/* * Log-linearized model * DSGE with 3 sectors: * [1] Tradable goods and services * [2] Not-tradable goods and services * [3] Public services (state, education, health) * 3 types of jobs: * [A] High-skilled * [B] Low-skilled in tradable sector and public sector * [C] Low-skilled in non-tradable sector * Paul Cahu * Version 1.0: March 2017 */ /******************************* LIST OF ENDOGENOUS VARIABLES ************/ var lA,lB,lC,pA,pB,pC,wA,wB,wC, q2,q3,q, l1,l2,l3, y1,y2, inv1,inv2,inv3,di11,di12,di13,di21,di22,di23,mi1,mi2,mi3, dz11,dz12,dz13,dz21,dz22,dz23,mz1,mz2,mz3, y_c,tr, tax,tax_P,tax_K,tax_L,tax_C, mc_c,mc_o,dc1_o,dc2_o,dc1_c,dc2_c,qx_o,qc_o,qx_c,qc_c, nA,nB, GDP, H_C,H_A,H_B,HC_A,HC_B,HC_C, mc1,mc2,GammaP, l1A,l1B,l2A,l3A,l3B, e_rate, FB,iratef,irate,GammaPf,GammaP2, c_o,lambda,mu,k,k1,k2,k3,inv,def,det,g3, wA_bar,wB_bar,wC_bar, A1,Gamma, cs, gi_obs,ginv_obs,gc_obs,gg3_obs,gq2_obs,gy1_obs,gy2_obs,gGammaP_obs,gw_obs,gl_obs, qi,R,qz1,qz2,qz3; //EXOGENOUS VARIABLES varexo e_a1,e_a2,e_e,e_x,e_nA,e_nB,e_c,e_if,e_g,e_h,e_wu,e_G; /******************************* DEFINITION OF PARAMETERS ****************/ parameters varsigmaA,varsigmaB,varsigmaC,pA_star,pB_star,pC_star,nA_star,nB_star,lA_star,lB_star,lC_star,varpiU_A,varpiU_B,varpiU_C,tau_o_star,tau_c_star,wU_A_star,wU_B_star,wU_C_star,beta,chiC_star,chiB_star,wA_star,wB_star,wC_star, varsigmaA_star,varsigmaB_star,varsigmaC_star,chiA_star,betaC_star,betaB_star,betaA_star,q2_star,q3_star,qz1_star,qz2_star,qz3_star, varpiP_A,varpiP_B,varpiP_C,varpi_A,varpi_B,varpi_C,zeta_1,zeta_2,zeta_3,varpiF_B,varpiF_C, theta1_star,theta2_star,psi_1,psi_2,psi_3,gamma1,gamma2,gamma3, iota_1,iota_2,sq_3,sg_1,sg_2,sg_3,sf_1,sf_2,sf_3,eta_i,eta_ix, tau_k_star,tau_P_star,tau_m_star,tau_C_star, sigma,sA1,sA2,sB13,wage1,wage2,wage3, eta_z1,eta_z2,eta_x1,eta_x2,eta_z3,eta_x3, nu0,nu0_star,nu1A_star,nu1B_star,nu2A_star,nu2B_star,nu3A_star,nu3B_star,yc_star,tr_star, tax_star,a_txk,a_C1,a_C2,aL1,aL2,aL3,aL4,aL5,inv3_star,def_star,interest_star, y1_star,y2_star,y3_star, tax_L_star,tax_P_star,tax_C_star,tax_K_star, dc1_o_star,dc2_o_star,dc1_c_star,dc2_c_star,mc_o_star,mc_c_star,eta_m,eta_c, x_star,mi1_star,mi2_star,mi3_star,mz1_star,mz2_star,mz3_star,eta_x, di11_star,di12_star,di13_star,di21_star,di22_star,di23_star, dz11_star,dz12_star,dz13_star,dz21_star,dz22_star,dz23_star,dz33_star,g3_star, ax1,tax_L2_star,tax2_star, UA_star,UB_star,U_star,c_star, HC_B_star,HC_C_star,HC_A_star,ldA_1,ldA_2,ldB_1,ldB_2,ldC_1,ldC_2, aT1,aT2,aT3,Gamma_star,delta,GammaP_star, rho_tr,eta_tr,rho_g,eta_g,rho_e, xi,phi_K,qi_star,irate_star,phi_C, iratef_star,eta_FB,k1_star,k2_star,k3_star,d_star,thetam,thetax, rho_P,alpha_P,rho_P2,alpha_P2,rho_W,alpha_W,rho_theta,rho_i,varalpha_P,varalpha_Y, rho_a1,rho_G,rho_c, //parameters that may be shocked betaA,betaB,betaC,chiA,chiB,chiC; /**************************** Long-term settings *************************/ beta=0.995; Gamma_star=1.02; GammaP_star=1.06; delta=0.02; xi=0.02; irate_star=Gamma_star*GammaP_star/beta-1; iratef_star=irate_star; d_star=0.4; rho_i=0.8; varalpha_P=1.5; varalpha_Y=0.1; /**************************** Prices parameter ***************************/ //Share of equipment in investment iota_2=0.478; //Share of domestic investment iota_1=0.449; //Share of inputs in production psi_1=0.64; psi_2=0.47; psi_3=0.313; //share of public services in inputs sq_3=0.05; //Shares of goods in inputs sg_1=0.858; sg_2=0.816; sg_3=0.885; //Share of imported goods in inputs sf_1=0.274; sf_2=0.273; sf_3=0.273; //capital shares gamma1=0.252; gamma2=0.46; gamma3=0.218; //elasticity of skilled and unskilled workers sigma=0.5; //share of skilled workers in sector 1 sA1=0.352; //share of skilled workers in sector 2 sA2=0.386; //share of unskilled workers in sector 1 (over 3) sB13=0.815; //Wage shares to skilled workers by sector wage1=0.741; wage2=0.815; wage3=0.903; //investment elasticities eta_i=0.6; eta_ix=0.9; //input elasticities eta_z1=0.6; eta_x1=0.9; eta_z2=0.6; eta_x2=0.9; eta_z3=0.6; eta_x3=0.9; //export elasticity eta_x=1.4; //import elasticity eta_m=0.9; eta_c=0.7; /**************************** Labour supply parameters *******************/ varsigmaA_star=0.19; varsigmaB_star=0.24; varsigmaC_star=0.24; wU_A_star=12135; wU_B_star=3501; wU_C_star=526; chiA_star=0.645; chiB_star=0.744; chiC_star=0.166; betaA_star=49905; betaB_star=28014; betaC_star=9687; /**************************** Consumption parameters *********************/ nu0_star=0.917; nu1A_star=0.274; nu2A_star=0.267; nu3A_star=0.213; nu1B_star=0.688; nu2B_star=0.770; nu3B_star=0.674; /**************************** Fiscal parameters **************************/ tau_o_star=0.191; tau_c_star=0.035; tau_k_star=0.25; tau_P_star=0.25; tau_C_star=0.147; tau_m_star=0.036; tau_i_star=0.011; tau_z_star=0.024; /**************************** Competition parameters *********************/ theta1_star=8.7; theta2_star=7.1; thetam=10; thetax=7; /**************************** Short-term adjustment parameters ***********/ phi_K=5; //Capital adjustment costs phi_C=0.9; //Consumption habits eta_FB=0.001; //Foreign debt elasticity rho_tr=0.8; eta_tr=0.9; rho_g=0.7; eta_g=0.000; rho_P=0.1; //Price adjustment costs in sector 1 alpha_P=0.5; rho_P2=0.1; //Price adjustment costs in sector 2 alpha_P2=0.5; rho_W=0.1; //Wage adjustemnt alpha_W=0.5; rho_theta=0.5; rho_e=0.99; rho_a1=0.9; rho_G=0.9; rho_c=0.9; /**************************** Steady state values ************************/ q2_star=1; q3_star=1; qz1_star=1; qz2_star=1; qz3_star=1; q_star=1; qi_star=1; lA_star=8167905; lB_star=3955962; lC_star=3804485; nA_star=10349496; nB_star=10930710; wA_star=45965; wB_star=17382; wC_star=5895; y1_star=4758; y2_star=2338; y3_star=1058; mc_c_star=67.7; mc_o_star=158.4; C_star=2134; c_star=2134; dc1_o_star=789; dc2_o_star=557; dc1_c_star=356; dc2_c_star=308; di11_star=71; di12_star=99; di13_star=34; di21_star=130; di22_star=181; di23_star=63; dz11_star=1720; dz12_star=487; dz13_star=119; dz21_star=676; dz22_star=429; dz23_star=115; dz33_star=53; mi1_star=71; mi2_star=99; mi3_star=34; mz1_star=649; mz2_star=183; mz3_star=44; mc_c_star=70; x_star=1275; k1_star=gamma1*y1_star*(1-psi_1);//2572; k2_star=gamma2*y2_star*(1-psi_2);//3657; k3_star=gamma3*y3_star*(1-psi_3);//1412; g3_star=820; tax_star=1131; tr_star=165; tax_L_star=235; inv3_star=130; def_star=116; interest_star=132; //DISPLAY parameters UA_star=21.1; UB_star=29; U_star=100-100*(lA_star+lB_star)/(lA_star/(1-UA_star/100)+lB_star/(1-UB_star/100)); /**************************** Shocked parameters *************************/ varsigmaA=varsigmaA_star; varsigmaB=varsigmaB_star; varsigmaC=varsigmaC_star; chiA=chiA_star; chiB=chiB_star; chiC=chiC_star; betaA=betaA_star; betaB=betaB_star; betaC=betaC_star; nu0=nu0_star; /**************************** Computed parameters ************************/ pA_star=varsigmaA*lA_star/((varsigmaA-1)*lA_star+nA_star); pB_star=varsigmaB*lB_star/((varsigmaB-1)*lB_star+(varsigmaC-1)*lC_star+nB_star); pC_star=varsigmaC*lC_star/((varsigmaB-1)*lB_star+(varsigmaC-1)*lC_star+nB_star); varpiU_A=wU_A_star/(1-tau_o_star)/wA_star; varpiU_B=wU_B_star/(1-tau_c_star)/wB_star; varpiU_C=wU_C_star/(1-tau_c_star)/wC_star; HC_A_star=betaA_star*pA_star^(1/2)*q2_star; HC_B_star=betaB_star*pB_star^(1/2)*q2_star; HC_C_star=betaC_star*pC_star^(1/2)*q2_star; varpi_A=1/(1-beta*(1-varsigmaA_star)*(1-pA_star)); varpi_B=chiB_star/(1-chiB_star)*HC_B_star/(chiB_star/(1-chiB_star)*HC_B_star-beta*chiB_star/(1-chiB_star)*(1-varsigmaB_star)*(1-pB_star)*HC_B_star-beta*chiC_star/(1-chiC_star)*(1-varsigmaC_star)*pC_star*HC_C_star); varpiF_B=beta*chiB_star/(1-chiB_star)*(1-varsigmaB_star)*(1-pB_star)*HC_B_star/(chiB_star/(1-chiB_star)*HC_B_star-beta*chiB_star/(1-chiB_star)*(1-varsigmaB_star)*(1-pB_star)*HC_B_star-beta*chiC_star/(1-chiC_star)*(1-varsigmaC_star)*pC_star*HC_C_star); varpi_C=chiC_star/(1-chiC_star)*HC_C_star/(1-beta*chiC_star/(1-chiC_star)*(1-varsigmaC_star)*(1-pC_star)*HC_C_star-beta*chiB_star/(1-chiB_star)*(1-varsigmaB_star)*pB_star*HC_B_star); varpiF_C=beta*chiC_star/(1-chiC_star)*(1-varsigmaC_star)*(1-pC_star)*HC_C_star/(chiC_star/(1-chiC_star)*HC_C_star-beta*chiC_star/(1-chiC_star)*(1-varsigmaC_star)*(1-pC_star)*HC_C_star-beta*chiB_star/(1-chiB_star)*(1-varsigmaB_star)*pB_star*HC_B_star); varpiP_A=beta/(1-beta*(1-varsigmaA_star)*(1-pA_star)); varpiP_B=beta/(1-beta*(1-varsigmaB_star)*(1-pB_star)); varpiP_C=beta/(1-beta*(1-varsigmaC_star)*(1-pC_star)); zeta_1=(theta1_star-1)/((theta1_star-1)-psi_1*qz1_star); zeta_2=(theta2_star-1)/((theta2_star-1)*q2_star-psi_2*qz2_star); zeta_3=q3_star/(q3_star-psi_3*qz1_star); yc_star=793.2; tax2_star= tau_P_star*(y1_star/theta1_star+q2_star*y2_star/theta2_star)+tau_k_star*(gamma1*y1_star*((1-1/theta1_star)-psi_1*qz1_star)+gamma2*y2_star*((1-1/theta2_star)-psi_2*qz2_star))+lA_star*wA_star*((nu1A_star+nu2A_star+nu3A_star)*tau_c_star+(1-nu1A_star+nu2A_star+nu3A_star)*tau_o_star)+lB_star*wB_star*((nu1B_star+nu3B_star)*tau_c_star+(1-nu1B_star+nu3B_star)*tau_o_star)+lC_star*wC_star*(tau_c_star*nu2B_star+(1-nu2B_star)*tau_o_star)+tau_m_star*(mc_c_star+mc_o_star)*q_star+tau_C_star*C_star; tax_P_star=tau_P_star*(y1_star/theta1_star+q2_star*y2_star/theta2_star); tax_C_star=tau_m_star*(mc_c_star+mc_o_star)*q_star+tau_C_star*C_star; tax_K_star=tau_k_star*(gamma1*y1_star*((1-1/theta1_star)-psi_1*qz1_star)+gamma2*y2_star*((1-1/theta2_star)-psi_2*qz2_star)); tax_L2_star=lA_star*wA_star*((nu1A_star+nu2A_star+nu3A_star)*tau_c_star+(1-nu1A_star+nu2A_star+nu3A_star)*tau_o_star)+lB_star*wB_star*((nu1B_star+nu3B_star)*tau_c_star+(1-nu1B_star+nu3B_star)*tau_o_star)+lC_star*wC_star*(tau_c_star*nu2B_star+(1-nu2B_star)*tau_o_star); a_txk=(gamma1*y1_star*((1-1/theta1_star)-psi_1*qz1_star)/(gamma1*y1_star*((1-1/theta1_star)-psi_1*qz1_star)+gamma2*y2_star*((1-1/theta2_star)-psi_2*qz2_star))); a_C1=(tau_m_star*(mc_c_star+mc_o_star)*q_star/(tau_m_star*(mc_c_star+mc_o_star)*q_star+tau_C_star*C_star)); a_C2=mc_c_star/(mc_c_star+mc_o_star); aL1=(lA_star*wA_star*((nu1A_star+nu2A_star+nu3A_star)*tau_c_star+(1-nu1A_star+nu2A_star+nu3A_star)*tau_o_star))/tax_L2_star; aL2=(lB_star*wB_star*((nu1B_star+nu3B_star)*tau_c_star+(1-nu1B_star+nu3B_star)*tau_o_star))/tax_L2_star; aL3=(nu1A_star+nu2A_star+nu3A_star)*tau_c_star/((nu1A_star+nu2A_star+nu3A_star)*tau_c_star+(1-nu1A_star+nu2A_star+nu3A_star)*tau_o_star); aL4=(nu1B_star+nu3B_star)*tau_c_star/((nu1B_star+nu3B_star)*tau_c_star+(1-nu1B_star+nu3B_star)*tau_o_star); aL5=tau_c_star*nu2B_star/(tau_c_star*nu2B_star+(1-nu2B_star)*tau_o_star); aT1=nu0_star*tr_star/yc_star; aT2=(nu1A_star+nu2A_star+nu3A_star)*lA_star*wA_star*(1-tau_c_star)/((nu1A_star+nu2A_star+nu3A_star)*lA_star*wA_star*(1-tau_c_star)+(nu1B_star+nu3B_star)*lB_star*wB_star*(1-tau_c_star)+nu2B_star*lC_star*wC_star*(1-tau_c_star)); aT3=(nu1B_star+nu3B_star)*lB_star*wB_star*(1-tau_c_star)/((nu1A_star+nu2A_star+nu3A_star)*lA_star*wA_star*(1-tau_c_star)+(nu1B_star+nu3B_star)*lB_star*wB_star*(1-tau_c_star)+nu2B_star*lC_star*wC_star*(1-tau_c_star)); ax1=tr_star/tax_star; ldA_1=wA_star/(wA_star+HC_A_star*(1-beta*(1-varsigmaA_star))); ldB_1=wB_star/(wB_star+HC_B_star*(1-beta*(1-varsigmaB_star))); ldC_1=wC_star/(wC_star+HC_C_star*(1-beta*(1-varsigmaC_star))); ldA_2=HC_A_star/(wA_star+HC_A_star*(1-beta*(1-varsigmaA_star))); ldB_2=HC_B_star/(wB_star+HC_B_star*(1-beta*(1-varsigmaB_star))); ldC_2=HC_C_star/(wC_star+HC_C_star*(1-beta*(1-varsigmaC_star))); model(linear); /****** Block A: Forward looking equations *******************************/ //Equation 1: Foreign bonds (iratef)/(1+iratef_star)=Gamma(1)+GammaP(1)+lambda-lambda(1)+eta_FB*FB; //Equation 2: Domestic bonds (irate)/(1+irate_star)=Gamma(1)+GammaP(1)+lambda-lambda(1); //Marginal costs: Price setting equation (Calvo pricing with dynamic indexation) //Inflation in sector 1 GammaP/GammaP_star=rho_P*(GammaP(-1)/GammaP_star)+beta*(GammaP(1)/GammaP_star-rho_P*(GammaP/GammaP_star))+(1-beta*alpha_P)*(1-alpha_P)/alpha_P*(mc1); //Inflation in sector 2 GammaP2/GammaP_star=rho_P2*(GammaP2(-1)/GammaP_star)+beta*(GammaP2(1)/GammaP_star-rho_P2*(GammaP2/GammaP_star))+(1-beta*alpha_P2)*(1-alpha_P2)/alpha_P2*(mc2-q2); //Labour demand //Sector 1, type A (mc1*(1-1/theta1_star)-psi_1*qz1*qz1_star)/((1-1/theta1_star)-psi_1*qz1_star)+y1-(1-1/sigma)*l1-1/sigma*l1A=ldA_1*wA+ldA_2*HC_A+(1-ldA_1-ldA_2)*(HC_A(1)); //Sector 1, type B (mc1*(1-1/theta1_star)-psi_1*qz1*qz1_star)/((1-1/theta1_star)-psi_1*qz1_star)+y1-(1-1/sigma)*l1-1/sigma*l1B=ldB_1*wB+ldB_2*HC_B+(1-ldB_1-ldB_2)*(HC_B(1)); //Sector 2, type A (mc2*(1-1/theta2_star)-psi_2*qz2*qz2_star)/((1-1/theta2_star)*q2_star-psi_2*qz2_star)+y2-(1-1/sigma)*l2-1/sigma*l2A=ldA_1*wA+ldA_2*HC_A+(1-ldA_1-ldA_2)*(HC_A(1)); //Sector 2, type C (mc2*(1-1/theta2_star)-psi_2*qz2*qz2_star)/((1-1/theta2_star)*q2_star-psi_2*qz2_star)+y2-(1-1/sigma)*l2-1/sigma*lC=ldC_1*wC+ldC_2*HC_C+(1-ldC_1-ldC_2)*(HC_C(1)); //Sector 3, type A (q3-psi_3*qz3*qz3_star)/(q3_star-psi_3*qz3_star)+g3-(1-1/sigma)*l3-1/sigma*l3A=ldA_1*wA+ldA_2*HC_A+(1-ldA_1-ldA_2)*(HC_A(1)); //Sector 3, type B (q3-psi_3*qz3*qz3_star)/(q3_star-psi_3*qz3_star)+g3-(1-1/sigma)*l3-1/sigma*l3B=ldB_1*wB+ldB_2*HC_B+(1-ldB_1-ldB_2)*(HC_B(1)); //Capital cost mu=beta*(1-delta)/Gamma_star*(mu(1)-Gamma)+(1-beta*(1-delta)/Gamma_star)*(lambda-Gamma+R); //Wage bargaining: wage target wA_bar=varpiU_A*(e_wu)+(1-varpiU_A)*(varpi_A*(HC_A)+(1-varpi_A)*(-pA(1)*pA_star/(1-pA_star)+HC_A(1))); wB_bar=varpiU_B*(e_wu)+(1-varpiU_B)*(varpi_B*(HC_B)-varpiF_B*(-pB(1)*pB_star/(1-pB_star)+HC_B(1))+(1-varpi_B+varpiF_B)*(pC(1)+HC_C(1))); wC_bar=varpiU_C*(e_wu)+(1-varpiU_C)*(varpi_C*(HC_C)-varpiF_C*(-pC(1)*pC_star/(1-pC_star)+HC_C(1))+(1-varpi_C+varpiF_C)*(pB(1)+HC_B(1))); //Wage setting: Calvo wA-wA(-1)+GammaP/GammaP_star-rho_W*(GammaP(-1)/GammaP_star)=beta*(wA(1)-wA+GammaP(1)/GammaP_star-rho_W*(GammaP/GammaP_star))+(1-beta*alpha_W)*(1-alpha_W)/alpha_W*(wA_bar-wA); wB-wB(-1)+GammaP/GammaP_star-rho_W*(GammaP(-1)/GammaP_star)=beta*(wB(1)-wB+GammaP(1)/GammaP_star-rho_W*(GammaP/GammaP_star))+(1-beta*alpha_W)*(1-alpha_W)/alpha_W*(wB_bar-wB); wC-wC(-1)+GammaP/GammaP_star-rho_W*(GammaP(-1)/GammaP_star)=beta*(wC(1)-wC+GammaP(1)/GammaP_star-rho_W*(GammaP/GammaP_star))+(1-beta*alpha_W)*(1-alpha_W)/alpha_W*(wC_bar-wC); /************** Block B: Autoregressive processes ************************/ //Public debt dynamics det=(det(-1)+GDP-GDP(-1)-(GammaP/GammaP_star))/(Gamma_star*GammaP_star)+(1-1/(Gamma_star*GammaP_star))*def; //Dynamics of hiring lA=(1-varsigmaA)*lA(-1)+varsigmaA*H_A; lB=(1-varsigmaB)*lB(-1)+varsigmaB*H_B; lC=(1-varsigmaC)*lC(-1)+varsigmaC*H_C; //Hiring probabilities pA=H_A-pA_star*(1-1/varsigmaA)*lA(-1)-(1-pA_star*(1-1/varsigmaA))*nA(-1); pB=H_B-pC_star*(1-1/varsigmaC)*lC(-1)-pB_star*(1-1/varsigmaB)*lB(-1)-(1-pB_star*(1-1/varsigmaB)-pC_star*(1-1/varsigmaC))*nB(-1); pC=H_C-pC_star*(1-1/varsigmaC)*lC(-1)-pB_star*(1-1/varsigmaB)*lB(-1)-(1-pB_star*(1-1/varsigmaB)-pC_star*(1-1/varsigmaC))*nB(-1); //Participation reacts to employment nA=0.9*nA(-1)+0.04*lA(-1)+e_nA; nB=0.9*nB(-1)+0.06*lB(-1)+e_nB; //Hiring costs HC_A=1/2*pA+q2+(betaA/betaA_star-1)+e_h; HC_B=1/2*pB+q2+(betaB/betaB_star-1)+e_h; HC_C=1/2*pC+q2+(betaC/betaC_star-1)+e_h; //Shadow price of consumption lambda=cs-qc_o-(c_o-phi_C*c_o(-1))/(1-phi_C); //Shadow price of capital mu=lambda+qi+phi_K*(inv-k(-1)); //Capital accumulation k=(1-delta)/Gamma_star*k(-1)+(1-(1-delta)/Gamma_star)*inv; //exchange rate e_rate=rho_e*e_rate(-1)+e_e; //SHOCKS DYNAMICS //Productivity in sector 1 A1=rho_a1*A1(-1)+e_a1; //Productivity growth Gamma=rho_G*Gamma(-1)+e_G; //Consumption shock cs=rho_c*cs(-1)+e_c; /************** Block C: Variables definition ****************************/ //Equation 4: Real exchange rate q=q(-1)+GammaPf-GammaP+e_rate-e_rate(-1); //Definition of inflation in sector 2 GammaP2=q2-q2(-1)+GammaP; //Definition of aggregate labour demand by sector l1=wage1*l1A+(1-wage1)*l1B; l2=wage2*l2A+(1-wage2)*lC; l3=wage3*l3A+(1-wage3)*l3B; //Definition of labour demand by skill level lA=sA1*l1A+sA2*l2A+(1-sA1-sA2)*l3A; lB=sB13*l1B+(1-sB13)*l3B; //Definition of the total capital stock k=(k1*k1_star+k2*k2_star+k3*k3_star)/(k1_star+k2_star+k3_star); //Definition of iquidity-constrained households income y_c=aT1*tr+(1-aT1)*(aT2*(wA+lA)+aT3*(wB+lB)+(1-aT2-aT3)*(wC+lC)); //Definition of taxes tax_P=((y1)*(y1_star/theta1_star/(y1_star/theta1_star+q2_star*y2_star/theta2_star))+(y2)*(1-(y1_star/theta1_star/(y1_star/theta1_star+q2_star*y2_star/theta2_star)))); tax_K=((1-zeta_1)*qz1+y1)*a_txk+(1-a_txk)*(zeta_2*(q2)+(1-zeta_2)*qz2+y2); tax_C=(q+(mc_c*a_C2+mc_o*(1-a_C2)))*a_C1+(1-a_C1)*((dc1_o*dc1_o_star+dc1_c*dc1_c_star+(dc2_o*dc2_o_star+dc2_c*dc2_c_star)*q2_star+q2*(dc2_c_star+dc1_c_star))/(dc1_c_star+dc1_o_star+q2_star*(dc2_c_star+dc2_o_star))); tax_L=aL1*(lA+wA)+aL2*(lB+wB)+(1-aL1-aL2)*(wC+lC); tax=(tax_P*tax_P_star+tax_K*tax_K_star+tax_C*tax_C_star+tax_L*tax_L_star)/tax_star; //Public deficit definition (def+GDP)*def_star+tax*tax_star=tr*tr_star+g3*g3_star+inv3*inv3_star+(irate(-1)/irate_star+det(-1)+GDP(-1)-GammaP/GammaP_star)*interest_star; //Definition of GDP GDP=(y1*y1_star-dz11*dz11_star-dz21*dz21_star+y2*y2_star-dz12*dz12_star-dz22*dz22_star+g3*y3_star-dz13*dz13_star-dz23*dz23_star-g3*dz33_star)/(y1_star-dz11_star-dz21_star+y2_star-dz12_star-dz22_star+y3_star-dz13_star-dz23_star-dz33_star); /************** Block D: Optimal prices definition ***********************/ //Investment prices: 22 qi=iota_2*(1-iota_1)*q+(1-iota_2)*q2; //Intermediate input prices: 24-26 qz1=(1-sg_1)*q2+(sg_1)*sf_1*q; qz2=(1-sg_2)*q2+(sg_2)*sf_2*q; qz3=sq_3*q3+(1-sq_3)*((1-sg_3)*q2+(sg_3)*sf_3*q); //Production prices: 27-29 y1-l1=1/(1-gamma1)*(-gamma1*R+A1+gamma1*(mc1*(1-1/theta1_star)-psi_1*qz1*qz1_star)/((1-1/theta1_star)-psi_1*qz1_star)); y2-l2=1/(1-gamma2)*(-gamma2*R+e_a2+gamma2*(mc2*(1-1/theta2_star)-psi_2*qz2*qz2_star)/((1-1/theta2_star)*q2_star-psi_2*qz2_star)); g3-l3=1/(1-gamma3)*(-gamma3*R+gamma3*(q3-psi_3*qz3*qz3_star)/(q3_star-psi_3*qz3_star)); //Consumption prices for optimizing agents: 48 & 49 qx_o=(q)*mc_o_star/(mc_o_star+dc1_o_star); qc_o=(mc_o_star+dc1_o_star)/((mc_o_star+dc1_o_star)+q2_star*dc2_o_star)*qx_o+(1-(mc_o_star+dc1_o_star)/((mc_o_star+dc1_o_star)+q2_star*dc2_o_star))*(q2); //Consumption prices for liquidity-constrained agents" 53 & 54 qx_c=(q)*mc_c_star/(mc_c_star+dc1_c_star); qc_c=(mc_c_star+dc1_c_star)/((mc_c_star+dc1_c_star)+q2_star*dc2_c_star)*qx_c+(1-(mc_c_star+dc1_c_star)/((mc_c_star+dc1_c_star)+q2_star*dc2_c_star))*(q2); /************** Block E: Optimal demand definition ***********************/ //Capital demand k1=y1+(mc1*(1-1/theta1_star)-psi_1*qz1*qz1_star)/((1-1/theta1_star)-psi_1*qz1_star)-R; k2=y2+(mc2*(1-1/theta2_star)-psi_2*qz2*qz2_star)/((1-1/theta2_star)*q2_star-psi_2*qz2_star)-R; k3=g3+(q3-psi_3*qz3*qz3_star)/(q3_star-psi_3*qz3_star)-R; //Investment k1=(1-delta)/Gamma_star*k1(-1)+(1-(1-delta)/Gamma_star)*inv1; k2=(1-delta)/Gamma_star*k2(-1)+(1-(1-delta)/Gamma_star)*inv2; k3=(1-delta)/Gamma_star*k3(-1)+(1-(1-delta)/Gamma_star)*inv3; //Sector 1 di11=inv1+eta_i*qi+(eta_ix-eta_i)*(1-iota_1)*q; di21=inv1+eta_i*(qi-q2); mi1=inv1+eta_i*qi-(eta_ix*iota_1+eta_i*(1-iota_1))*q; //sector 2 di12=inv2+eta_i*qi+(eta_ix-eta_i)*(1-iota_1)*q; di22=inv2+eta_i*(qi-q2); mi2=inv2+eta_i*qi-(eta_ix*iota_1+eta_i*(1-iota_1))*q; //sector 3 di13=inv3+eta_i*qi+(eta_ix-eta_i)*(1-iota_1)*q; di23=inv3+eta_i*(qi-q2); mi3=inv3+eta_i*qi-(eta_ix*iota_1+eta_i*(1-iota_1))*q; //Intermediate inputs //sector 1 dz21=y1+eta_z1*(qz1-q2); dz11=y1+eta_z1*qz1+(eta_x1-eta_z1)*sf_1*q; mz1=y1+eta_z1*qz1-(eta_x1*(1-sf_1)+eta_z1*sf_1)*q; //sector 2 dz22=y2+eta_z2*(qz2-q2); dz12=y2+eta_z2*qz2+(eta_x2-eta_z2)*sf_2*q; mz2=y2+eta_z2*qz2-(eta_x2*(1-sf_2)+eta_z2*sf_2)*q; //Sector 3 dz23=g3+eta_z3*(qz3-q2); dz13=g3+eta_z3*qz3+(eta_x3-eta_z3)*sf_3*q; mz3=g3+eta_z3*qz3-(eta_x3*(1-sf_3)+eta_z3*sf_3)*q; //consumption of optimizing agents dc1_o=mc_o+eta_m*(q); dc2_o=mc_o+eta_m*(q-qx_o)+eta_c*(q2+qx_o); c_o=(dc2_o*dc2_o_star+dc1_o*dc1_o_star+mc_o*mc_o_star)/(dc2_o_star+dc1_o_star+mc_o_star); //consumption of constrained agents dc1_c=y_c+eta_c*qc_c+(eta_m-eta_c)*qx_c; dc2_c=y_c+eta_c*(qc_c-q2); mc_c=y_c-eta_m*(q)+eta_c*qc_c+(eta_m-eta_c)*qx_c; /************** Block F: Policy rules ************************************/ //Equation 3: Taylor rule for the domestic economy (irate)=rho_i*(irate(-1))+varalpha_P*(GammaP)+varalpha_Y*(GDP-GDP(-1)); //Equation 5: Taylor rule for the foreign economy iratef=0.8*iratef(-1)+1.5*(GammaPf)+e_if; //Fiscal rule: Transfer tr=rho_tr*tr(-1)-(1-rho_tr)*eta_tr*(det(-1)); //Fiscal rule: Spending g3=rho_g*g3(-1)+(1-rho_g)*(-eta_g*(det(-1)))+e_g; /**************************** Bloc G: Market clearing ********************/ //Market clearing in sector 1 y1*y1_star=di11*di11_star+di12*di12_star+di13*di13_star+dz11*dz11_star+dz12*dz12_star+dz13*dz13_star+(e_x+eta_x*q)*x_star+dc1_c*dc1_c_star+dc1_o*dc1_o_star; //Market clearing in sector 2 y2*y2_star=di21*di21_star+di22*di22_star+di23*di23_star+dz21*dz21_star+dz22*dz22_star+dz23*dz23_star+dc2_c*dc2_c_star+dc2_o*dc2_o_star; //Trade account balance gives the import of optimizing agents x_star*(e_x+(eta_x-1)*q)=mc_c_star*mc_c+mc_o*mc_o_star+mi1*mi1_star+mi2*mi2_star+mi3*mi3_star+mz1*mz1_star+mz2*mz2_star+mz3*mz3_star+FB*(1-(1+iratef_star)/(Gamma_star*GammaP_star)); /****************************** Bloc H: Observed variables ***************/ gi_obs=irate; ginv_obs=inv; gg3_obs=g3; gy1_obs=y1; gy2_obs=y2; gq2_obs=q2; gGammaP_obs=GammaP; gw_obs=((wA+lA)*wA_star*lA_star+(wB+lB)*wB_star*lB_star+(wC+lC)*wC_star*lC_star)/(wA_star*lA_star+wB_star*lB_star+wC_star*lC_star); gl_obs=(lA*lA_star+lB*lB_star+lC*lC_star)/(lA_star+lB_star+lC_star); gc_obs=c_o*(1-yc_star/c_star)+(y_c-qc_c)*yc_star/c_star; end; initval; lA=0; lB=0; lC=0; pA=0; pB=0; pC=0; wA=0; wB=0; wC=0; q2=0; q3=0; q=0; l1=0; l2=0; l3=0; y1=0; y2=0; inv1=0; inv2=0; inv3=0; di11=0; di12=0; di13=0; di21=0; di22=0; di23=0; mi1=0; mi2=0; mi3=0; dz11=0; dz12=0; dz13=0; dz21=0; dz22=0; dz23=0; mz1=0; mz2=0; mz3=0; y_c=0; tr=0; tax=0; tax_P=0; tax_K=0; tax_L=0; tax_C=0; mc_c=0; mc_o=0; dc1_o=0; dc2_o=0; dc1_c=0; dc2_c=0; qx_o=0; qc_o=0; qx_c=0; qc_c=0; nA=0; nB=0; GDP=0; H_C=0; H_A=0; H_B=0; HC_A=0; HC_B=0; HC_C=0; mc1=0; mc2=0; GammaP=0; l1A=0; l1B=0; l2A=0; l3A=0; l3B=0; e_rate=0; FB=0; iratef=0; irate=0; GammaPf=0; GammaP2=0; c_o=0; lambda=0; mu=0; k=0; k1=0; k2=0; k3=0; inv=0; def=0; det=0; g3=0; wA_bar=0; wB_bar=0; wC_bar=0; qi=0; R=0; qz1=0; qz2=0; qz3=0; A1=0; Gamma=0; end; steady; //resid(1); //check; stoch_simul; estimated_params; phi_C, beta_pdf, 0.95, 0.1; phi_K, normal_pdf, 10, 2; //eta_FB, normal_pdf, 0.001, 0.01; rho_g, normal_pdf, 0.35, 0.2; eta_g, beta_pdf, 0.5, 0.2; rho_P, beta_pdf, 0.6, 0.2; alpha_P, beta_pdf, 0.5, 0.2; rho_P2, beta_pdf, 0.65, 0.2; alpha_P2, beta_pdf, 0.5, 0.2; rho_W, beta_pdf, 0.5, 0.2; alpha_W, beta_pdf, 0.55, 0.2; rho_i, beta_pdf, 0.5, 0.2; varalpha_P, normal_pdf, 1.9, 0.5; varalpha_Y, normal_pdf, 0.01, 0.5; rho_a1, beta_pdf, 0.9, 0.1; rho_G,beta_pdf, 0.9, 0.1; stderr e_a1, inv_gamma_pdf, 0.02, inf; stderr e_a2, inv_gamma_pdf, 0.02, inf; stderr e_nA, inv_gamma_pdf, 0.02, inf; stderr e_nB, inv_gamma_pdf, 0.02, inf; stderr e_x, inv_gamma_pdf, 0.04, inf; stderr e_e, inv_gamma_pdf, 0.05, inf; stderr e_c, inv_gamma_pdf, 0.02, inf; stderr e_if, inv_gamma_pdf, 0.03, inf; stderr e_g, inv_gamma_pdf, 0.03, inf; stderr e_h, inv_gamma_pdf, 0.1, inf; stderr e_wu, inv_gamma_pdf, 0.1, inf; stderr e_G, inv_gamma_pdf, 0.02, inf; end; varobs gi_obs ginv_obs gy1_obs gy2_obs gGammaP_obs gg3_obs gl_obs gw_obs gc_obs gq2_obs; model_info; identification;