150 lines
4.6 KiB
Modula-2
150 lines
4.6 KiB
Modula-2
/*
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* This file implements the baseline New Keynesian model of Jordi Gal<61> (2008): Monetary Policy, Inflation,
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* and the Business Cycle, Princeton University Press, Chapter 5
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*
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* This implementation was written by Johannes Pfeifer.
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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 © 2013-21 Johannes Pfeifer
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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 pi
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y_gap
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r_e
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y_e
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r_nat
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i
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u
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a
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p
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;
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varexo eps_a
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eps_u;
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parameters alppha
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betta
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rho_a
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rho_u
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siggma
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phi
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phi_y
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eta
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epsilon
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theta
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;
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%----------------------------------------------------------------
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% Parametrization, p. 52
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%----------------------------------------------------------------
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siggma = 1;
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phi=1;
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phi_y = .5/4;
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theta=2/3;
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rho_u = 0;
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rho_a = 0.9;
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betta = 0.99;
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eta =4;
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alppha=1/3;
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epsilon=6;
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%----------------------------------------------------------------
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% First Order Conditions
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%----------------------------------------------------------------
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model(linear);
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//Composite parameters
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#Omega=(1-alppha)/(1-alppha+alppha*epsilon); //defined on page 47
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#psi_n_ya=(1+phi)/(siggma*(1-alppha)+phi+alppha); //defined on page 48
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#lambda=(1-theta)*(1-betta*theta)/theta*Omega; //defined on page 47
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#kappa=lambda*(siggma+(phi+alppha)/(1-alppha)); //defined on page 49
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#alpha_x=kappa/epsilon; //defined on page 96
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#phi_pi=(1-rho_u)*kappa*siggma/(alpha_x)+rho_u; //defined on page 101
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r_e=siggma*(y_e(+1)-y_e);
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y_e=psi_n_ya*a;
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pi=betta*pi(+1)+kappa*y_gap + u;
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y_gap=-1/siggma*(i-pi(+1)-r_e)+y_gap(+1);
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//3. Interest Rate Rule eq. (25)
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% i=r_e+phi_pi*pi;
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r_nat=siggma*psi_n_ya*(a(+1)-a);
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u=rho_u*u(-1)+eps_u;
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a=rho_a*a(-1)+eps_a;
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pi=p-p(-1);
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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_u = 1;
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end;
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planner_objective pi^2 +(((1-theta)*(1-betta*theta)/theta*((1-alppha)/(1-alppha+alppha*epsilon)))*(siggma+(phi+alppha)/(1-alppha)))/epsilon*y_gap^2;
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discretionary_policy(instruments=(i),irf=20,planner_discount=betta,discretionary_tol=1e-12) y_gap pi p u;
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verbatim;
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%% Check correctness
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Omega=(1-alppha)/(1-alppha+alppha*epsilon); %defined on page 47
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lambda=(1-theta)*(1-betta*theta)/theta*Omega; %defined on page 47
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kappa=lambda*(siggma+(phi+alppha)/(1-alppha)); %defined on page 49
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alpha_x=kappa/epsilon; %defined on page 96
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Psi=1/(kappa^2+alpha_x*(1-betta*rho_u)); %defined on page 99
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Psi_i=Psi*(kappa*siggma*(1-rho_u)+alpha_x*rho_u); %defined on page 101
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phi_pi=(1-rho_u)*kappa*siggma/(alpha_x)+rho_u; %defined on page 101
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%Compute theoretical solution
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var_pi_theoretical=(alpha_x*Psi)^2; %equation (6), p.99
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var_y_gap_theoretical=(-kappa*Psi)^2; %equation (7), p.99
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pi_pos=strmatch('pi',var_list_,'exact');
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y_gap_pos=strmatch('y_gap',var_list_,'exact');
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if abs(oo_.var(pi_pos,pi_pos)-var_pi_theoretical)>1e-10 || abs(oo_.var(y_gap_pos,y_gap_pos)-var_y_gap_theoretical)>1e-10
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error('Variances under optimal policy are wrong')
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end
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%Compute theoretical objective function
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V=betta/(1-betta)*(var_pi_theoretical+alpha_x*var_y_gap_theoretical); %evaluate at steady state in first period
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if any( [ isnan(oo_.planner_objective_value.conditional.zero_initial_multiplier), abs(V-oo_.planner_objective_value.conditional.zero_initial_multiplier)>1e-10 ] )
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error('Computed welfare deviates from theoretical welfare')
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end
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end;
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%% repeat exercise with initial shock of 1 to check whether planner objective is correctly specified
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initval;
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eps_u = 1;
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end;
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%Compute theoretical objective function
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V=var_pi_theoretical+alpha_x*var_y_gap_theoretical+ betta/(1-betta)*(var_pi_theoretical+alpha_x*var_y_gap_theoretical); %evaluate at steady state in first period
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discretionary_policy(instruments=(i),irf=20,discretionary_tol=1e-12,planner_discount=betta) y_gap pi p u;
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if any( [ isnan(oo_.planner_objective_value.conditional.steady_initial_multiplier), abs(V-oo_.planner_objective_value.conditional.steady_initial_multiplier)>1e-10 ] )
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error('Computed welfare deviates from theoretical welfare')
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end
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