diff --git a/tests/Makefile.am b/tests/Makefile.am index 7648c381877ffb0e3ec0f2033d617c8c3269a1a7..a1fe16771727115345acbf2db84ed97de4f8704a 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -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 \ diff --git a/tests/steady_state/Gali_2015_chapter_6_4.mod b/tests/steady_state/Gali_2015_chapter_6_4.mod new file mode 100644 index 0000000000000000000000000000000000000000..64c5df3c05c35a371124759049cf6c9072b187dd --- /dev/null +++ b/tests/steady_state/Gali_2015_chapter_6_4.mod @@ -0,0 +1,277 @@ +/* + * 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