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