// A TWO COUNTRY MONETARY UNION MODEL var R LZ_Z_star LYhf_Z_star LYhh_Z LYfh_Z LYhf LYhh LYfh LY_Z LC_Z LI_Z LZ LY LC LI LI_K LA LL LMUC_Z LMRS LW MC LRK Q G_Y G_K G_C G_Z G_A G_L GUC PIw LPh LPf PI PIh PIf LY_star E_A E_PI E_R E_K E_D E_P E_W PI_obs Y_obs;//LZ_star //R: Nominal interest rate; LZ_Z_star: Home demand to foreign demand ratio; LYhf_Z_star;Export to foreign demand ratio; LYhh_Z;Home production for the dometic economy to home demand ratio; LYfh_Z:Import to home demand ratio; LYhf:Export; LYhh:Home production for the home economy; LYfh:Import; LY_Z:GDP to demand ratio; LC_Z:Consumption to demand ratio; LI_Z:Investment to demand ratio; LZ:real demand; LY:real gdp; LC:real consumption; LI:investment; LI_K:investment to capital ratio; LA:technology; LL:labor; MUC_Z:marginal utility of consumption to demand ratio; LW;real wage; MC:marginal cost; LRK:Real return on capital; Q:Tobin's Q; G_Y:GDP growth; G_K:Capital growth; G_C:consumption growth; G_Z:demand growth; G_A:technology growth; G_Llabor growth; GUCmarginal consumption utility growth; PIw:Nominal wage growth; LPh:home prices; LPf:foreign prices; PI:home inflation; PIh:local producer inflation; PIf:foreign inflation; LZ_star:foreign demand; LY_star:foreign gdp; E_A E_PI E_R E_K E_D PI_obs Y_obs varexo EPS_A EPS_PI EPS_R EPS_K EPS_D EPS_P EPS_W; parameters betae alphae h sigmae phi eta theta_h delta_h rhoA rhoPI rhoS rhoR rhoK rhoW rhoD rhoP phi1 phi2 phi3 phi4 theta_st delta_st gamai gamaw delta viw tetaw gamap Tech_G Tech_G_star gamaw_star Infl alphae_st MC_ss LW_ss LL_ss LMRS_ss I_Y C_Y; gamai = 30; //Investment adjustment cost parameter gamaw = 1; // degree of wage indexation to the CPI delta = 0.025; //DEPRECIATION RATE viw = 0.6; //Calvo parameters for wage tetaw = 6; // elasticity of substitution of labor service gamap = 0.588; //wage share in output //Growth rate steady state Tech_G_star = 0.005; Tech_G = Tech_G_star; Infl = 0.005; alphae_st = 0.6; //degree of openess of the foreign economy betae = 0.99; // rate of time preferences alphae = 0.65; //degree of openness h = 0.65; //habit persistence sigmae = 2; // inverse elasticity of substitution phi = 3; //Inverse labor elasticity eta = 0.8; //Elasticity of substitution between domestic and foreign goods //Philips curve parameters theta_h = 0.75; delta_h = 0.50; theta_st= 0.93; delta_st= 0.29; //Shocks parameters rhoA = 0.75; rhoPI = 0.5; rhoD = 0.25; rhoS = 0.5; rhoR = 0.5; rhoK = 0.5; rhoW = 0.5; rhoP = 0.5; //Monetary policy parameters phi1 = 1.70; phi2 = 0.32; phi3 = 0.2; phi4 = 0.13; //Steady-state value I_Y = 0.15; C_Y = 0.85; MC_ss = gamap*(1 - 1/(gamap)*(1-(1-gamap)*(log(delta + Tech_G_star)-log(I_Y)-1)) + log(alphae)) + (1-gamap)* (log(1/betae-1 + delta+Tech_G_star)) -(1-gamap)*log(1-gamap) + gamap*log(gamap); LL_ss = 1/(gamap)*(1-(1-gamap)*(log(delta + Tech_G_star)-log(I_Y)-1)); LW_ss = 1-LL_ss+ log(alphae); LMRS_ss = sigmae*log(C_Y*(1-h))-sigmae + phi*LL_ss; // MODEL EQUATIONS model; #mu_f_d = betae/(1+delta_h*betae); #mu_b_d = delta_h/(1+delta_h*betae); #lambda_d = (1-theta_h)*(1-theta_h*betae)/(theta_h*(1+delta_h*betae)); //DOMESTIC ECONOMY //------------------------------------------------------------------------------------------------------------------ // 1 (A) Demand definition 1 = exp(LI_Z) + exp(LC_Z)+1/(2*gamai)*(exp(LI_K(+1))-Tech_G_star-delta)^2*exp(LI_Z-LI_K(-1))/(1+G_Z); // 2 (B) Export demand //exp(LYhf_Z_star) = alphae_st*exp(LPh-LPf)^-eta; LYhf_Z_star = log(alphae_st) - (LPh-LPf)*eta; // 3 (C) Home production demand //exp(LYhh_Z) = (1-alphae)* exp(LPh)^-eta; LYhh_Z = log(1-alphae) - (LPh)*eta; // 4 (D) Import demand //exp(LYfh_Z) = alphae*exp(LPf)^-eta; LYfh_Z = log(alphae) -(LPf)*eta; // 5 (F) GDP def, exp approach exp(LY_Z) = 1 + exp(LYfh_Z)*exp(LPf) - exp(LYhf_Z_star)*exp(-LZ_Z_star)*exp(LPh); // 6 (H) Intermediate goods production G_Y = (1-gamap)*G_K(-1) + gamap*(G_A+G_L); // 7 (I) Technology G_A = Tech_G + LA - LA(-1) + E_A; // 8 (J) Inputs market condition LRK - LRK(-1) = G_L + PIw-PI - G_K(-1); // 9 (K) Log real Marginal cost MC = gamap*LW + (1-gamap)* LRK -(1-gamap)*log(1-gamap) + gamap*log(gamap) + E_PI; // 10 (L) Philips curve for home prices (PIh) =Infl+ mu_f_d*(PIh(+1)-Infl) + mu_b_d*(PIh(-1)-Infl) + lambda_d*(MC-MC_ss); // 11 (N) Wages curve (PIw-Infl-Tech_G_star) = betae*(PIw(+1)-Infl-Tech_G_star) + gamaw*((PI(-1)-Infl)-betae*(PI-Infl)) + (1-viw)*(1-betae*viw)* (LMRS-(-phi*LL_ss+sigmae-sigmae*log(C_Y*(1-h))) +LW_ss-LW + E_W) /(viw*(1+phi*tetaw)); // 12 (O) Capital accumulation equation G_K - Tech_G_star= exp(LI_K) - delta-Tech_G_star ; // 13 (Definition) Marginal utility of consumption + Add preference shock ? 1/betae-1= GUC(+1) + (R - (PI(+1)-Infl)); // 14 (R) Tobin's Q equation //Q = 1/(((1+R-PI(+1)+Infl)))*(exp(LRK(+1)+(1-delta-Tech_G_star)*Q(+1)); //-0.5/gamai*((exp(LI_K(+1)))^2-(Tech_G+delta)^2) Q = 1/(((1+R-PI(+1)+E_K+Infl)))*(exp(LRK(+1) -1/(2*gamai)*((exp(LI_K(+1)))^2-(Tech_G_star+delta)^2))+(1-delta-Tech_G_star)*Q(+1)); //15 Log mqrginql utility of consumtion LMUC_Z = -sigmae*log(exp(E_P)*exp(LC_Z)*(1-h/(1+G_C-G_Z))); //Q = 1 - 1/gamai*(exp(LI_K)-delta-Tech_G_star); // 16 Marginal rate of substitution LMUC - LMUL //LMRS =(LMUC_Z+sigmae*log(C_Y*(1-h))) + sigmae*(LZ-1) - phi*(LL-LL_ss); LMRS =(LMUC_Z) + sigmae*(LZ) - phi*(LL); //DOMESTIC VARIABLE DEFINITION //-------------------------------------------------------------------------------------------------------------------- //17 LYhh_Z = LYhh - LZ; //18 LYfh_Z = LYfh - LZ; //19 LYhf_Z_star = LYhf - LY_star; //LZ_star //20 LZ_Z_star = LZ - LY_star; //LZ_star //21 LY_Z = LY - LZ; //22 LI_Z = LI - LZ; //23 LC_Z = LC - LZ; //24 G_L = LL - LL(-1); //25 G_C = Tech_G_star + LC - LC(-1); //26 G_Z = Tech_G_star + LZ - LZ(-1); //27 G_Y = Tech_G_star + LY - LY(-1); //28 G_A = Tech_G_star + LA- LA(-1)+ E_A; //29 Marginal utility of consumtion grozth GUC = LMUC_Z - LMUC_Z(-1) + sigmae*(G_Z-Tech_G_star); //30 LI_K - LI_K(-1) = LI-LI(-1) - (G_K(-1)-Tech_G_star); // 31 Ph definition ( ) PIh - PI = LPh - LPh(-1); // 32 Wage definition PIw = PI+ Tech_G_star + LW - LW(-1); // 33 CPI PIh - PI= -(1-alphae)/alphae * (PIf- PI); // 34 Foreign price definition PIf - PI = LPf - LPf(-1); // DOMESTIC SHOCKS //--------------------------------------------------------------------------------------------------------------------- // 35 E_K = rhoK*E_K(-1) + EPS_K; // 36 Technology shock E_A = rhoA*E_A(-1) + EPS_A; // 37 Cost-push shock E_PI = rhoPI*E_PI(-1) + EPS_PI; //38 Monetary policy shock E_R = rhoR*E_R(-1) +EPS_R; //39 preference shock policy shock E_P = rhoP*E_P(-1) +EPS_P; //40 wage shock E_W = rhoW*E_W(-1) +EPS_W; //COMMON BLOCK //--------------------------------------------------------------------------------------------------------------------- //41 (S) Risk sharing condition (In deviation from steady state) LMUC_Z+sigmae*log(C_Y*(1-h)) = (LY_star-(1+log(alphae/alphae_st))) - h*(LY_star(-1)-(1+log(alphae/alphae_st))) + (1-h)/sigmae*LPf; // MONETARY POLICY // 42 R = rhoR*R(-1) +(1-rhoR)*(1/betae-1) + (1-rhoR)*(phi1*(PIf-Infl) + phi2*(LY_star-LY_star(-1))) + phi3*(PIf-PIf(-1)) + phi4*(LY_star-LY_star(-1)) + E_R; //FOREIGN BLOCK //--------------------------------------------------------------------------------------------------------------------- #lambda_st= ((1-theta_st)*(1-theta_st*betae))/(theta_st*(1-delta*theta_st)); //43 LY_star = (1/(1+h))*LY_star(+1) + (h/(1+h))*LY_star(-1) - ((1-h)/(sigmae*(1+h)))*(R-(1/betae-1) - (PIf(+1)-Infl)) + E_D; //44 Philips curve PIf =Infl+ (delta/(1+delta*betae))*(PIf(-1)-Infl) + (betae/(1+delta*betae))*(PIf(+1)-Infl) + lambda_st*(LY_star-(1+log(alphae/alphae_st))); //LZ_star = LY_star; //45 E_D = rhoD*E_D(-1)+ EPS_D; //END ---------------------------------------------------------------------------------------------------------------- //OBSERVATION EQUATIONS PI_obs = PI ; Y_obs-Y_obs(-1) = LY-LY(-1); end; // CALCULATION OF THE STEADY STATE //resid(1); steady; check; // SHOCK STRUCTURE shocks; var EPS_A; stderr 0.015; var EPS_PI; stderr 0.005; var EPS_R; stderr 0.0035; var EPS_K; stderr 0.005;//.1063; var EPS_P; stderr 0.08; var EPS_D; stderr 0.04; var EPS_W; stderr 0.3; end; varobs Y_obs PI_obs ; observation_trends; Y_obs (Tech_G_star); end; // STOCHASTIC SIMULATION Stoch_simul(periods=1000,order = 2) PI Q G_A G_Y G_Z; //options_.ftol=1.e-6; estimated_params; //phi1, normal_pdf, 1.7, 0.1; //phi2, normal_pdf, 0.125, 0.1; //phi3, normal_pdf, 0.3, 0.1; //phi4, normal_pdf, 0.0625, 0.05; //rhoA, BETA_PDF, 0.85, 0.075,0,0.99; //rhoPI, BETA_PDF, 0.85, 0.075,0,0.99; //rhoD, BETA_PDF, 0.85, 0.075,0,0.99; rhoS, BETA_PDF, 0.85, 0.075,0,0.99; //rhoR , BETA_PDF, 0.85, 0.075,0,0.99; rhoK, BETA_PDF, 0.85, 0.075,0,0.99; //rhoW, BETA_PDF, 0.85, 0.075,0,0.99; //rhoP, BETA_PDF, 0.85, 0.075,0,0.99; stderr EPS_A, GAMMA_PDF, 0.01, 0.006, 0, inf; stderr EPS_PI, GAMMA_PDF, 0.01, 0.0006, 0, inf; stderr EPS_R, GAMMA_PDF, 0.01, 0.006, 0, inf; stderr EPS_K, GAMMA_PDF, 0.001, 0.00006, 0, inf; stderr EPS_P, GAMMA_PDF, 0.01, 0.006, 0, inf; stderr EPS_W, GAMMA_PDF, 0.01, 0.006, 0, inf; end; //estimation(datafile=data, mode_compute=5,mh_replic=20000, mh_nblocks=2, mh_drop=0.30, mh_jscale=0.60, filtered_vars, bayesian_irf) PI; //shock_decomposition PI R G_Y G_Z Q;