// Two Country // BENCHMARK MODEL: OUTPUT GROWTH RULE, DEMEANED DATA var PI PI_star PI_H PI_Hstar PI_F PI_Fstar LAM LAM_star C C_star calC calC_star R R_star Y Y_star Q Q_star S E_del PSI_F PSI_Hstar A A_star G G_star Z INF_US INF_F R_US R_F Ygr_US Ygr_F ; varexo EPS_R EPS_Rstar EPS_A EPS_Astar EPS_G EPS_Gstar EPS_Z EPS_Edel; parameters theta_H theta_F theta_Hstar theta_Fstar tau h alp eta bet rhoR psi1 psi2 psi3 rhoRstar psi1star psi2star psi3star rhoA rhoAstar rhoG rhoGstar rhoZ gam_steady rr_steady pi_steady pi_steadystar; // pi_steady = pi_steadystar // corr_RRstar = 0 // To be substituted // bet = 1/(1+rr_steady/400); // kap_H = (1-theta_H)/theta_H*(1-theta_H*bet); // kap_F = (1-theta_F)/theta_F*(1-theta_F*bet); // kap_Hstar = (1-theta_Hstar)/theta_Hstar*(1-theta_Hstar*bet); // kap_Fstar = (1-theta_Fstar)/theta_Fstar*(1-theta_Fstar*bet); model(linear); // 1. Domestic firms price setting PI_H = 1/(1+rr_steady/400)*PI_H(+1) + (1-theta_H)/theta_H*(1-theta_H/(1+rr_steady/400))*( -LAM - alp*Q - A ); // 2. Domestic habits (1-h)*calC = C - h*C(-1) + h*Z; // 3. Domestic Marginal utility of consumption -LAM = tau/(1-h/(1+rr_steady/400))*calC - h/(1+rr_steady/400)/(1-h/(1+rr_steady/400))*(tau*calC(+1)+Z(+1)); // 4. Domestic importers' price setting PI_F = 1/(1+rr_steady/400)*PI_F(+1) + (1-theta_F)/theta_F*(1-theta_F/(1+rr_steady/400))*PSI_F; // 5. Definition of CPI PI = alp*PI_F + (1-alp)*PI_H; // 6. Terms of Trade Dynamics Q = Q(-1) + PI_H - PI_F; // 7. Real Exchange Rate Dynamics S = PSI_F - (1-alp)*Q - alp*Q_star; // 8. Nominal Depreciation Rate E_del = PI - PI_star + S - S(-1) + EPS_Edel; // 9. Home goods market clearing Y = C + G -(alp/tau)*S - alp*(1-alp)*eta*(Q-Q_star); // 10. Risk Sharing Condition LAM = LAM_star - S; // 11. Monetary Policy Rule R = rhoR*R(-1) + (1-rhoR)*(psi1*PI +psi2*(Y-Y(-1)+Z) + psi3*E_del) + EPS_R; // 12. UIP equation R - R_star = PI(+1) - PI_star(+1) + S(+1) -S; // 13. Foreign firms price setting PI_Fstar = 1/(1+rr_steady/400)*PI_Fstar(+1) + (1-theta_Fstar)/theta_Fstar*(1-theta_Fstar/(1+rr_steady/400))*( -LAM_star - alp*Q_star - A_star); // 14. Foreign habits (1-h)*calC_star = C_star - h*C_star(-1) + h*Z; // 15. Foreign Marginal utility of consumption -LAM_star = tau/(1-h/(1+rr_steady/400))*calC_star - h/(1+rr_steady/400)/(1-h/(1+rr_steady/400))*(tau*calC_star(+1)+Z(+1)); // 16. Foreign importers' price setting PI_Hstar = 1/(1+rr_steady/400)*PI_Hstar(+1) + (1-theta_Hstar)/theta_Hstar*(1-theta_Hstar/(1+rr_steady/400))*PSI_Hstar; // 17. Definition of CPI PI_star = alp*PI_Hstar + (1-alp)*PI_Fstar; // 18. Terms of Trade Dynamics Q_star = Q_star(-1) + PI_Fstar - PI_Hstar; // 19. Real Exchange Dynamics S = -PSI_Hstar + (1-alp)*Q_star + alp*Q; // 20. Foreign goods market clearing Y_star = C_star + G_star -((1-alp)/tau)*S + alp*(1-alp)*eta*(Q-Q_star); // 21. Foreign Monetary policy rule R_star = rhoRstar*R_star(-1) + (1-rhoRstar)*(psi1star*PI_star + psi2star*(Y_star-Y_star(-1)+Z) - psi3star*E_del) + EPS_Rstar; // 22. Euler Equation -LAM = -LAM(+1) -(R - PI(+1)) + Z(+1); // Exogenous shocks A = rhoA*A(-1) + EPS_A; A_star = rhoAstar*A_star(-1) + EPS_Astar; G = rhoG*G(-1) + EPS_G; G_star = rhoGstar*G_star(-1) + EPS_Gstar; Z = rhoZ*Z(-1) + EPS_Z; // Measurement equations INF_US = 4*PI; R_US = 4*R; Ygr_US = Y - Y(-1) + Z; INF_F = 4*PI_star; R_F = 4*R_star; Ygr_F = Y_star - Y_star(-1) + Z; end; initval; PI=0; PI_star=0; PI_H=0; PI_Hstar=0; PI_F=0; PI_Fstar=0; LAM=0; LAM_star=0; C=0; C_star=0; calC=0; calC_star=0; R=0; R_star=0; Y=0; Y_star=0; Q =0; Q_star=0; S=0; E_del=0; PSI_F=0; PSI_Hstar=0; A=0; A_star=0; G=0; G_star=0; Z =0; INF_US=0; INF_F=0; R_US=0; R_F=0; Ygr_US=0; Ygr_F=0; steady; check; estimated_params; // STARTING VALUES & PRIORS theta_H, 0.5,1E-5,0.999, BETA_PDF,0.5,0.15; theta_F, 0.5,1E-5,0.999, BETA_PDF,0.5,0.15; theta_Hstar, 0.5,1E-5,0.999, BETA_PDF,0.75,0.15; theta_Fstar, 0.5,1E-5,0.999, BETA_PDF,0.75,0.15; tau, 2.7,1E-5,10, GAMMA_PDF,2,0.5; h, 0.3,1E-5,0.999, BETA_PDF,0.3,0.1; alp, 0.1,1E-5,0.999, BETA_PDF,0.12,0.05; eta, 1,1E-5,10, GAMMA_PDF,1,0.5; psi1, 1.5,0.95,10, GAMMA_PDF,1.5,0.25; psi2, 0.5,1E-5,10, GAMMA_PDF,0.5,0.25; psi3, 0.1,1E-5,10, GAMMA_PDF,0.1,0.05; psi1star, 1.1,0.95,10, GAMMA_PDF,1.5,0.25; psi2star, 0.5,1E-5,10, GAMMA_PDF,0.5,0.25; psi3star, 0.1,1E-5,10, GAMMA_PDF,0.1,0.05; rhoA, 0.86,1E-5,1, BETA_PDF,0.8,0.1; rhoR, 0.81,1E-5,1, BETA_PDF,0.5,0.2; rhoG, 0.96,1E-5,1, BETA_PDF,0.8,0.1; rhoAstar, 0.97,1E-5,1, BETA_PDF,0.6,0.2; rhoRstar, 0.82,1E-5,1, BETA_PDF,0.5,0.2; rhoGstar, 0.81,1E-5,1, BETA_PDF,0.8,0.1; rhoZ, 0.54,1E-5,1, BETA_PDF,0.66,0.15; rr_steady, 0.5,0,10, GAMMA_PDF,0.5,0.5; gam_steady, 0.5,-5,5, NORMAL_PDF,0.4,0.2; pi_steady, 3.33,0,10, GAMMA_PDF,7,2; // pi_steadystar, 4.2,0,10, GAMMA_PDF,8.8,2; stderr EPS_A, 2,1E-8,5, INV_GAMMA_PDF,1.253314,0.655136; //fs_dyn(1,4) stderr EPS_G, 0.6,1E-8,5, INV_GAMMA_PDF,1.253314,0.655136; //fs_dyn(1,4) stderr EPS_R, 0.15,1E-8,5, INV_GAMMA_PDF,0.501326,0.262055; //fs_dyn(0.4,4) stderr EPS_Astar, 0.5,1E-8,5, INV_GAMMA_PDF,0.501326,0.262055; //fs_dyn(0.4,4) stderr EPS_Gstar, 0.7,1E-8,5, INV_GAMMA_PDF,1.253314,0.655136; //fs_dyn(1,4) stderr EPS_Rstar, 0.1,1E-8,5, INV_GAMMA_PDF,0.250663,0.131027; //fs_dyn(0.2,4) stderr EPS_Z, 0.34,1E-8,5, INV_GAMMA_PDF,0.626657,0.327568; //fs_dyn(0.5,4) stderr EPS_Edel, 4,1E-8,10, INV_GAMMA_PDF,4.386599,2.292977; //fs_dyn(3.5,4) end; varobs Ygr_US INF_US R_US Ygr_F INF_F R_F E_del; estimation(datafile=us_euro_data_demeaned,mode_compute=4,mh_replic=20000,mh_jscale=0.15,presample=4); // mode_compute=3 // load_mh_file // nodiagnostic // mode_file=MODEL1_mode