191 lines
6.2 KiB
Modula-2
191 lines
6.2 KiB
Modula-2
/*
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* This file is based on the cash in advance model described
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* Frank Schorfheide (2000): "Loss function-based evaluation of DSGE models",
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* Journal of Applied Econometrics, 15(6), 645-670.
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*
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* The equations are taken from J. Nason and T. Cogley (1994): "Testing the
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* implications of long-run neutrality for monetary business cycle models",
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* Journal of Applied Econometrics, 9, S37-S70.
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* Note that there is an initial minus sign missing in equation (A1), p. S63.
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*
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* This implementation was written by Michel Juillard. Please note that the
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* following copyright notice only applies to this Dynare implementation of the
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* model.
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*/
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/*
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* Copyright © 2004-2016 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 <https://www.gnu.org/licenses/>.
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*/
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var m ${m}$ (long_name='Money Stock')
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P ${P}$ (long_name='Price Level')
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c ${c}$ (long_name='Consumption')
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e ${e}$ (long_name='exp(Tech. Shock)')
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W ${W}$ (long_name='Nominal Wage')
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R ${R}$ (long_name='Nominal Rental Rate of Capital')
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k ${k}$ (long_name='Capital')
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d ${d}$ (long_name='Deposits')
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n ${n}$ (long_name='Hours worked')
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l ${l}$ (long_name='Loans')
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gy_obs ${\Delta y^{obs}}$ (long_name='Observed growth rate of output')
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gp_obs ${\Delta m^{obs}}$ (long_name='Observed growth rate of prices')
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y ${y}$ (long_name='Output')
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dA ${\Delta A}$ (long_name='Labor Augm. Techn. Growth Rate')
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;
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varexo e_a ${\varepsilon_a}$ (long_name='Technology shock')
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e_m ${\varepsilon_m}$ (long_name='Observed money growth rate')
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;
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parameters alp ${\alpha}$ (long_name='capital share')
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bet ${\beta}$ (long_name='discount factor')
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gam ${\gamma}$ (long_name='Average technology growth')
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mst ${\bar m}$ (long_name='Average money stock')
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rho ${\rho}$ (long_name='Autocorrelation money process')
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psi ${\psi}$ (long_name='Leisure weight in utility')
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del ${\delta}$ (long_name='depreciation')
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;
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alp = 0.33;
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bet = 0.99;
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gam = 0.003;
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mst = 1.011;
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rho = 0.7;
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psi = 0.787;
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del = 0.02;
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model;
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[name='technology growth: $\Delta A_{t}$', eq='\#1']
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dA = exp(gam+e_a);
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[name='money supply rule']
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log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
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-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
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W = l/n;
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-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
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R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
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1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
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c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
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P*c = m;
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m-1+d = l;
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e = exp(e_a);
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[name='Production function']
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y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
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[name='observed output growth']
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gy_obs = dA*y/y(-1);
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[name='observed inflation']
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gp_obs = (P/P(-1))*m(-1)/dA;
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end;
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steady_state_model;
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dA = exp(gam);
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gst = 1/dA;
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m = mst;
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khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
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xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
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nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
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n = xist/(nust+xist);
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P = xist + nust;
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k = khst*n;
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l = psi*mst*n/( (1-psi)*(1-n) );
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c = mst/P;
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d = l - mst + 1;
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y = k^alp*n^(1-alp)*gst^alp;
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R = mst/bet;
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W = l/n;
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ist = y-c;
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q = 1 - d;
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e = 1;
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gp_obs = m/dA;
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gy_obs = dA;
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end;
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varobs gp_obs gy_obs;
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shocks;
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var e_a; stderr 0.014;
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var e_m; stderr 0.005;
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corr gy_obs,gp_obs = 0.5;
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end;
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steady;
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stoch_simul(order=1,irf=20,graph_format=eps,periods=1000,contemporaneous_correlation,conditional_variance_decomposition=[1,3],tex);
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options_.rplottype=0;
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rplot y e_a gy_obs;
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options_.rplottype=1;
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rplot l e_m gp_obs;
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options_.rplottype=2;
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rplot n e_a e_m m;
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stoch_simul(order=1,irf=20,graph_format=eps,periods=0,contemporaneous_correlation,conditional_variance_decomposition=[1,3]);
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write_latex_original_model;
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write_latex_static_model;
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write_latex_dynamic_model(write_equation_tags);
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write_latex_parameter_table;
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write_latex_definitions;
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write_latex_steady_state_model;
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estimated_params;
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alp, 0.356;
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gam, 0.0085;
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del, 0.01;
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stderr e_a, 0.035449;
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stderr e_m, 0.008862;
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corr e_m, e_a, 0;
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stderr gp_obs, 1;
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stderr gy_obs, 1;
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corr gp_obs, gy_obs,0;
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end;
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estimation(order=1,mode_compute=4,datafile='../fs2000/fsdat_simul',brooks_gelman_plotrows=4, mode_check,smoother,filter_covariance,filter_decomposition,forecast = 8,filtered_vars,filter_step_ahead=[1,3],irf=20,contemporaneous_correlation) m P c e W R k d y gy_obs;
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estimated_params(overwrite);
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//alp, beta_pdf, 0.356, 0.02;
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gam, normal_pdf, 0.0085, 0.003;
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//del, beta_pdf, 0.01, 0.005;
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stderr e_a, inv_gamma_pdf, 0.035449, inf;
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stderr e_m, inv_gamma_pdf, 0.008862, inf;
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corr e_m, e_a, normal_pdf, 0, 0.2;
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stderr gp_obs, inv_gamma_pdf, 0.001, inf;
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stderr gy_obs, inv_gamma_pdf, 0.001, inf;
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corr gp_obs, gy_obs,normal_pdf, 0, 0.2;
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end;
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write_latex_prior_table;
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estimation(mode_compute=8,order=1,datafile='../fs2000/fsdat_simul',mode_check,smoother,filter_decomposition,mh_replic=4000, mh_nblocks=1, mh_jscale=0.8,forecast = 8,bayesian_irf,filtered_vars,filter_step_ahead=[1,3],irf=20,
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moments_varendo,contemporaneous_correlation,conditional_variance_decomposition=[1 2 4],smoothed_state_uncertainty,raftery_lewis_diagnostics) m P c e W R k d y gy_obs;
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trace_plot(options_,M_,estim_params_,'PosteriorDensity',1);
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trace_plot(options_,M_,estim_params_,'StructuralShock',1,'e_a')
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shock_decomposition y W R;
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stoch_simul(order=1,irf=20,graph_format=eps,periods=0,contemporaneous_correlation,conditional_variance_decomposition=[1,3]);
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collect_latex_files;
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//identification(advanced=1,max_dim_cova_group=3,prior_mc=250);
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if system(['pdflatex -halt-on-error -interaction=batchmode ' M_.fname '_TeX_binder.tex'])
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error('TeX-File did not compile.')
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end
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