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Commit f89c1b58 authored by Johannes Pfeifer's avatar Johannes Pfeifer
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Add integration test for steady state parameter updating

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1 merge request!1714Output M_ in stoch_simul.m and discretionary_policy.m
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tests/Makefile.am
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......@@ -124,6 +124,7 @@ MODFILES = \
steady_state/walsh1_ssm_block.mod \
steady_state/multi_leads.mod \
steady_state/example1_trust_region.mod \
steady_state/Gali_2015_chapter_6_4.mod \
steady_state_operator/standard.mod \
steady_state_operator/use_dll.mod \
steady_state_operator/block.mod \
......
tests/steady_state/Gali_2015_chapter_6_4.mod 0 → 100644
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View file @ f89c1b58
/*
* This file implements the New Keynesian model with price and wage rigidities under optimal policy
* with commitment (Ramsey) of Jordi Gal (2015): Monetary Policy, Inflation, and the Business Cycle, Princeton
* University Press, Second Edition, Chapter 6.4
*
* THIS MOD-FILE REQUIRES DYNARE 4.6 OR HIGHER
*
* Notes:
* - all model variables are expressed in deviations from steady state, i.e. in contrast to
* to the chapter, the nominal interest rate, natural output, and the natural real wage are not in log-levels, but rather mean 0
* - in the LOM for the discount rate shock z the shock enters with a minus sign in this mod-file to generate the
* IRF to a -0.5% shock
*
* This implementation was written by Johannes Pfeifer. In case you spot mistakes,
* email me at jpfeifer@gmx.de
*
* Please note that the following copyright notice only applies to this Dynare
* implementation of the model.
*/
/*
* Copyright (C) 2020 Dynare Team
*
* This 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.
*
* It 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.
*
* For a copy of the GNU General Public License,
* see <http://www.gnu.org/licenses/>.
*/
%define whether to use interest rate or money growth rate rule
@#define money_growth_rule=1
var pi_p ${\pi^p}$ (long_name='price inflation')
y_gap ${\tilde y}$ (long_name='output gap')
y_nat ${y^{nat}}$ (long_name='natural output') //(in contrast to the textbook defined in deviation from steady state)
y ${y}$ (long_name='output')
yhat ${\hat y}$ (long_name='output deviation from steady state')
r_nat ${r^{nat}}$ (long_name='natural interest rate')
r_real ${r^r}$ (long_name='real interest rate')
i ${i}$ (long_name='nominal interrst rate')
n ${n}$ (long_name='hours worked')
m_real ${(m-p)}$ (long_name='real money stock')
m_growth_ann ${\Delta m}$ (long_name='money growth annualized')
m_nominal ${m}$ (long_name='nominal money stock')
nu ${\nu}$ (long_name='AR(1) monetary policy shock process')
a ${a}$ (long_name='AR(1) technology shock process')
r_real_ann ${r^{r,ann}}$ (long_name='annualized real interest rate')
i_ann ${i^{ann}}$ (long_name='annualized nominal interest rate')
r_nat_ann ${r^{nat,ann}}$ (long_name='annualized natural interest rate')
pi_p_ann ${\pi^{p,ann}}$ (long_name='annualized inflation rate')
z ${z}$ (long_name='AR(1) preference shock process')
p ${p}$ (long_name='price level')
w ${w}$ (long_name='nominal wage')
c ${c}$ (long_name='consumption')
w_real $\omega$ (long_name='real wage')
w_gap ${\tilde \omega}$ (long_name='real wage gap')
pi_w ${\pi^w}$ (long_name='wage inflation')
w_nat ${w^{nat}}$ (long_name='natural real wage')
mu_p ${\mu^p}$ (long_name='markup')
pi_w_ann ${\pi^{w,ann}}$ (long_name='annualized wage inflation rate')
;
varexo eps_a ${\varepsilon_a}$ (long_name='technology shock')
eps_nu ${\varepsilon_\nu}$ (long_name='monetary policy shock')
eps_z ${\varepsilon_z}$ (long_name='preference shock innovation')
;
parameters alppha ${\alpha}$ (long_name='capital share')
betta ${\beta}$ (long_name='discount factor')
rho_a ${\rho_a}$ (long_name='autocorrelation technology shock')
rho_nu ${\rho_{\nu}}$ (long_name='autocorrelation monetary policy shock')
rho_z ${\rho_{z}}$ (long_name='autocorrelation monetary demand shock')
siggma ${\sigma}$ (long_name='inverse EIS')
varphi ${\varphi}$ (long_name='inverse Frisch elasticity')
phi_pi ${\phi_{\pi}}$ (long_name='inflation feedback Taylor Rule')
phi_y ${\phi_{y}}$ (long_name='output feedback Taylor Rule')
eta ${\eta}$ (long_name='semi-elasticity of money demand')
epsilon_p ${\epsilon_p}$ (long_name='demand elasticity goods')
theta_p ${\theta_p}$ (long_name='Calvo parameter prices')
epsilon_w ${\epsilon_w}$ (long_name='demand elasticity labor services')
theta_w ${\theta_w}$ (long_name='Calvo parameter wages')
lambda_p ${\lambda_p}$ (long_name='composite parameter Phillips Curve')
lambda_w ${\lambda_w}$ (long_name='composite parameter wage Phillips Curve')
;
%----------------------------------------------------------------
% Parametrization, p. 67 and p. 113-115
%----------------------------------------------------------------
siggma = 1;
varphi=5;
phi_pi = 1.5;
phi_y = 0.125;
theta_p=3/4;
rho_nu =0.5;
rho_z = 0.5;
rho_a = 0.9;
betta = 0.99;
eta =3.77; %footnote 11, p. 115
alppha=1/4;
epsilon_p=9;
epsilon_w=4.5;
theta_w=3/4;
%----------------------------------------------------------------
% First Order Conditions
%----------------------------------------------------------------
model(linear);
//Composite parameters
#Omega=(1-alppha)/(1-alppha+alppha*epsilon_p); %defined on page 166
#psi_n_ya=(1+varphi)/(siggma*(1-alppha)+varphi+alppha); %defined on page 171
#psi_n_wa=(1-alppha*psi_n_ya)/(1-alppha); %defined on page 171
#aleph_p=alppha*lambda_p/(1-alppha); %defined on page 172
#aleph_w=lambda_w*(siggma+varphi/(1-alppha)); %defined on page 172
[name='New Keynesian Phillips Curve eq. (18)']
pi_p=betta*pi_p(+1)+aleph_p*y_gap+lambda_p*w_gap;
[name='New Keynesian Wage Phillips Curve eq. (22)']
pi_w=betta*pi_w(+1)+aleph_w*y_gap-lambda_w*w_gap;
[name='Dynamic IS Curve eq. (22)']
y_gap=-1/siggma*(i-pi_p(+1)-r_nat)+y_gap(+1);
[name='Definition natural rate of interest eq. (24)']
r_nat=-siggma*psi_n_ya*(1-rho_a)*a+(1-rho_z)*z;
w_gap=w_gap(-1)+pi_w-pi_p-(w_nat-w_nat(-1));
[name='Definition natural wage, eq (16)']
w_nat=psi_n_wa*a;
[name='Definition markup']
mu_p=-alppha/(1-alppha)*y_gap-w_gap;
[name='Definition real wage gap, p. 171']
w_gap=w_real-w_nat;
[name='Definition real interest rate']
r_real=i-pi_p(+1);
[name='Definition natural output, eq. (20)']
y_nat=psi_n_ya*a;
[name='Definition output gap']
y_gap=y-y_nat;
[name='Monetary policy shock']
nu=rho_nu*nu(-1)+eps_nu;
[name='TFP shock']
a=rho_a*a(-1)+eps_a;
[name='Production function, p. 171']
y=a+(1-alppha)*n;
[name='Preference shock, p. 54']
z = rho_z*z(-1) - eps_z;
[name='Money growth (derived from eq. (4))']
m_growth_ann=4*(y-y(-1)-eta*(i-i(-1))+pi_p);
[name='Real money demand (eq. 4)']
m_real=y-eta*i;
[name='Annualized nominal interest rate']
i_ann=4*i;
[name='Annualized real interest rate']
r_real_ann=4*r_real;
[name='Annualized natural interest rate']
r_nat_ann=4*r_nat;
[name='Annualized inflation']
pi_p_ann=4*pi_p;
[name='Annualized wage inflation']
pi_w_ann=4*pi_w;
[name='Output deviation from steady state']
yhat=y-steady_state(y);
[name='Definition price level']
pi_p=p-p(-1);
[name='resource constraint, eq. (12)']
y=c;
[name='definition real wage']
w_real=w-p;
[name='definition real wage']
m_nominal=m_real+p;
end;
steady_state_model;
lambda_p=(1-theta_p)*(1-betta*theta_p)/theta_p*((1-alppha)/(1-alppha+alppha*epsilon_p)); %defined on page 166
lambda_w=(1-theta_w)*(1-betta*theta_w)/(theta_w*(1+epsilon_w*varphi)); %defined on page 170
end;
%----------------------------------------------------------------
% define shock variances
%---------------------------------------------------------------
shocks;
var eps_a = 1;
var eps_z = 1;
end;
%----------------------------------------------------------------
% generate IRFs for technology shock under optimal policy, replicates Figures 6.3, p. 182
%----------------------------------------------------------------
//planner objective, uses lambda_w and lambda_p updated in steady_state_model-block
planner_objective 0.5*((siggma+(varphi+alppha)/(1-alppha))*y_gap^2+ epsilon_p/lambda_p*pi_p^2+epsilon_w*(1-alppha)/lambda_w*pi_w^2);
ramsey_model(instruments=(i),planner_discount=betta, planner_discount_latex_name = $\delta$);
stoch_simul(order=1,irf=16,noprint) y_gap pi_p_ann pi_w_ann w_real;
evaluate_planner_objective;
oo_baseline=oo_;
%flexible wage case
set_param_value('theta_w',0.0000000001);
set_param_value('theta_p',3/4);
stoch_simul(order=1,irf=16,noprint) y_gap pi_p_ann pi_w_ann w_real;
evaluate_planner_objective;
oo_flexible_wages=oo_;
%flexible price case
set_param_value('theta_w',3/4)
set_param_value('theta_p',0.000000001)
stoch_simul(order=1,irf=16,noprint) y_gap pi_p_ann pi_w_ann w_real;
evaluate_planner_objective;
oo_flexible_prices=oo_;
figure('Name','Dynamic Responses to a technology shock under optimal policy')
subplot(2,2,1)
plot(1:options_.irf,oo_baseline.irfs.y_gap_eps_a,'-o',1:options_.irf,oo_flexible_wages.irfs.y_gap_eps_a,'-d',1:options_.irf,oo_flexible_prices.irfs.y_gap_eps_a,'-s')
ylim([-0.1 0.1])
title('Output gap')
ll=legend('baseline','flexible wages','flexible prices');
set(ll,'Location','SouthEast');
subplot(2,2,2)
plot(1:options_.irf,oo_baseline.irfs.pi_p_ann_eps_a,'-o',1:options_.irf,oo_flexible_wages.irfs.pi_p_ann_eps_a,'-d',1:options_.irf,oo_flexible_prices.irfs.pi_p_ann_eps_a,'-s')
title('Price Inflation')
subplot(2,2,3)
plot(1:options_.irf,oo_baseline.irfs.pi_w_ann_eps_a,'-o',1:options_.irf,oo_flexible_wages.irfs.pi_w_ann_eps_a,'-d',1:options_.irf,oo_flexible_prices.irfs.pi_w_ann_eps_a,'-s')
title('Wage inflation')
subplot(2,2,4)
plot(1:options_.irf,oo_baseline.irfs.w_real_eps_a,'-o',1:options_.irf,oo_flexible_wages.irfs.w_real_eps_a,'-d',1:options_.irf,oo_flexible_prices.irfs.w_real_eps_a,'-s')
title('Real wage')
%----------------------------------------------------------------
% generate first row of Table 6.1, p. 186
%----------------------------------------------------------------
shocks;
var eps_a = 1;
end;
set_param_value('theta_w',3/4);
set_param_value('theta_p',3/4);
stoch_simul(order=1,irf=16,noprint) y_gap y_gap pi_p pi_w;
oo_baseline=oo_;
y_gap_pos=strmatch('y_gap',var_list_ ,'exact');
pi_p_pos=strmatch('pi_p',var_list_ ,'exact');
pi_w_pos=strmatch('pi_w',var_list_ ,'exact');
%read out current parameter values
par.alppha=M_.params(strmatch('alppha',M_.param_names,'exact'));
par.epsilon_p=M_.params(strmatch('epsilon_p',M_.param_names,'exact'));
par.epsilon_w=M_.params(strmatch('epsilon_w',M_.param_names,'exact'));
par.siggma=M_.params(strmatch('siggma',M_.param_names,'exact'));
par.varphi=M_.params(strmatch('varphi',M_.param_names,'exact'));
par.lambda_w=M_.params(strmatch('lambda_w',M_.param_names,'exact'));
par.lambda_p=M_.params(strmatch('lambda_p',M_.param_names,'exact'));
variance.y_gap=oo_.var(y_gap_pos,y_gap_pos);
variance.pi_p=oo_.var(pi_p_pos,pi_p_pos);
variance.pi_w=oo_.var(pi_w_pos,pi_w_pos);
L=0.5*((par.siggma+(par.varphi+par.alppha)/(1-par.alppha))*variance.y_gap+ par.epsilon_p/par.lambda_p*variance.pi_p+par.epsilon_w*(1-par.alppha)/par.lambda_w*variance.pi_w)
labels={'sigma(pi_p)';'sigma(pi_w)';'sigma(tilde y)';'L'};
headers={' ';'Optimal'};
values=[sqrt([variance.pi_p;variance.pi_w;variance.y_gap]);L];
options_.noprint=0;
dyntable(options_,'Evaluation of Simple Rules',headers,labels,values,size(labels,2)+2,4,3)
if any(isnan(values))
error('Parameter updating in steady state went wrong')
end
\ No newline at end of file
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