527 lines
16 KiB
PHP
527 lines
16 KiB
PHP
% DSGE model based on replication files of
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% Andreasen, Fernandez-Villaverde, Rubio-Ramirez (2018), The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications, Review of Economic Studies, 85, p. 1-49
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% Original code by Martin M. Andreasen, Jan 2016
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% Adapted for Dynare by Willi Mutschler (@wmutschl, willi@mutschler.eu), Jan 2021
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% =========================================================================
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% Copyright © 2021 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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%--------------------------------------------------------------------------
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% Variable declaration
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%--------------------------------------------------------------------------
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var
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ln_k
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ln_s
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ln_a
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ln_g
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ln_d
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ln_c
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ln_r
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ln_pai
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ln_h
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ln_q
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ln_evf
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ln_iv
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ln_x2
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ln_la
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ln_goy
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ln_Esdf
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xhr20
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xhr40
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Exhr
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@#for i in 1:40
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ln_p@{i}
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@#endfor
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Obs_Gr_C
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Obs_Gr_I
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Obs_Infl
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Obs_r1
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Obs_r40
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Obs_xhr40
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Obs_GoY
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Obs_hours
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;
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predetermined_variables ln_k ln_s;
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varobs Obs_Gr_C Obs_Gr_I Obs_Infl Obs_r1 Obs_r40 Obs_xhr40 Obs_GoY Obs_hours;
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%--------------------------------------------------------------------------
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% Exogenous shocks
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%--------------------------------------------------------------------------
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varexo
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eps_a
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eps_d
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eps_g
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;
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%--------------------------------------------------------------------------
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% Parameter declaration
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%--------------------------------------------------------------------------
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parameters
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BETTA
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B
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INHABIT
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H
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PHI1
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PHI2
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RRA
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PHI4
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KAPAone
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KAPAtwo
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DELTA
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THETA
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ETA
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ALFA
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CHI
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RHOR
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BETTAPAI
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BETTAY
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MYYPS
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MYZ
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RHOA
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%STDA
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RHOG
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%STDG
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RHOD
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%STDD
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CONSxhr40
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BETTAxhr
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BETTAxhr40
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CONSxhr20
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PAI
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GAMA
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GoY
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%auxiliary
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PHIzero
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AA
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PHI3
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negVf
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;
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%--------------------------------------------------------------------------
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% Model equations
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%--------------------------------------------------------------------------
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% Based on DSGE_model_NegVf_yieldCurve.m and DSGE_model_PosVf_yieldCurve.m
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% Note that we include an auxiliary parameter negVf to distinguish whether
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% the steady state value function is positive (negVf=0) or negative (negVf=1).
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% This parameter is endogenously determined in the steady_state_model block.
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model;
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%--------------------------------------------------------------------------
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% Auxiliary expressions
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%--------------------------------------------------------------------------
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% do exp transform such that variables are logged variables
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@#for var in [ "k", "s", "c", "r", "a", "g", "d", "pai", "h", "q", "evf", "iv", "x2", "la", "goy", "Esdf" ]
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#@{var}_ba1 = exp(ln_@{var}(-1));
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#@{var}_cu = exp(ln_@{var});
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#@{var}_cup = exp(ln_@{var}(+1));
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@#endfor
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@#for i in 1:40
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#p@{i}_cu = exp(ln_p@{i});
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#p@{i}_cup = exp(ln_p@{i}(+1));
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@#endfor
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% these variables are not transformed
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#xhr20_cu = xhr20;
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#xhr20_cup = xhr20(+1);
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#xhr40_cu = xhr40;
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#xhr40_cup = xhr40(+1);
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#Exhr_cu = Exhr;
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#Exhr_cup = Exhr(+1);
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% auxiliary steady state variables
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#K = exp(steady_state(ln_k));
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#IV = exp(steady_state(ln_iv));
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#C = exp(steady_state(ln_c));
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#Y = (C + IV)/(1-GoY);
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#R = exp(steady_state(ln_r));
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#G = Y-C-IV;
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#removeMeanXhr = 1;
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% The atemporal relations if possible
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% No stochastic trend in investment specific shocks
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#myyps_cu = MYYPS;
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#myyps_cup = MYYPS;
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% No stochastic trend in non-stationary technology shocks
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#myz_cu = MYZ;
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#myz_cup = MYZ;
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% Defining myzstar
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#MYZSTAR = MYYPS^(THETA/(1-THETA))*MYZ;
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#myzstar_cu = myyps_cu ^(THETA/(1-THETA))*myz_cu;
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#myzstar_cup= myyps_cup^(THETA/(1-THETA))*myz_cup;
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% The expression for the value function (only valid for deterministic trends!)
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% Note that we make use of auxiliary parameter negVf to switch signs
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#mvf_cup = -negVf*(d_cup/(1-PHI2)*((c_cup-B*c_cu*MYZSTAR^-1)^(1-PHI2)-1) + d_cup*PHIzero/(1-PHI1)*(1-h_cup)^(1-PHI1) - negVf* BETTA*MYZSTAR^((1-PHI4)*(1-PHI2))*AA*evf_cup^(1/(1-PHI3)));
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% The growth rate in lambda
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#myla_cup = (la_cup/la_cu)*(AA*evf_cu^(1/(1-PHI3))/mvf_cup)^PHI3*myzstar_cup^(-PHI2*(1-PHI4)-PHI4);
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% The relation between the optimal price for the firms and the pris and inflation
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%ptil_cu = ((1-ALFA*(pai_ba1^CHI/pai_cu )^(1-ETA))/(1-ALFA))^(1/(1-ETA));
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%ptil_cup = ((1-ALFA*(pai_cu ^CHI/pai_cup)^(1-ETA))/(1-ALFA))^(1/(1-ETA));
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#ptil_cu = ((1-ALFA*(1/pai_cu )^(1-ETA))/(1-ALFA))^(1/(1-ETA));
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#ptil_cup = ((1-ALFA*(1/pai_cup)^(1-ETA))/(1-ALFA))^(1/(1-ETA));
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% From the households' FOC for labor
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#w_cu = d_cu*PHIzero*(1-h_cu )^(-PHI1)/la_cu;
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#w_cup = d_cu*PHIzero*(1-h_cup)^(-PHI1)/la_cup;
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% Shouldn't w_cup include d_cup? Let's stick to the original (wrong) code in the replication files as results don't change dramatically... [@wmutschl]
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% The firms' FOC for labor
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#mc_cu = w_cu /((1-THETA)*a_cu *myyps_cu ^(-THETA/(1-THETA))*myz_cu ^-THETA *k_cu ^THETA*h_cu ^(-THETA));
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#mc_cup = w_cup/((1-THETA)*a_cup*myyps_cup^(-THETA/(1-THETA))*myz_cup^-THETA *k_cup^THETA*h_cup^(-THETA));
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% The firms' FOC for capital
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#rk_cu = mc_cu *THETA* a_cu *myyps_cu *myz_cu ^(1-THETA)*k_cu ^(THETA-1)*h_cu ^(1-THETA);
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#rk_cup = mc_cup*THETA* a_cup*myyps_cup*myz_cup^(1-THETA)*k_cup^(THETA-1)*h_cup^(1-THETA);
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% The income identity
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#y_cu = c_cu + iv_cu + g_cu;
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%--------------------------------------------------------------------------
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% Actual model equations
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%--------------------------------------------------------------------------
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[name='Expected value of the value function']
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0 = -evf_cu + (mvf_cup/AA)^(1-PHI3);
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[name='Households FOC for capital']
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0 = -q_cu+BETTA*myla_cup/myyps_cup*(rk_cup+q_cup*(1-DELTA) -q_cup*KAPAtwo/2*(iv_cup/k_cup*myyps_cup*myzstar_cup - IV/K*MYYPS*MYZSTAR)^2 +q_cup*KAPAtwo*(iv_cup/k_cup*myyps_cup*myzstar_cup - IV/K*MYYPS*MYZSTAR)*iv_cup/k_cup*myyps_cup*myzstar_cup);
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[name='Households FOC for investments']
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0 = -1+q_cu*(1-KAPAone/2*(iv_cu/IV-1)^2-iv_cu/IV*KAPAone*(iv_cu/IV-1)-KAPAtwo*(iv_cu/k_cu*myyps_cu*myzstar_cu - IV/K*MYYPS*MYZSTAR));
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[name='Euler equation for consumption']
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0 = -1+BETTA*r_cu*exp(CONSxhr40*xhr40_cu + CONSxhr20*xhr20_cu)*myla_cup/pai_cup;
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[name='Households FOC for consumption']
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0 = -la_cu + d_cu*(c_cu -B*c_ba1*myzstar_cu^-1)^(-PHI2) -INHABIT*B*BETTA*d_cup*(AA*evf_cu^(1/(1-PHI3))/mvf_cup)^PHI3*(c_cup -B*c_cu*myzstar_cup^-1)^(-PHI2)*myzstar_cup^(-PHI2*(1-PHI4)-PHI4);
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[name='Nonlinear pricing, relation for x1 = (ETA-1)/ETA*x2']
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0= -(ETA-1)/ETA*x2_cu+y_cu*mc_cu*ptil_cu^(-ETA-1) +ALFA*BETTA*myla_cup*(ptil_cu/ptil_cup)^(-ETA-1)*(1/pai_cup)^(-ETA)*(ETA-1)/ETA*x2_cup*myzstar_cup;
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[name='Nonlinear pricing, relation for x2']
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0=-x2_cu+y_cu*ptil_cu^-ETA +ALFA*BETTA*myla_cup*(ptil_cu/ptil_cup)^(-ETA)*(1/pai_cup)^(1-ETA)*x2_cup*myzstar_cup;
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[name='Nonlinear pricing, relation for s']
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0= -s_cup+(1-ALFA)*ptil_cu^(-ETA)+ALFA*(pai_cu/1)^ETA*s_cu;
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[name='Interest rate rule']
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0 = -log(r_cu/R)+RHOR*log(r_ba1/R)+(1-RHOR)*(BETTAPAI*log(pai_cu/PAI)+BETTAY*log(y_cu/Y) + BETTAxhr*(BETTAxhr40*xhr40_cu - removeMeanXhr*Exhr_cu));
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[name='Production function']
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0 = -y_cu*s_cup + a_cu *(k_cu *myyps_cu ^(-1/(1-THETA))*myz_cu ^-1)^THETA*h_cu ^(1-THETA);
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[name='Relation for physical capital stock']
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0= -k_cup + (1-DELTA)*k_cu*(myyps_cu*myzstar_cu)^-1 + iv_cu - iv_cu*KAPAone/2*(iv_cu/IV-1)^2 - k_cu*(myyps_cu*myzstar_cu)^-1*KAPAtwo/2*(iv_cu/k_cu*myyps_cu*myzstar_cu - IV/K*MYYPS*MYZSTAR)^2;
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[name='Goverment spending over output']
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0=-goy_cu + g_cu/y_cu;
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[name='The yield curve: p1']
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0= -p1_cu + 1/r_cu;
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@#for i in 2:40
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[name='The yield curve: p@{i}']
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0= -p@{i}_cu + BETTA*myla_cup/pai_cup*p@{i-1}_cup;
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@#endfor
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[name='Stochastic discount factor']
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0= -Esdf_cu+ BETTA*myla_cup/pai_cup;
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[name='Expected 5 year excess holding period return']
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0= -xhr20_cu+ log(p19_cup) - log(p20_cu) - log(r_cu);
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[name='Expected 10 year excess holding period return']
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0= -xhr40_cu+ log(p39_cup) - log(p40_cu) - log(r_cu);
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[name='Mean of expected excess holding period return in Taylor rule']
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0= -Exhr_cu + (1-GAMA)*(BETTAxhr40*xhr40_cu) + GAMA*Exhr_cup;
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[name='Exogenous process for productivity']
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0 = -log(a_cu)+RHOA*log(a_ba1) + eps_a;
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[name='Exogenous process for government spending']
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0 = -log(g_cu/G)+RHOG*log(g_ba1/G) + eps_g;
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[name='Exogenous process for discount factor shifter']
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0 = -log(d_cu)+RHOD*log(d_ba1) + eps_d;
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[name='Observable annualized consumption growth']
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Obs_Gr_C = 4*( ln_c -ln_c(-1) + log(MYZSTAR));
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[name='Observable annualized investment growth']
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Obs_Gr_I = 4*( ln_iv - ln_iv(-1) + log(MYZSTAR)+log(MYYPS));
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[name='Observable annualized inflation']
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Obs_Infl = 4*( ln_pai);
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[name='Observable annualized one-quarter nominal yield']
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Obs_r1 = 4*( ln_r);
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[name='Observable annualized 10-year nominal yield']
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Obs_r40 = 4*( -1/40*ln_p40);
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[name='Observable annualized 10-year ex post excess holding period return']
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Obs_xhr40 = 4*( ln_p39 - ln_p40(-1) - ln_r(-1) );
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[name='Observable annualized log ratio of government spending to GDP']
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Obs_GoY = 4*( 1/4*ln_goy);
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[name='Observable annualized log of hours']
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Obs_hours = 4*( 1/100*ln_h);
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end;
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%--------------------------------------------------------------------------
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% Steady State Computations
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%--------------------------------------------------------------------------
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% Based on DSGE_model_yieldCurve_ss.m, getPHI3.m, ObjectGMM.m
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% Note that we include an auxiliary parameter negVf to distinguish whether
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% the steady state value function is positive (negVf=0) or negative (negVf=1).
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% This parameter is endogenously determined in the steady_state_model block.
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steady_state_model;
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% The growth rate in the firms' fixed costs
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MYZSTARBAR = MYYPS^(THETA/(1-THETA))*MYZ;
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% The growth rate for lampda
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MYLABAR = MYZSTARBAR^(-PHI2*(1-PHI4)-PHI4);
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% The relative optimal price for firms
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PTILBAR = ((1-ALFA*PAI^((CHI-1)*(1-ETA)))/(1-ALFA))^(1/(1-ETA));
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% The state variable s for distortions between output and produktion
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SBAR = ((1-ALFA)*PTILBAR^(-ETA))/(1-ALFA*PAI^((1-CHI)*ETA));
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% The 1-period interest rate
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RBAR = PAI/(BETTA*MYLABAR);
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% The market price of capital
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QBAR = 1;
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% The real price of renting capital
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RKBAR = QBAR*(MYYPS/(BETTA*MYLABAR)-(1-DELTA));
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% The marginal costs in the firms
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MCBAR = (1-ALFA*BETTA*MYLABAR*PAI^((1-CHI)*ETA)*MYZSTARBAR)*(ETA-1)/ETA*PTILBAR/(1-ALFA*BETTA*MYLABAR*PAI^((CHI-1)*(1-ETA))*MYZSTARBAR);
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% The capital stock
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KBAR = H*(RKBAR/(MCBAR*THETA*MYYPS*MYZ^(1-THETA)))^(1/(THETA-1));
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% The wage level
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WBAR = MCBAR*(1-THETA)*MYYPS^(-THETA/(1-THETA))*MYZ^-THETA*(KBAR/H)^THETA;
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% The level of investment
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IVBAR = KBAR - (1-DELTA)*KBAR*MYYPS^(-1/(1-THETA))*MYZ^-1;
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% The consumption level
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CBAR = ((1-GoY)*(KBAR*MYYPS^(-1/(1-THETA))*MYZ^-1)^THETA*H^(1-THETA))/SBAR-IVBAR;
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% The output level
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YBAR = (CBAR + IVBAR)/(1-GoY);
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% The value of lambda
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LABAR = (CBAR-B*CBAR*MYZSTARBAR^-1)^-PHI2 - INHABIT*B*BETTA*(CBAR-B*CBAR*MYZSTARBAR^-1)^-PHI2*MYZSTARBAR^(-PHI2*(1-PHI4)-PHI4);
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% The value of PHIzero
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PHIzero = LABAR*WBAR*(1-H)^PHI1;
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% The level of the value function
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VFBAR = 1/(1-BETTA*MYZSTARBAR^((1-PHI4)*(1-PHI2)))*(1/(1-PHI2)*((CBAR-B*CBAR*MYZSTARBAR^-1)^(1-PHI2)-1)+PHIzero/(1-PHI1)*(1-H)^(1-PHI1));
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UBAR = 1/(1-PHI2)*((CBAR-B*CBAR*MYZSTARBAR^-1)^(1-PHI2)-1)+PHIzero/(1-PHI1)*(1-H)^(1-PHI1);
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[AA, EVFBAR, PHI3, negVf, info]= AFVRR_steady_helper(VFBAR,RBAR,IVBAR,CBAR,KBAR,LABAR,QBAR,YBAR, BETTA,B,PAI,H,PHIzero,PHI1,PHI2,THETA,MYYPS,MYZ,INHABIT,RRA,CONSxhr40);
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% The value of X2
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X2BAR = YBAR*PTILBAR^(-ETA)/(1-BETTA*ALFA*MYLABAR*PAI^((CHI-1)*(1-ETA))*MYZSTARBAR);
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% Government spending
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GBAR = GoY*YBAR;
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%**************************************************************************
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% map into model variables
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ln_k = log(KBAR);
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ln_s = log(SBAR);
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ln_c_ba1 = log(CBAR);
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ln_r_ba1 = log(RBAR);
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ln_a = log(1);
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ln_g = log(GBAR);
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ln_d = log(1);
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ln_c = log(CBAR);
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ln_r = log(RBAR);
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ln_pai = log(PAI);
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ln_h = log(H);
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ln_q = log(QBAR);
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ln_evf = log(EVFBAR);
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ln_iv = log(IVBAR);
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ln_x2 = log(X2BAR);
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ln_la = log(LABAR);
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ln_goy = log(GoY);
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ln_Esdf = log(1/RBAR);
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xhr20 = 0;
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xhr40 = 0;
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Exhr = 0;
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% The yield curve
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ln_p1 = log((1/RBAR)^1);
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ln_p2 = log((1/RBAR)^2);
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ln_p3 = log((1/RBAR)^3);
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ln_p4 = log((1/RBAR)^4);
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ln_p5 = log((1/RBAR)^5);
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ln_p6 = log((1/RBAR)^6);
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ln_p7 = log((1/RBAR)^7);
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ln_p8 = log((1/RBAR)^8);
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ln_p9 = log((1/RBAR)^9);
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ln_p10 = log((1/RBAR)^10);
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ln_p11 = log((1/RBAR)^11);
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ln_p12 = log((1/RBAR)^12);
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ln_p13 = log((1/RBAR)^13);
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ln_p14 = log((1/RBAR)^14);
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ln_p15 = log((1/RBAR)^15);
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ln_p16 = log((1/RBAR)^16);
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ln_p17 = log((1/RBAR)^17);
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ln_p18 = log((1/RBAR)^18);
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ln_p19 = log((1/RBAR)^19);
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ln_p20 = log((1/RBAR)^20);
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|
ln_p21 = log((1/RBAR)^21);
|
|
ln_p22 = log((1/RBAR)^22);
|
|
ln_p23 = log((1/RBAR)^23);
|
|
ln_p24 = log((1/RBAR)^24);
|
|
ln_p25 = log((1/RBAR)^25);
|
|
ln_p26 = log((1/RBAR)^26);
|
|
ln_p27 = log((1/RBAR)^27);
|
|
ln_p28 = log((1/RBAR)^28);
|
|
ln_p29 = log((1/RBAR)^29);
|
|
ln_p30 = log((1/RBAR)^30);
|
|
ln_p31 = log((1/RBAR)^31);
|
|
ln_p32 = log((1/RBAR)^32);
|
|
ln_p33 = log((1/RBAR)^33);
|
|
ln_p34 = log((1/RBAR)^34);
|
|
ln_p35 = log((1/RBAR)^35);
|
|
ln_p36 = log((1/RBAR)^36);
|
|
ln_p37 = log((1/RBAR)^37);
|
|
ln_p38 = log((1/RBAR)^38);
|
|
ln_p39 = log((1/RBAR)^39);
|
|
ln_p40 = log((1/RBAR)^40);
|
|
|
|
Obs_Gr_C = 4*( log(MYZSTARBAR) );
|
|
Obs_Gr_I = 4*( log(MYZSTARBAR)+log(MYYPS) );
|
|
Obs_Infl = 4*( ln_pai );
|
|
Obs_r1 = 4*( ln_r );
|
|
Obs_r40 = 4*( -1/40*ln_p40 );
|
|
Obs_xhr40 = 4*( xhr40 );
|
|
Obs_GoY = 4*( 1/4*ln_goy );
|
|
Obs_hours = 4*( 1/100*ln_h );
|
|
end;
|
|
|
|
%--------------------------------------------------------------------------
|
|
% Declare moments to use in estimation
|
|
%--------------------------------------------------------------------------
|
|
% These are the moments used in the paper; corresponds to momentSet=2 in the replication files
|
|
|
|
matched_moments;
|
|
%first moments: all
|
|
Obs_Gr_C;
|
|
Obs_Gr_I;
|
|
Obs_Infl;
|
|
Obs_r1;
|
|
Obs_r40;
|
|
Obs_xhr40;
|
|
Obs_GoY;
|
|
Obs_hours;
|
|
|
|
%second moments
|
|
% (i) all variances, (2) all covariances excluding GoY and hours, (3) own first autocovariances
|
|
Obs_Gr_C*Obs_Gr_C;
|
|
Obs_Gr_C*Obs_Gr_I;
|
|
Obs_Gr_C*Obs_Infl;
|
|
Obs_Gr_C*Obs_r1;
|
|
Obs_Gr_C*Obs_r40;
|
|
Obs_Gr_C*Obs_xhr40;
|
|
|
|
Obs_Gr_I*Obs_Gr_I;
|
|
Obs_Gr_I*Obs_Infl;
|
|
Obs_Gr_I*Obs_r1;
|
|
Obs_Gr_I*Obs_r40;
|
|
Obs_Gr_I*Obs_xhr40;
|
|
|
|
Obs_Infl*Obs_Infl;
|
|
Obs_Infl*Obs_r1;
|
|
Obs_Infl*Obs_r40;
|
|
Obs_Infl*Obs_xhr40;
|
|
|
|
Obs_r1*Obs_r1;
|
|
Obs_r1*Obs_r40;
|
|
Obs_r1*Obs_xhr40;
|
|
|
|
Obs_r40*Obs_r40;
|
|
Obs_r40*Obs_xhr40;
|
|
|
|
Obs_xhr40*Obs_xhr40;
|
|
|
|
Obs_GoY*Obs_GoY;
|
|
|
|
Obs_hours*Obs_hours;
|
|
|
|
Obs_Gr_C*Obs_Gr_C(-1);
|
|
Obs_Gr_I*Obs_Gr_I(-1);
|
|
Obs_Infl*Obs_Infl(-1);
|
|
Obs_r1*Obs_r1(-1);
|
|
Obs_r40*Obs_r40(-1);
|
|
Obs_xhr40*Obs_xhr40(-1);
|
|
Obs_GoY*Obs_GoY(-1);
|
|
Obs_hours*Obs_hours(-1);
|
|
end;
|
|
|
|
|
|
%--------------------------------------------------------------------------
|
|
% Create Data
|
|
%--------------------------------------------------------------------------
|
|
@#ifdef CreateData
|
|
verbatim;
|
|
% From 1961Q3 to 2007Q4
|
|
DataUS = xlsread('Data_PruningPaper_v5.xlsx','Data_used','E3:M188');
|
|
% ANNUALIZED (except for hours and GoY)
|
|
% 1 2 3 4 5 6 7 8 9
|
|
% Lables: Date Gr_C Gr_I GoY hours Infl_C r1 r40 xhr40
|
|
%label_data = {'Gr_C ', 'Gr_I ','Infl ', 'r1 ', 'r40 ', 'xhr40 ','GoY ', 'hours '};
|
|
%DataUS = [DataUS(:,2:3) DataUS(:,6:8) DataUS(:,9) log(DataUS(:,4)) 4*log(DataUS(:,5))/100];
|
|
Obs_Gr_C = DataUS(:,2);
|
|
Obs_Gr_I = DataUS(:,3);
|
|
Obs_Infl = DataUS(:,6);
|
|
Obs_r1 = DataUS(:,7);
|
|
Obs_r40 = DataUS(:,8);
|
|
Obs_xhr40 = DataUS(:,9);
|
|
Obs_GoY = log(DataUS(:,4));
|
|
Obs_hours = 4*log(DataUS(:,5))/100;
|
|
|
|
save('AFVRR_data.mat','Obs_Gr_C','Obs_Gr_I','Obs_Infl','Obs_r1','Obs_r40','Obs_xhr40','Obs_GoY','Obs_hours');
|
|
pause(1);
|
|
end;
|
|
@#endif
|