229 lines
8.7 KiB
Modula-2
229 lines
8.7 KiB
Modula-2
/*
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* This file implements the baseline New Keynesian model of Jordi Galí (2015): Monetary Policy, Inflation,
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* and the Business Cycle, Princeton University Press, Second Edition, Chapter 3
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*
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* Note that this mod-file implements the non-linear first order conditions and that the IRFs show the log-deviations
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* from steady state.
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*
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* THIS MOD-FILE REQUIRES DYNARE 4.5 OR HIGHER
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*
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* Notes:
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* - in the LOM for the discount rate shock z the shock enters with a minus sign in this mod-file to generate the
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* IRF to a -0.5% shock
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*
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* This implementation was written by Johannes Pfeifer. In case you spot mistakes,
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* email me at jpfeifer@gmx.de
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*
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* Please note that the following copyright notice only applies to this Dynare
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* implementation of the model.
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*/
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/*
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* Copyright (C) 2016-20 Johannes Pfeifer
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* Copyright (C) 2020 Dynare Team
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*
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* This 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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* It 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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* For a copy of the GNU General Public License,
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* see <https://www.gnu.org/licenses/>.
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*/
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var C ${C}$ (long_name='Consumption')
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W_real ${\frac{W}{P}}$ (long_name='Real Wage')
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Pi ${\Pi}$ (long_name='inflation')
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A ${A}$ (long_name='AR(1) technology process')
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N ${N}$ (long_name='Hours worked')
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R ${R^n}$ (long_name='Nominal Interest Rate')
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realinterest ${R^{r}}$ (long_name='Real Interest Rate')
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Y ${Y}$ (long_name='Output')
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Q ${Q}$ (long_name='Bond price')
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Z ${Z}$ (long_name='AR(1) preference shock process')
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S ${S}$ (long_name='Price dispersion')
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Pi_star ${\Pi^*}$ (long_name='Optimal reset price')
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x_aux_1 ${x_1}$ (long_name='aux. var. 1 recursive price setting')
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x_aux_2 ${x_2}$ (long_name='aux. var. 2 recursive price setting')
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MC ${mc}$ (long_name='real marginal costs')
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M_real ${M/P}$ (long_name='real money stock')
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i_ann ${i^{ann}}$ (long_name='annualized nominal interest rate')
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pi_ann ${\pi^{ann}}$ (long_name='annualized inflation rate')
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r_real_ann ${r^{r,ann}}$ (long_name='annualized real interest rate')
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P ${P}$ (long_name='price level')
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log_m_nominal ${log(M)}$ (long_name='log nominal money stock')
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log_y ${log(Y)}$ (long_name='log output')
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log_W_real ${log(W/P)}$ (long_name='log real wage')
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log_N ${log(N)}$ (long_name='log hours')
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log_P ${log(P)}$ (long_name='log price level')
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log_A ${log(A)}$ (long_name='log technology level')
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log_Z ${log(Z)}$ (long_name='log preference shock')
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y_hat
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pi
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;
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varexo eps_a ${\varepsilon_a}$ (long_name='technology shock')
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eps_z ${\varepsilon_z}$ (long_name='preference shock')
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;
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parameters alppha ${\alpha}$ (long_name='capital share')
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betta ${\beta}$ (long_name='discount factor')
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rho_a ${\rho_a}$ (long_name='autocorrelation technology shock')
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rho_z ${\rho_{z}}$ (long_name='autocorrelation monetary demand shock')
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siggma ${\sigma}$ (long_name='inverse EIS')
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varphi ${\varphi}$ (long_name='inverse Frisch elasticity')
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phi_pi ${\phi_{\pi}}$ (long_name='inflation feedback Taylor Rule')
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phi_y ${\phi_{y}}$ (long_name='output feedback Taylor Rule')
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eta ${\eta}$ (long_name='semi-elasticity of money demand')
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epsilon ${\epsilon}$ (long_name='demand elasticity')
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theta ${\theta}$ (long_name='Calvo parameter')
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tau ${\tau}$ (long_name='labor subsidy')
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;
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%----------------------------------------------------------------
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% Parametrization, p. 67 and p. 113-115
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%----------------------------------------------------------------
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siggma = 1;
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varphi=5;
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phi_pi = 1.5;
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phi_y = 0.125;
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theta=3/4;
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rho_z = 0.5;
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rho_a = 0.9;
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betta = 0.99;
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eta =3.77; %footnote 11, p. 115
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alppha=1/4;
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epsilon=9;
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tau=0; //1/epsilon;
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%----------------------------------------------------------------
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% First Order Conditions
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%----------------------------------------------------------------
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model;
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[name='FOC Wages, eq. (2)']
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W_real=C^siggma*N^varphi;
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[name='Euler equation eq. (3)']
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Q=betta*(C(+1)/C)^(-siggma)*(Z(+1)/Z)/Pi(+1);
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[name='Definition nominal interest rate), p. 22 top']
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R=1/Q;
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[name='Aggregate output, above eq. (14)']
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Y=A*(N/S)^(1-alppha);
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[name='Definition Real interest rate']
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R=realinterest*Pi(+1);
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% @#if money_growth_rule==0
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% [name='Monetary Policy Rule, p. 26 bottom/eq. (22)']
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% R=1/betta*Pi^phi_pi*(Y/steady_state(Y))^phi_y;
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% @#endif
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[name='Market Clearing, eq. (15)']
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C=Y;
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[name='Technology Shock, eq. (6)']
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log(A)=rho_a*log(A(-1))+eps_a;
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[name='Preference Shock, p.54']
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log(Z)=rho_z*log(Z(-1))-eps_z;
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[name='Definition marginal cost']
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MC=W_real/((1-alppha)*Y/N*S);
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[name='LOM prices, eq. (7)']
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1=theta*Pi^(epsilon-1)+(1-theta)*(Pi_star)^(1-epsilon);
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[name='LOM price dispersion']
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S=(1-theta)*Pi_star^(-epsilon/(1-alppha))+theta*Pi^(epsilon/(1-alppha))*S(-1);
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[name='FOC price setting']
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Pi_star^(1+epsilon*(alppha/(1-alppha)))=x_aux_1/x_aux_2*(1-tau)*epsilon/(epsilon-1);
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[name='Auxiliary price setting recursion 1']
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x_aux_1=Z*C^(-siggma)*Y*MC+betta*theta*Pi(+1)^(epsilon+alppha*epsilon/(1-alppha))*x_aux_1(+1);
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[name='Auxiliary price setting recursion 2']
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x_aux_2=Z*C^(-siggma)*Y+betta*theta*Pi(+1)^(epsilon-1)*x_aux_2(+1);
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[name='Definition log output']
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log_y = log(Y);
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[name='Definition log real wage']
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log_W_real=log(W_real);
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[name='Definition log hours']
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log_N=log(N);
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[name='Annualized inflation']
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pi_ann=4*log(Pi);
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[name='Annualized nominal interest rate']
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i_ann=4*log(R);
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[name='Annualized real interest rate']
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r_real_ann=4*log(realinterest);
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[name='Real money demand, eq. (4)']
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M_real=Y/R^eta;
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[name='definition nominal money stock']
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log_m_nominal=log(M_real*P);
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[name='Definition price level']
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Pi=P/P(-1);
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[name='Definition log price level']
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log_P=log(P);
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[name='Definition log TFP']
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log_A=log(A);
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[name='Definition log preference']
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log_Z=log(Z);
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[mcp='a']
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y_hat=log(Y)-STEADY_STATE(log(Y));
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pi=log(Pi)-STEADY_STATE(log(Pi));
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end;
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%----------------------------------------------------------------
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% Steady state values
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%---------------------------------------------------------------
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steady_state_model;
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A=1;
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Z=1;
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S=1;
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Pi_star=1;
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P=1;
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MC=(epsilon-1)/epsilon/(1-tau);
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R=1/betta;
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Pi=1;
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Q=1/R;
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realinterest=R;
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N=((1-alppha)*MC)^(1/((1-siggma)*alppha+varphi+siggma));
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C=A*N^(1-alppha);
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W_real=C^siggma*N^varphi;
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Y=C;
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money_growth=0;
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money_growth_ann=0;
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nu=0;
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x_aux_1=C^(-siggma)*Y*MC/(1-betta*theta*Pi^(epsilon/(1-alppha)));
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x_aux_2=C^(-siggma)*Y/(1-betta*theta*Pi^(epsilon-1));
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log_y = log(Y);
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log_W_real=log(W_real);
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log_N=log(N);
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pi_ann=4*log(Pi);
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i_ann=4*log(R);
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r_real_ann=4*log(realinterest);
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M_real=Y/R^eta;
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log_m_nominal=log(M_real*P);
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log_P=log(P);
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log_A=0;
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log_Z=0;
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end;
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%----------------------------------------------------------------
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% define shock variances
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%---------------------------------------------------------------
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shocks;
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var eps_a = 0.5^2; //unit shock to preferences
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end;
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% steady;
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% check;
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% stoch_simul;
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planner_objective 0.5*((siggma+(varphi+alppha)/(1-alppha))*y_hat^2+epsilon/0.0215*pi^2)/100;
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discretionary_policy(order=1,instruments=(R),irf=20,planner_discount=betta, periods=0) y_hat pi_ann log_y log_N log_W_real log_P;
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temp=load(['Gali_2015_chapter_3' filesep 'Output' filesep 'Gali_2015_chapter_3_results.mat']);
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if abs(oo_.planner_objective_value-temp.oo_.planner_objective_value)>1e-6
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warning('Planner objective does not match linear model')
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end
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if max(max(abs([temp.oo_.irfs.y_eps_a; temp.oo_.irfs.w_real_eps_a; temp.oo_.irfs.n_eps_a; temp.oo_.irfs.pi_ann_eps_a]-...
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[oo_.irfs.log_y_eps_a; oo_.irfs.log_W_real_eps_a; oo_.irfs.log_N_eps_a; oo_.irfs.pi_ann_eps_a])))>1e-6
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error('Policy is different')
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end |