185 lines
7.5 KiB
Modula-2
185 lines
7.5 KiB
Modula-2
/*
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* This file shows how to use "system prior"-type prior restrictions as in
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* Michal Andrle/Miroslav Plašil (2018): "Econometrics with system priors",
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* Economics Letters, 172, pp. 134-137 during estimation based on
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* 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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* THIS MOD-FILE REQUIRES DYNARE 4.5 OR HIGHER
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*
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* Notes:
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* - The estimation will automatically take the Gali_2015_prior_restrictions.m into
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* account, which has the required name and format
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* - Estimation is based on simulated data
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* - The file also shows how to use a prior/posterior-function
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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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*/
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/*
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* Copyright © 2021-2023 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 <http://www.gnu.org/licenses/>.
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*/
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var pi ${\pi}$ (long_name='inflation')
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y_gap ${\tilde y}$ (long_name='output gap')
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y_nat ${y^{nat}}$ (long_name='natural output') //(in contrast to the textbook defined in deviation from steady state)
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y ${y}$ (long_name='output')
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yhat ${\hat y}$ (long_name='output deviation from steady state')
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r_nat ${r^{nat}}$ (long_name='natural interest rate')
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i ${i}$ (long_name='nominal interrst rate')
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n ${n}$ (long_name='hours worked')
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nu ${\nu}$ (long_name='AR(1) monetary policy shock process')
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a ${a}$ (long_name='AR(1) technology shock process')
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z ${z}$ (long_name='AR(1) preference shock process')
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p ${p}$ (long_name='price level')
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w ${w}$ (long_name='nominal wage')
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c ${c}$ (long_name='consumption')
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;
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varexo eps_a ${\varepsilon_a}$ (long_name='technology shock')
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eps_nu ${\varepsilon_\nu}$ (long_name='monetary policy shock')
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eps_z ${\varepsilon_z}$ (long_name='preference shock innovation')
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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_nu ${\rho_{\nu}}$ (long_name='autocorrelation monetary policy 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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;
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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_nu =0.5;
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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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%----------------------------------------------------------------
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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 60
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#psi_n_ya=(1+varphi)/(siggma*(1-alppha)+varphi+alppha); %defined on page 62
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#lambda=(1-theta)*(1-betta*theta)/theta*Omega; %defined on page 61
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#kappa=lambda*(siggma+(varphi+alppha)/(1-alppha)); %defined on page 63
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[name='New Keynesian Phillips Curve eq. (22)']
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pi=betta*pi(+1)+kappa*y_gap;
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[name='Dynamic IS Curve eq. (23)']
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y_gap=-1/siggma*(i-pi(+1)-r_nat)+y_gap(+1);
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[name='Interest Rate Rule eq. (26)']
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i=phi_pi*pi+phi_y*yhat+nu;
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[name='Definition natural rate of interest eq. (24)']
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r_nat=-siggma*psi_n_ya*(1-rho_a)*a+(1-rho_z)*z;
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[name='Definition natural output, eq. (20)']
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y_nat=psi_n_ya*a;
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[name='Definition output gap']
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y_gap=y-y_nat;
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[name='Monetary policy shock']
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nu=rho_nu*nu(-1)+eps_nu;
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[name='TFP shock']
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a=rho_a*a(-1)+eps_a;
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[name='Production function (eq. 14)']
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y=a+(1-alppha)*n;
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[name='Preference shock, p. 54']
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z=rho_z*z(-1) - eps_z;
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[name='Output deviation from steady state']
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yhat=y-steady_state(y);
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[name='Definition price level']
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pi=p-p(-1);
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[name='resource constraint, eq. (12)']
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y=c;
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[name='FOC labor, eq. (2)']
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w-p=siggma*c+varphi*n;
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end;
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shocks;
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var eps_nu = 0.0025^2; //1 standard deviation shock of 25 basis points, i.e. 1 percentage point annualized
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end;
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% simulate data
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stoch_simul(periods=100,drop=0,irf=0) yhat;
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% save data
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datatomfile('sim_data',{'yhat'});
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estimated_params;
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theta,0.75,beta_pdf,0.5,0.1;
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betta, beta_pdf, 0.993, 0.002;
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alppha, beta_pdf, 0.25, 0.02;
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end;
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varobs yhat;
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% Run prior function to get prior slope of the PC based on independent priors
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hh_fig=figure('Name','Slope of the Phillips Curve');
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prior_function(function='Gali_2015_PC_slope');
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PC_slope_vec=cell2mat(oo_.prior_function_results(:,1));
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optimal_bandwidth = mh_optimal_bandwidth(PC_slope_vec,length(PC_slope_vec),0,'gaussian');
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[density(:,1),density(:,2)] = kernel_density_estimate(PC_slope_vec,512,length(PC_slope_vec),optimal_bandwidth,'gaussian');
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figure(hh_fig)
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subplot(3,1,1)
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plot(density(:,1),density(:,2));
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title('Prior')
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% Run estimation with 1 observation to show effect of _prior_restriction .m
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% on independent prior
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estimation(datafile='sim_data',mode_compute=5,mh_replic=2001,mh_nblocks=1,diffuse_filter,nobs=1,mh_jscale=0.8);
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posterior_function(function='Gali_2015_PC_slope');
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PC_slope_vec=cell2mat(oo_.posterior_function_results(:,1));
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optimal_bandwidth = mh_optimal_bandwidth(PC_slope_vec,length(PC_slope_vec),0,'gaussian');
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[density(:,1),density(:,2)] = kernel_density_estimate(PC_slope_vec,512,length(PC_slope_vec),optimal_bandwidth,'gaussian');
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figure(hh_fig)
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subplot(3,1,2)
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plot(density(:,1),density(:,2));
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title('Updated Prior')
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% Run estimation with full observations
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estimation(datafile='sim_data',mode_compute=5,mh_replic=2001,mh_nblocks=1,diffuse_filter,nobs=100,mh_jscale=0.8);
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posterior_function(function='Gali_2015_PC_slope');
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PC_slope_vec=cell2mat(oo_.posterior_function_results(:,1));
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optimal_bandwidth = mh_optimal_bandwidth(PC_slope_vec,length(PC_slope_vec),0,'gaussian');
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[density(:,1),density(:,2)] = kernel_density_estimate(PC_slope_vec,512,length(PC_slope_vec),optimal_bandwidth,'gaussian');
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figure(hh_fig)
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subplot(3,1,3)
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plot(density(:,1),density(:,2));
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title('Posterior')
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