|
@ -1,72 +1,72 @@
|
|||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model(block);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
steady_state_model;
|
||||
// solving in levels
|
||||
// calibrating n = 1/3 and recovering the value of Psi
|
||||
// adapting solution Walsh (2003) p. 84
|
||||
pi = thetass-1;
|
||||
en = 1/3;
|
||||
eR = 1/beta;
|
||||
y_k = (1/alpha)*(1/beta-1+delta);
|
||||
ek = en*y_k^(-1/(1-alpha));
|
||||
ec = ek*(y_k-delta);
|
||||
em = ec*(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^(-1/b);
|
||||
ey = ek*y_k;
|
||||
Xss = a*ec^(1-b)*(1+(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^((b-1)/b));
|
||||
Psi = (1-alpha)*(ey/en)*Xss^((b-phi1)/(1-b))*a*ec^(-b)*(1-en)^eta;
|
||||
n = log(en);
|
||||
k = log(ek);
|
||||
m = log(em);
|
||||
c = log(ec);
|
||||
y = log(ey);
|
||||
R = log(eR);
|
||||
end;
|
||||
|
||||
steady;
|
||||
|
||||
var y c k m n R pi z u;
|
||||
varexo e sigma;
|
||||
// sigma stands for phi in the eq 2.37 p.69
|
||||
|
||||
parameters alpha beta delta gamm phi1 eta a b rho phi2 Psi thetass;
|
||||
//phi1 stands for capital phi in eq.2.68 and 2.69
|
||||
//phi2 stands for lowercase phi in eq. 2.66
|
||||
|
||||
alpha = 0.36;
|
||||
beta = 0.989;
|
||||
gamm = 0.5;
|
||||
delta = 0.019;
|
||||
phi1 = 2;
|
||||
phi2 = 0;
|
||||
eta = 1;
|
||||
a = 0.95;
|
||||
b = 2.56;
|
||||
rho = 0.95;
|
||||
Psi = 1.47630583;
|
||||
thetass = 1.0125;
|
||||
|
||||
model(block);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = (a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*(1-a)*exp(m)^(-b)+beta*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b)/(1+pi(+1));
|
||||
|
||||
Psi*(1-exp(n))^(-eta)/(a*exp(c)^(-b)*(a*exp(c)^(1-b) + (1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))) = (1-alpha)*exp(y)/exp(n);
|
||||
|
||||
(a*exp(c)^(1-b)+(1-a)*exp(m)^(1-b))^((b-phi1)/(1-b))*a*exp(c)^(-b) = beta*exp(R(+1))*(a*exp(c(+1))^(1-b)+(1-a)*exp(m(+1))^(1-b))^((b-phi1)/(1-b))*a*exp(c(+1))^(-b);
|
||||
|
||||
exp(R) = alpha*exp(y)/exp(k(-1)) + 1-delta;
|
||||
|
||||
exp(k) = (1-delta)*exp(k(-1))+exp(y)-exp(c);
|
||||
|
||||
exp(y) = exp(z)*exp(k(-1))^alpha*exp(n)^(1-alpha);
|
||||
|
||||
exp(m) = exp(m(-1))*(u+thetass)/(1+pi);
|
||||
|
||||
z = rho*z(-1) + e;
|
||||
|
||||
u = gamm*u(-1) + phi2*z(-1) + sigma;
|
||||
|
||||
end;
|
||||
|
||||
shocks;
|
||||
var e; stderr 0.007;
|
||||
var sigma;stderr 0.0089;
|
||||
end;
|
||||
|
||||
steady_state_model;
|
||||
// solving in levels
|
||||
// calibrating n = 1/3 and recovering the value of Psi
|
||||
// adapting solution Walsh (2003) p. 84
|
||||
pi = thetass-1;
|
||||
en = 1/3;
|
||||
eR = 1/beta;
|
||||
y_k = (1/alpha)*(1/beta-1+delta);
|
||||
ek = en*y_k^(-1/(1-alpha));
|
||||
ec = ek*(y_k-delta);
|
||||
em = ec*(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^(-1/b);
|
||||
ey = ek*y_k;
|
||||
Xss = a*ec^(1-b)*(1+(a/(1-a))^(-1/b)*((thetass-beta)/thetass)^((b-1)/b));
|
||||
Psi = (1-alpha)*(ey/en)*Xss^((b-phi1)/(1-b))*a*ec^(-b)*(1-en)^eta;
|
||||
n = log(en);
|
||||
k = log(ek);
|
||||
m = log(em);
|
||||
c = log(ec);
|
||||
y = log(ey);
|
||||
R = log(eR);
|
||||
end;
|
||||
|
||||
steady;
|
||||
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
function test(a,b,n)
|
||||
if max(max(abs(a)-abs(b))) > 1e-5
|
||||
error(['Test error in test ' int2str(n)])
|
||||
function test(a,b,n)
|
||||
if max(max(abs(a)-abs(b))) > 1e-5
|
||||
error(['Test error in test ' int2str(n)])
|
||||
end
|
||||
Loading…
Reference in New Issue