%---------------------------------------------------------------------------------------------------------------------------------------------------------; % Two countries a and b, and a rest of the world (star); var %U_a %U_b C_a %Aggregate households consumption C_b L_a %Labor supply of Household L_b P_a % Consumer price index P_b W_a % Wage level W_b tau_a % Implicit tax on consumption tau_b R_a % Nominal Return R_b R_star % Rest of the world nominal return TR_a % Transfers TR_b R_k_a % Return on capital R_k_b C_star_a % Domestic consumption of rest of the word's goods C_star_b C_z_a % Domestic consumption of goods providing from the z area C_z_b C_a_a % Domestic consomption of national goods C_b_a % Domestic consomption of goods providing from the country b C_b_b % Domestic consomption of national goods C_a_b % Domestic consomption of goods providing from the country a I_a % Aggregate investment I_b I_star_a %Rest of the Wold investment in domestic country I_star_b I_z_a % Area z's investment in domestic country I_z_b I_a_a % Domestic investment I_b_a % Investment of b in country a I_b_b % Domestic investment I_a_b % Investment of a in country a P_star_a % Price of RW's good in country a P_star_b P_z_a %Price of Z area's goods and services sold in country a P_z_b P_a_a % Domestic price of national goods P_b_a P_b_b P_a_b s_ab % Nominal exchange rate between country a and b s_a % Nominal exchange rate betweeen Country a and te RW s_b % Nominal exchange rate betweeen Country b and te RW TT_b_a % Terms of trade between b and a TT_a_b % Terms of trade between a and b TT_star_a % Terms of trade between RW and a TT_star_b % Terms of trade between RW and b Upsilon_a % Relative price (CPI and domestic price of national goods Country a) Upsilon_b % Relative price (CPI and domestic price of national goods Country b) Y_a % Output of country a Y_b A_a % Productivity shock A_b K_a % Capital K_b Cm_a % Marginal cost Cm_b RMC_a % Real marginal cost RMC_b lmbd_a % Lagragian multiplicator lmbd_b %P_opt_aa % Optimizing price %P_opt_bb %Y_opt_a % Optimizing price %Y_opt_b Pi_a_a % Inflation rate of domestic good Pi_b_b Pi_a % Gross inflation rate Pi_b Lambda_a % Willingness to lend Lambda_b Nw_a % Financial intermediairies net worth Nw_b TS_a % Total Saving TS_b B_a % Domestic bonds B_b Z_a % Loans allocations shock Z_b D_a % Financial intermediairies foreign debt D_b F_a % External risk premium F_b TW_a % Total Worth of financial internediairies TW_b EX_a % Exogenous export shock EX_b G_a % Public expenditures G_b P_star ; %91 equations %---------------------------------------------------------------------------------------------------------------------------------------------------------; % Déclaration des variables endogènes %---------------------------------------------------------------------------------------------------------------------------------------------------------; varexo eps_aa eps_ab eps_za eps_zb eps_r_star eps_tr_a eps_tr_b eps_tau_a eps_tau_b eps_ex_a eps_ex_b eps_p_star ; %-------------------------------------------------------------------------------------------------------------------------------------------------------; % Parameters; %-------------------------------------------------------------------------------------------------------------------------------------------------------; parameters beta eta phi delta nu alpha gamma mu varpi theta psi varphi vartheta kappa varsigma Lambda_bar omega rho_r_star rho_za rho_zb rho_aa rho_ab rho_tr_a rho_tr_b rho_tau_a rho_tau_b rho_ex_a rho_ex_b sigma_r_star sigma_za sigma_zb sigma_aa sigma_ab sigma_tr_a sigma_tr_b sigma_tau_a sigma_tau_b sigma_ex_a sigma_ex_b Y_bar_a Y_bar_b tau_bar_a tau_bar_b TR_bar_a TR_bar_b varrho rho_p_star sigma_p_star ; beta=0.99; eta=2; phi=1; delta=0.025; nu=0.37; gamma=0.5; mu=1.5; varpi=1.5; theta=7; alpha=0.63; psi=0.67; % 0.66, 0.74, 0.9; %0.79, 0.87, 0.9; varphi=0.5; vartheta=0.75; kappa=0.02; varsigma=1.47; Lambda_bar=0.793; omega=0.94; rho_r_star=0.95; rho_za=0.8; rho_zb=0.8; rho_aa=0.8; rho_ab=0.8; rho_tr_a=0.8; rho_tr_b=0.8; rho_tau_a=0.8; rho_tau_b=0.8; rho_ex_a=0.8; rho_ex_b=0.8; sigma_r_star=0.05; sigma_za=0.02; sigma_zb=0.02; sigma_aa=0.02; sigma_ab=0.02; sigma_tr_a=0.02; sigma_tr_b=0.02; sigma_tau_a=0.02; sigma_tau_b=0.02; sigma_ex_a=0.02; sigma_ex_b=0.02; Y_bar_a=1.; Y_bar_b=1.; tau_bar_a=0.15; tau_bar_b=0.05; TR_bar_a=0.09; TR_bar_b=0.09; varrho=((1-vartheta)*(1-beta*vartheta))/vartheta; rho_p_star=0.8; sigma_p_star=0.02; %----------------------------------------------------------------------------------------------------------------------------------------------------; %Model; %----------------------------------------------------------------------------------------------------------------------------------------------------; model; %---; % Households(26); %---; %U_a=(C_a^(1-eta))/(1-eta)-(L_a^(1+phi))/(1+phi); %U_b=(C_b^(1-eta))/(1-eta)-(L_b^(1+phi))/(1+phi); lmbd_a=C_a^(-eta)/((1-tau_a)*P_a); lmbd_b=C_b^(-eta)/((1-tau_b)*P_b); C_a^eta*L_a^phi=(W_a/(1+tau_a)*P_a_a)*Upsilon_a^(-1); C_b^eta*L_b^phi=(W_b/(1+tau_b)*P_b_b)*Upsilon_b^(-1); Upsilon_a=P_a/P_a_a; P_a/P_a_a=(alpha*TT_star_a^(1-mu)+(1-alpha)*((gamma+(1-gamma)*TT_b_a^(1-varpi))^(1/(1-varpi)))^(1-mu))^(1/(1-mu)); Upsilon_b=P_b/P_b_b; P_b/P_b_b=(psi*TT_star_b^(1-mu)+(1-psi)*((varpi+(1-varpi)*TT_a_b^(1-varpi))^(1/(1-varpi)))^(1-mu))^(1/(1-mu)); ((1+tau_a)/(1+tau_a(-1)))=beta*R_a*(C_a^eta(-1)/(Pi_a*C_a^eta)); Pi_a=P_a/P_a(-1); ((1+tau_b)/(1+tau_b(-1)))=beta*R_b*(C_b^eta(-1)/(Pi_b*C_b^eta)); Pi_b=P_b/P_b(-1); % C_a=(alpha^(1/mu)*C_star_a^((mu-1)/mu)+ (1-alpha)^(1/mu)*C_z_a^((mu-1)/mu))^(mu/(mu-1)); % C_z_a=(gamma^(1/varpi)*C_a_a^((varpi-1)/varpi)+ (1-gamma)^(1/varpi)*C_b_a^((varpi-1)/varpi))^(varpi/(varpi-1)); P_a=(alpha*P_star_a^(1-mu)+(1-alpha)*P_z_a^(1-mu))^(1/(1-mu)); P_z_a=(gamma*P_a_a^(1-varpi)+(1-gamma)*P_b_a^(1-varpi))^(1/(1-varpi)); C_b_a=(1-gamma)*(1-alpha)*(P_b_a/P_z_a)^(-varpi)*(P_z_a/P_a)^(-mu)*C_a; C_a_a=(1-alpha)*gamma*(P_a_a/P_z_a)^(-varpi)*(P_z_a/P_a)^(-mu)*C_a; C_z_a= (1-alpha)*(P_z_a/P_a)^(-mu)*C_a; C_star_a= alpha*(P_star_a/P_a)^(-mu)*C_a; % C_b=(psi^(1/mu)*C_star_b^((mu-1)/mu)+ (1-psi)^(1/mu)*C_z_b^((mu-1)/mu))^(mu/(mu-1)); % C_z_b=(varphi^(1/varpi)*C_b_b^((varpi-1)/varpi)+ (1-varphi)^(1/varpi)*C_a_b^((varpi-1)/varpi))^(varpi/(varpi-1)); P_b=(psi*P_star_b^(1-mu)+(1-psi)*P_z_b^(1-mu))^(1/(1-mu)); P_z_b=(varphi*P_b_b^(1-varpi)+(1-varphi)*P_a_b^(1-varpi))^(1/(1-varpi)); C_z_b=(1-varphi)*(P_z_b/P_b)^(-mu)*C_b; C_star_b=varphi*(P_star_b/P_b)^(-mu)*C_b; C_a_b=(1-psi)*(1-varphi)*(P_a_b/P_z_b)^(-varpi)*(P_z_b/P_b)^(-mu)*C_b; C_b_b/C_a_b=(varphi/(1-varphi))*(P_b_b/P_a_b)^(-varpi); %---; %Open economy (4); %---; TT_star_a=P_star_a/P_a_a; TT_star_b=P_star_b/P_b_b; TT_b_a=P_b_a/P_a_a; TT_a_b=P_a_b/P_b_b; %s_ab=P_b_b/P_b_a; s_a=P_star/P_a; s_b=P_star/P_b; s_ab=P_a_b/P_a_a; %---; %Financial intermediairies (16); %---; K_a=Lambda_a(-1)*(Nw_a(-1)+TS_a); TS_a=B_a+s_a(-1)*D_a; Lambda_a=Lambda_bar*(Y_a/Y_bar_a)^varsigma*Z_a; R_k_a=R_star*(s_a(-1)/s_a)*F_a; %R_a=R_star*(s_a(-1)/s_a)*F_a; F_a=(K_a/Nw_a(-1))^kappa; Nw_a=omega*(R_k_a*K_a-R_a*B_a-R_star*s_a*D_a*F_a); R_k_a=R_a+(1-delta); K_b=Lambda_b(-1)*(Nw_b(-1)+TS_b); TS_b=B_b+s_b(-1)*D_b; Lambda_b=Lambda_bar*(Y_b/Y_bar_b)^varsigma*Z_b; R_k_b=R_star*(s_b(-1)/s_b)*F_b; %R_b=R_star*(s_b(-1)/s_b)*F_b; F_b=(K_b/Nw_b(-1))^kappa; Nw_b=omega*(R_k_b*K_b-R_b*B_b-R_star*s_b*D_b*F_b); R_k_b=R_b+(1-delta); TW_a=R_k_a*K_a-R_a*B_a-R_star*s_a*D_a*F_a; TW_b=R_k_b*K_b-R_b*B_b-R_star*s_b*D_b*F_b; s_a(-1)*Lambda_a(-1)*D_a=I_a(-1)+(1-delta)*K_a-Lambda_a*Nw_a-Lambda_a*(W_a(-1)*L_a(-1)+R_a(-1)*B_a(-1)+TR_a(-1)-P_a(1)*(1+tau_a(-1))*C_a(-1)); s_b(-1)*Lambda_b(-1)*D_b=I_b(-1)+(1-delta)*K_b-Lambda_b*Nw_b-Lambda_b*(W_b(-1)*L_b(-1)+R_b(-1)*B_b(-1)+TR_b(-1)-P_b(1)*(1+tau_b(-1))*C_b(-1)); %---; % Public authorities (2); %---; G_a=tau_a*C_a-(TR_a/P_a_a)*Upsilon_a^(-1); G_b=tau_b*C_b-(TR_b/P_b_b)*Upsilon_b^(-1); %---; % Firms (24); %---; Y_a=A_a*K_a^nu*L_a^(1-nu); W_a/P_a_a=(1-nu)*(Y_a/L_a); %R_k_a/P_a_a=nu*(Y_a/K_a); (1-nu)*R_k_a*K_a=nu*W_a*L_a; Cm_a=(R_k_a^nu*W_a^(1-nu))/((1-nu)^(1-nu)*nu^nu*A_a); RMC_a=Cm_a/P_a_a; Y_b=A_b*K_b^nu*L_b^(1-nu); W_b/P_b_b=(1-nu)*(Y_b/L_b); % R_k_b/P_b_b=nu*(Y_b/K_b); (1-nu)*R_k_b*K_b=nu*W_b*L_b; Cm_b=(R_k_b^nu*W_b^(1-nu))/((1-nu)^(1-nu)*nu^nu*A_b); RMC_b=Cm_b/P_b_b; K_a=(1-delta)*K_a(-1)+I_a(-1); K_b=(1-delta)*K_b(-1)+I_b(-1); I_b_a=(1-gamma)*(1-alpha)*(P_b_a/P_z_a)^(-varpi)*(P_z_a/P_a)^(-mu)*I_a; I_a_a=(1-alpha)*gamma*(P_a_a/P_z_a)^(-varpi)*(P_z_a/P_a)^(-mu)*I_a; I_z_a= (1-alpha)*(P_z_a/P_a)^(-mu)*I_a; I_star_a= alpha*(P_star_a/P_a)^(-mu)*I_a; %I_a=(alpha^(1/mu)*I_star_a^((mu-1)/mu)+ (1-alpha)^(1/mu)*I_z_a^((mu-1)/mu))^(mu/(mu-1)); % I_z_a=(gamma^(1/varpi)*I_a_a^(varpi-1)/varpi)+ (1-gamma)^(1/varpi)*I_b_a^((varpi-1)/varpi))^(varpi/(varpi-1)); %I_b=(psi^(1/mu)*I_star_b^((mu-1)/mu)+ (1-psi)^(1/mu)*I_z_b^((mu-1)/mu))^(mu/(mu-1)); % I_z_b=(varphi^(1/varpi)*I_b_b^(varpi-1)/varpi)+ (1-varphi)^(1/varpi)*I_a_b^((varpi-1)/varpi))^(varpi/(varpi-1)); I_z_b=(1-varphi)*(P_z_b/P_b)^(-mu)*I_b; I_star_b=varphi*(P_star_b/P_b)^(-mu)*I_b; I_a_b=(1-psi)*(1-varphi)*(P_a_b/P_z_b)^(-varpi)*(P_z_b/P_b)^(-mu)*I_b; I_b_b/I_a_b=(varphi/(1-varphi))*(P_b_b/P_a_b)^(-varpi); Pi_a_a=P_a_a/P_a_a(-1); Pi_b_b=P_b_b/P_b_b(-1); Pi_a_a(-1)=beta*Pi_a_a+varrho*RMC_a; Pi_b_b(-1)=beta*Pi_b_b+varrho*RMC_b; %---; % Market clearing (2); %---; Y_a=(1-alpha)*gamma*(P_a_a/P_z_a)^(-varpi)*(P_z_a/P_a)^(-mu)*(C_a+I_a)+(1-psi)*(1-varphi)*(P_a_b/P_z_b)^(-varpi)*(P_z_b/P_b)^(-mu)*(C_b+I_b)+G_a+s_a*EX_a+(1-omega)*TW_a; Y_b=(1-psi)*varphi*(P_b_b/P_z_b)^(-varpi)*(P_z_b/P_b)^(-mu)*(C_b+I_b)+(1-gamma)*(1-alpha)*(P_b_a/P_z_a)^(-varpi)*(P_z_a/P_a)^(-mu)*(C_a+I_a)+G_b+s_b*EX_b+(1-omega)*TW_b; %---; % Exogenuous processus (11); %---; log(EX_a)=rho_ex_a*log(EX_a(-1))+eps_ex_a; log(EX_b)=rho_ex_b*log(EX_b(-1))+eps_ex_b; log(A_a)=rho_aa*log(A_a(-1))+eps_aa; log(A_b)=rho_ab*log(A_b(-1))+eps_ab; log(R_star)=rho_r_star*log(R_star(-1))+eps_r_star; log(Z_a)=rho_za*log(Z_a(-1))+eps_za; log(Z_b)=rho_zb*log(Z_b(-1))+eps_zb; log(tau_b/tau_bar_b)=rho_tau_b*log(tau_b(-1)/tau_bar_b)+eps_tau_b; log(TR_b/TR_bar_b)=rho_tr_b*log(TR_b(-1)/TR_bar_b)+eps_tr_b; log(tau_a/tau_bar_a)=rho_tau_a*log(tau_a(-1)/tau_bar_a)+eps_tau_a; log(TR_a/TR_bar_a)=rho_tr_a*log(TR_a(-1)/TR_bar_a)+eps_tr_a; log(P_star)=rho_p_star*log(P_star(-1))+eps_p_star; end; %----------------------------------------------------------------------------------------------------------------------------------------------------; %Steady state; %----------------------------------------------------------------------------------------------------------------------------------------------------; initval; %U_a=0; %U_b=0; C_a=1; C_b=1; C_star_a=alpha*C_a; C_b_a=(1-gamma)*(1-alpha)*C_a; C_a_a=gamma*(1-alpha)*C_a; C_z_a=(1-alpha)*C_a; C_star_b=psi*C_b; C_z_b=(1-psi)*C_b; C_b_b=(1-psi)*varphi*C_b; C_a_b=(1-psi)*(1-varphi)*C_b; %----; I_a=1; I_b=1; %I_a=0.089*Y_bar_a; %I_b=0.09*Y_bar_b; I_star_a=alpha*I_a; I_b_a=(1-gamma)*(1-alpha)*I_a; I_a_a=gamma*(1-alpha)*I_a; I_z_a=(1-alpha)*I_a; I_star_b=psi*I_b; I_z_b=(1-psi)*I_b; I_b_b=(1-psi)*varphi*I_b; I_a_b=(1-psi)*(1-varphi)*I_b; %----; P_a=1; P_b=1; Pi_a=1; Pi_b=1; Pi_a_a=1; Pi_b_b=1; Cm_a=1; Cm_b=1; RMC_a=1; RMC_b=1; P_star_a=1; P_star_b=1; P_z_a=1; P_z_b=1; P_a_a=1; P_b_a=1; P_b_b=1; P_a_b=1; TT_star_a=1; TT_star_b=1; TT_a_b=11; TT_b_a=1; P_star=1; %---; %Y_a=(1-alpha)*gamma*(C_a+I_a)+(1-psi)*(1-varphi)*(C_b+I_b)+tau_a-TR_a+(1-omega)*TW_a; %Y_b=(1-psi)*varphi*(C_b+I_b)+(1-gamma)*(1-alpha)*(C_a+I_a)+ tau_b-TR_b+(1-omega)*TW_b; Y_a=Y_bar_a; Y_b=Y_bar_b; Lambda_a=Lambda_bar; Lambda_b=Lambda_bar; TR_a=TR_bar_a; TR_b=TR_bar_b; tau_a=tau_bar_a; tau_b=tau_bar_b; R_star=1; R_a=1/beta; R_b=R_a; Z_a=1; Z_b=1; Upsilon_a=1; Upsilon_b=1; R_k_a=beta^(-1)+(1-delta); R_k_b=beta^(-1)+1-delta; W_a=(1-nu)*(R_k_a/nu)^(-nu/(1-nu)); W_b=(1-nu)*(R_k_b/nu)^(-nu/(1-nu)); A_a=1; A_b=1; EX_a=1; EX_b=1; K_a=I_a/delta; K_b=I_b/delta; Nw_a=K_a/2.2; F_a=(K_a/Nw_a)^kappa; Nw_b=K_b/2.2; F_b=(K_b/Nw_b)^kappa; L_a=R_k_a*K_a*(1-nu)/(nu*W_a); L_b=R_k_b*K_b*(1-nu)/(nu*W_b); G_a=0.141*Y_a; G_b=0.131*Y_b; G_a=0.141*Y_bar_a; G_b=0.131*Y_bar_b; TW_a=R_k_a*K_a-R_a*B_a-R_star*s_a*D_a*F_a; TW_b=R_k_b*K_b-R_b*B_b-R_star*s_b*D_b*F_b; %s_a=P_star/P_a; %s_b=P_star/P_b; %s_ab=P_a_b/P_a_a; end; %----------------------------------------------------------------------------------------------------------------------------------------------------; %Shocks; %----------------------------------------------------------------------------------------------------------------------------------------------------; shocks; var eps_aa; stderr sigma_aa; var eps_ab; stderr sigma_ab; var eps_za; stderr sigma_za; var eps_zb; stderr sigma_zb; var eps_r_star; stderr sigma_r_star; var eps_tr_a; stderr sigma_tr_a; var eps_tr_b; stderr sigma_tr_b; var eps_tau_a; stderr sigma_tau_a; var eps_tau_b; stderr sigma_tau_b; var eps_ex_a; stderr sigma_ex_a; var eps_ex_b; stderr sigma_ex_b; var eps_p_star; stderr sigma_p_star; end; steady; check; write_latex_dynamic_model; model_diagnostics; stoch_simul(order=2, irf=40);