169 lines
5.9 KiB
Modula-2
169 lines
5.9 KiB
Modula-2
/*
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* This file replicates the estimation of the cash in advance model (termed M1
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* in the paper) described in Frank Schorfheide (2000): "Loss function-based
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* evaluation of DSGE models", Journal of Applied Econometrics, 15(6), 645-670.
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*
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* The data are taken from the replication package at
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* http://dx.doi.org/10.15456/jae.2022314.0708799949
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*
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* The prior distribution follows the one originally specified in Schorfheide's
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* paper. Note that the elicited beta prior for rho in the paper
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* implies an asymptote and corresponding prior mode at 0. It is generally
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* recommended to avoid this extreme type of prior.
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*
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* Because the data are already logged and we use the loglinear option to conduct
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* a full log-linearization, we need to use the logdata option.
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*
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* The equations are taken from J. Nason and T. Cogley (1994): "Testing the
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* implications of long-run neutrality for monetary business cycle models",
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* Journal of Applied Econometrics, 9, S37-S70, NC in the following.
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* Note that there is an initial minus sign missing in equation (A1), p. S63.
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*
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* This implementation was originally written by Michel Juillard. Please note that the
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* following copyright notice only applies to this Dynare implementation of the
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* model.
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*/
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/*
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* Copyright © 2004-2023 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Dynare is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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*/
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var m ${m}$ (long_name='money growth')
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P ${P}$ (long_name='Price level')
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c ${c}$ (long_name='consumption')
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e ${e}$ (long_name='capital stock')
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W ${W}$ (long_name='Wage rate')
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R ${R}$ (long_name='interest rate')
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k ${k}$ (long_name='capital stock')
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d ${d}$ (long_name='dividends')
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n ${n}$ (long_name='labor')
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l ${l}$ (long_name='loans')
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gy_obs ${\Delta \ln GDP}$ (long_name='detrended capital stock')
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gp_obs ${\Delta \ln P}$ (long_name='detrended capital stock')
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y ${y}$ (long_name='detrended output')
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dA ${\Delta A}$ (long_name='TFP growth')
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;
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varexo e_a ${\epsilon_A}$ (long_name='TFP shock')
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e_m ${\epsilon_M}$ (long_name='Money growth shock')
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;
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parameters alp ${\alpha}$ (long_name='capital share')
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bet ${\beta}$ (long_name='discount factor')
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gam ${\gamma}$ (long_name='long-run TFP growth')
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logmst ${\log(m^*)}$ (long_name='long-run money growth')
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rho ${\rho}$ (long_name='autocorrelation money growth')
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phi ${\phi}$ (long_name='labor weight in consumption')
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del ${\delta}$ (long_name='depreciation rate')
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;
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% roughly picked values to allow simulating the model before estimation
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alp = 0.33;
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bet = 0.99;
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gam = 0.003;
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logmst = log(1.011);
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rho = 0.7;
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phi = 0.787;
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del = 0.02;
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model;
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[name='NC before eq. (1), TFP growth equation']
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dA = exp(gam+e_a);
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[name='NC eq. (2), money growth rate']
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log(m) = (1-rho)*logmst + rho*log(m(-1))+e_m;
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[name='NC eq. (A1), Euler equation']
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-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)))))/(c(+2)*P(+2)*m(+1))=0;
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[name='NC below eq. (A1), firm borrowing constraint']
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W = l/n;
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[name='NC eq. (A2), intratemporal labour market condition']
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-(phi/(1-phi))*(c*P/(1-n))+l/n = 0;
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[name='NC below eq. (A2), credit market clearing']
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R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
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[name='NC eq. (A3), credit market optimality']
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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;
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[name='NC eq. (18), aggregate resource constraint']
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c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
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[name='NC eq. (19), money market condition']
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P*c = m;
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[name='NC eq. (20), credit market equilibrium condition']
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m-1+d = l;
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[name='Definition TFP shock']
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e = exp(e_a);
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[name='Implied by NC eq. (18), production function']
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y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
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[name='Observation equation GDP growth']
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gy_obs = dA*y/y(-1);
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[name='Observation equation price level']
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gp_obs = (P/P(-1))*m(-1)/dA;
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end;
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shocks;
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var e_a; stderr 0.014;
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var e_m; stderr 0.005;
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end;
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steady_state_model;
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dA = exp(gam);
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gst = 1/dA;
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m = exp(logmst);
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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)/m )^(-1);
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nust = phi*m^2/( (1-alp)*(1-phi)*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 = phi*m*n/( (1-phi)*(1-n) );
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c = m/P;
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d = l - m + 1;
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y = k^alp*n^(1-alp)*gst^alp;
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R = m/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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gp_obs = m/dA;
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gy_obs = dA;
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end;
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steady;
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check;
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% Table 1 of Schorfheide (2000)
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estimated_params;
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alp, beta_pdf, 0.356, 0.02;
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bet, beta_pdf, 0.993, 0.002;
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gam, normal_pdf, 0.0085, 0.003;
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logmst, normal_pdf, 0.0002, 0.007;
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rho, beta_pdf, 0.129, 0.223;
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phi, beta_pdf, 0.65, 0.05;
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del, beta_pdf, 0.01, 0.005;
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stderr e_a, inv_gamma_pdf, 0.035449, inf;
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stderr e_m, inv_gamma_pdf, 0.008862, inf;
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end;
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varobs gp_obs gy_obs;
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estimation(order=1, datafile=fs2000_data, loglinear,logdata, mode_compute=4, mh_replic=20000, nodiagnostic, mh_nblocks=2, mh_jscale=0.8, mode_check);
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%uncomment the following lines to generate LaTeX-code of the model equations
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%write_latex_original_model(write_equation_tags);
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%collect_latex_files;
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