// Dynare code for ARGEMmin (Dynare version 4.2.0) // Guillermo Escud? October 2011. // ARGEMmin: A DSGE model for a SOE that has systematic intervention in // FX market and uses 1 or 2 policy rules and hence 3 general regimes: // MER: Managed Exchange Rate regime: 2 feedback rules // FER: Floating Exchange Rate regime: 1 feedback rule (Taylor rule) for the interest rate // PER Pegged Exchange Rate regime: 1 (possibly feedback) rule for the rate of nominal depreciation // FOR SIMPLE POLICY RULES OR OPTIMAL SIMPLE RULES (osr): // For the MER regime: // Use the 2 simple policy rules // For the FER regime: // Replace the second policy rule by equation 'r=r_ss' // For the PER regime: // Replace the first policy rule by equation 'b=b_ss' // FOR OPTIMAL RULES UNDER COMMITMENT (ramsey_policy): // Comment out the 2 policy rules // Comment out 'steady', 'check', 'resid', and 'stoch_simul' // Use 'planner_objective' and 'ramsey_policy' // For MER regime use option 'instruments=(ii,delta)' // For FER regime use option 'instruments=(ii)' and the equation 'r=r_ss' // For PER regime use option 'instruments=(delta)' and the equation 'b=b_ss' close all; // ENDOGENOUS VARIABLES var ii delta r b e piC Y d C pii Q mc Deltta pC pStar varphiM tauM m X TB w z_piStar z_piStarX z_G z_epsilon z_iStar z_phiStar GammaP PsiP real_ii tax qf CA N Utility dii ddelta gammaD gammaM gammaR ; // EXOGENOUS VARIABLES varexo eps_epsilon eps_G eps_iStar eps_phiStar eps_piStar eps_piStarX ; // PARAMETERS parameters // Monetary and XR simple policy rules h_0 h_1 h_2 h_3 //Interest rate Simple Rule k_0 k_1 k_2 k_3 k_4 //Exchange rate Simple Rule //Weights for ramsey ad-hoc CB loss function omega_piC omega_Y omega_e omega_r omega_dii omega_ddelta // Persistence parameters in shock variables rhoPiStar rhoPiStarX rhoG rhoEpsilon rhoiStar rhoPhiStar rhoPiStarNX // Great ratios gammaR_ss gammaD_ss gammaM_ss pCCtoy mtoy btoy gtopCC tbetoy // General piT betta sigmaC a_D thetta thettaC sigmaN alfa bA bX kappaX varepsilon_L varepsvarphi_D alpha_1 alpha_2 tau_D xiN betta_1 betta_2 betta_3 EC_speed_N EC_speed_X Coint_param // Steady state values of endogenous variables Y_ss piStar_ss iStar_ss phiStar_ss pStar_ss e_ss C_ss d_ss r_ss m_ss b_ss mc_ss Q_ss GammaP_ss PsiP_ss N_ss pC_ss X_ss TB_ss Deltta_ss w_ss varphiM_ss tauM_ss tax_ss qf_ss Utility_ss ; // PARAMETER VALUES // Monetary and XR simple policy rules (these don't affect the SS) // If k_4<0, h_0+h_1 must be greater than 1 to avoid indeterminacy and unit root //MER (Managed XR) h_0=0.33; h_1=1.26; h_2=0.02; h_3=0.12; k_0=-0.03; k_1=-0.07; k_2=-0.08; k_3=-0.43; k_4=-0.08; //FER //h_0=0.01; h_1=2.04; h_2=-0.05; h_3=0.04; //PER //k_0=-0.26; k_1=-2.08; k_2=-2.36; k_3=-1.09; k_4=-2.18 ; // Calibrated steady state values of endogenous variables Y_ss=1.443; piStar_ss=1.0; iStar_ss=1.03^0.25; phiStar_ss=1.005^0.25; pStar_ss=1; // Persistence parameters in shock variables (these don't affect the SS) rhoEpsilon=0.8; rhoG=0.85; rhoiStar=0.7; rhoPhiStar=0.3; rhoPiStar=0.20; rhoPiStarX= 0.41 ; rhoPiStarNX=0.18; piT=1.015; //Inflation target alfa=0.66; //Probability of non-optimizing price betta=0.99; //Intertemporal discount factor sigmaC=1.5; //Constant relative risk aversion for consumption sigmaN=0.5 ; //Constant relative risk aversion for labor a_D=0.86; //Home bias in consumption thetta=6; //Elasticity of substitution for domestic goods thettaC=1.5; //Elasticity of substitution between domestic and imported bundles bA=0.5; //Parameter for exports demand varepsvarphi_D=2; //Debt/GDP ratio elasticity of varphiD (in UIP) varepsilon_L=1.02 ; //Elasticity of money/consumption function w.r. to ii gammaD_ss=0.5; //Household Foreign Debt to GDP ratio //Cointegration in trade prices parameters EC_speed_N=0.181; EC_speed_X=-0.255; Coint_param=1.0; bX=1/(1-bA); // Auxiliary parameter for exports demand kappaX=bA^(bA/(1-bA)); // Auxiliary parameter for exports demand // Risk premium parameters and variables alpha_2=1/((2/varepsvarphi_D)*(1-betta*iStar_ss*phiStar_ss)+gammaD_ss); alpha_1=(1-alpha_2*gammaD_ss)^2*(1/(betta*iStar_ss*phiStar_ss)-1); tau_D=1+alpha_1/(1-alpha_2*gammaD_ss); // RER determination gammaR_ss=0.13; //CB reserves to GDP ratio tbetoy=((iStar_ss/piStar_ss)*phiStar_ss*tau_D-1)*gammaD_ss-(iStar_ss/piStar_ss-1)*gammaR_ss; f_e = @(e_ss) (kappaX*(e_ss*pStar_ss)^bX*(a_D+(1-a_D)*(e_ss)^(1-thettaC))-(1-a_D)*e_ss^(1-thettaC))/a_D-tbetoy; e_ss=fzero(f_e,0.595); pC_ss=(a_D+(1-a_D)*(e_ss)^(1-thettaC))^(1/(1-thettaC)); // Transactions costs parameters and variables gammaM_ss=0.095522; //money/consumption ratio betta_3=160; //Should be >1/(varepsilon_L*(piT/betta-1))-1 betta_2=(1/gammaM_ss)*(1/(((betta_3+1)*varepsilon_L*(piT/betta-1))-1)); betta_1=(1-betta/piT)*((1+betta_2*gammaM_ss)^(betta_3+1))/(betta_2*betta_3); tauM_ss=1+betta_1/(1+betta_2*gammaM_ss)^betta_3; varphiM_ss=1+(tauM_ss-1)*(1+betta_3*((betta_2*gammaM_ss)/(1+betta_2*gammaM_ss))); // Other great ratios gtopCC=0.19; //Gov expenditure to private consumption ratio pCCtoy=(1-kappaX*(e_ss*pStar_ss)^bX)*(pC_ss^(1-thettaC)/(a_D*(1+gtopCC)*(tauM_ss))); mtoy=gammaM_ss*pCCtoy; //money/GDP ratio btoy=gammaR_ss-mtoy; //bonds/GDP ratio // Steady state values of remaining endogenous variables Deltta_ss=((1-alfa)/((1-alfa*piT^(thetta))))*((1-alfa*piT^(thetta-1))/(1-alfa))^(thetta/(thetta-1)); Q_ss=Y_ss*(1-(kappaX/bX)*(e_ss*pStar_ss)^bX); N_ss=Q_ss*Deltta_ss; C_ss=pCCtoy*Y_ss/pC_ss; GammaP_ss=((Q_ss/(pC_ss*C_ss^sigmaC))/(1-betta*alfa*piT^(thetta-1))); PsiP_ss=GammaP_ss/(((1-alfa*piT^(thetta-1))/(1-alfa))^(1/(thetta-1))); mc_ss=PsiP_ss*(1-betta*alfa*((piT)^thetta))/((thetta/(thetta-1))*(Q_ss/(pC_ss*C_ss^sigmaC))); w_ss=mc_ss; xiN=w_ss/(N_ss^sigmaN*pC_ss*C_ss^sigmaC*(varphiM_ss)); X_ss=Y_ss*kappaX*(e_ss*pStar_ss)^bX; r_ss=gammaR_ss*Y_ss/e_ss; b_ss=btoy*Y_ss; qf_ss=((iStar_ss)-1/(piT/piStar_ss))*(e_ss*r_ss/piStar_ss)-(piT/betta-1)*(b_ss/piT); tax_ss=gtopCC*tauM_ss*pC_ss*C_ss-qf_ss; TB_ss=tbetoy*Y_ss/e_ss; d_ss=gammaD_ss*Y_ss/e_ss; m_ss=mtoy*Y_ss; Utility_ss=(1/(1-sigmaC))*C_ss^(1-sigmaC)-(xiN/(1+sigmaN))*N_ss^(1+sigmaN); //Weights for CB ad-hoc loss function (for 'ramsey') omega_piC=100; omega_Y=1; omega_e=1; omega_r=1; omega_dii=50; omega_ddelta=50 ; // MODEL EQUATIONS model; // Simple policy rules (eliminate both for ramsey in MER regime) // 1 Taylor rule //ii=(piT/betta)^(1-h_0)*(ii(-1))^h_0*(piC/piT)^h_1*(Y/Y_ss)^h_2*(e/e_ss)^h_3; //For Pegged Exchange Rate (PER) policy use instead: //b=b_ss; // 2 Exchange rate depreciation rule: //delta=(piT/piStar_ss)^(1-k_0)*delta(-1)^k_0*(piC/piT)^k_1*(Y/Y_ss)^k_2*(e/e_ss)^k_3*(gammaR/gammaR_ss)^k_4; //For Floating Exchange Rate (FER) policy use instead: //r=r_ss; // 3 Central Bank balance sheet b=e*r-m; // 4 Money market clearing m=(1/betta_2)*(((betta_1*betta_2*betta_3/(1-1/ii))^(1/(betta_3+1)))-1)*pC*C; // 5 Trade Balance (in foreign currency) TB=(1/(a_D*e))*(pC^(1-thettaC)*X-(1-a_D)*e^(1-thettaC)*Y); // 6 Current account (in foreign currency) CA=(exp(z_iStar(-1))/exp(z_piStar)-1)*r(-1)-((exp(z_iStar(-1))/exp(z_piStar))*exp(z_phiStar(-1))*(1+alpha_1/(1-alpha_2*gammaD(-1)))-1)*d(-1)+TB; // 7 Balance of Payments (in foreign currency) r=d+CA+r(-1)-d(-1); // 8 Exports (in foreign currency) X=Y*kappaX*(e*pStar)^bX; // 9 RER identity e=e(-1)*delta*exp(z_piStar)/pii; // 10 Risk-adjusted uncovered interest parity ii=exp(z_iStar)*exp(z_phiStar)*(1+alpha_1/(1-alpha_2*gammaD)^2)*delta(+1); // 11 Labor market clearing w=xiN*N^sigmaN*pC*C^sigmaC*(varphiM); // 12 Hours worked N=Q*Deltta/exp(z_epsilon); // 13 Domestic goods market clearing Q=Y-(1-bA)*X; // 14 GDP DEFINITION Y=a_D*(exp(z_G)*tauM)*pC^thettaC*C+X; // 15 Dynamics of Price dispersion Deltta=alfa*pii^thetta*Deltta(-1)+(1-alfa)*((1-alfa*pii^(thetta-1))/(1-alfa))^(thetta/(thetta-1)); // 16-18 Domestic inflation Phillips equation GammaP=PsiP*((1-alfa*pii^(thetta-1))/(1-alfa))^(1/(thetta-1)); GammaP=Q/(pC*C^sigmaC)+betta*alfa*(pii(+1))^(thetta-1)*GammaP(+1); PsiP=(thetta/(thetta-1))*(Q/(pC*C^sigmaC))*mc+betta*alfa*((pii(+1))^thetta)*PsiP(+1); // 19 Real Marginal Cost mc=w/exp(z_epsilon); // 20 Transactions cost (net) tauM=1+betta_1/(1+betta_2*gammaM)^betta_3; // 21 Transactions cost effect on the Euler equation (gross) varphiM=1+(tauM-1)*(1+betta_3*((betta_2*gammaM)/(1+betta_2*gammaM))); // 22 Consumption relative price pC^(1-thettaC)=a_D+(1-a_D)*e^(1-thettaC); // 23 Consumption inflation identity piC=pii*pC/pC(-1); // 24 Euler equation C^(-sigmaC)/(varphiM)=betta*ii*(C(+1)^(-sigmaC)/piC(+1))/(varphiM(+1)); // 25 External Terms of Trade pStar=pStar(-1)*exp(z_piStarX)/(exp(z_piStar)^Coint_param); // 26-27 Cointegrated RW prices z_piStarX=z_piStarX(-1)*rhoPiStarX+log(pStar(-1))*EC_speed_X+(eps_piStarX); z_piStar=z_piStar(-1)*rhoPiStar+log(pStar(-1))*EC_speed_N+z_piStar(-1)*rhoPiStarNX+(eps_piStar); //TO GET THE SAME RESULTS AS IN THE PAPER TABLES USE THESE (WHICH CONTAIN AN ERROR): //z_piStarX=z_piStarX(-1)*rhoPiStarX+z_piStar(-1)*rhoPiStarNX+log(pStar(-1))*EC_speed_X+(eps_piStarX); //z_piStar=z_piStar(-1)*rhoPiStar+log(pStar(-1))*EC_speed_N+(eps_piStar); // 28 Government expenditure shock z_G=(z_G(-1))*rhoG+log(1+gtopCC)*(1-rhoG)+(eps_G); // 29 Transitory productivity shock z_epsilon=z_epsilon(-1)*rhoEpsilon+(eps_epsilon); // 30 RW riskfree interest rate shock z_iStar=(z_iStar(-1))*rhoiStar+log(iStar_ss)*(1-rhoiStar)+(eps_iStar); // 31 RW Financing liquidity shock z_phiStar=z_phiStar(-1)*rhoPhiStar+log(phiStar_ss)*(1-rhoPhiStar)+(eps_phiStar); // 32-33 Policy instruments differences for ramsey dii=ii-ii(-1); ddelta=delta-delta(-1); // EXTRAS // 34 Real interest rate real_ii=ii/piC(+1); // 35 Tax collection tax=(exp(z_G)-1)*tauM*pC*C-qf; // 36 Quasi-fiscal surplus qf=(exp(z_iStar(-1))-1/delta)*(e*r(-1)/exp(z_piStar))-(ii(-1)-1)*(b(-1)/pii); // 37 Period Utility Utility=(1/(1-sigmaC))*(C)^(1-sigmaC) - (xiN/(1+sigmaN))*(N)^(1+sigmaN); // 38-40 Great ratios gammaD=e*d/Y; gammaM=m/(pC*C); gammaR=e*r/Y; end; // Reminder: steady, check and resid canīt be used with ramsey //steady; //check; //resid; shocks; var eps_epsilon; stderr 0.01 ; var eps_G; stderr 0.03 ; var eps_iStar; stderr 0.0046 ; var eps_phiStar; stderr 0.05 ; var eps_piStar; stderr 0.0295 ; var eps_piStarX; stderr 0.0424 ; end; steady_state_model; ii=piT/betta; delta=piT/piStar_ss; r=r_ss; b=b_ss; e=e_ss; piC=piT; Y=Y_ss; pStar=pStar_ss; z_G=log(1+gtopCC); z_epsilon=log(1); z_piStar=log(piStar_ss); z_iStar=log(iStar_ss); z_phiStar=log(phiStar_ss); z_piStarX=log(piStar_ss); d=d_ss; GammaP=GammaP_ss; PsiP=PsiP_ss; C=C_ss; m=m_ss; N=N_ss; Deltta=Deltta_ss; pii=piT; Q=Q_ss; w=w_ss; mc=mc_ss; pC=pC_ss; varphiM=varphiM_ss; tauM=tauM_ss; X=X_ss; TB=TB_ss; real_ii=ii/piC; tax=tax_ss; qf=qf_ss; CA=0; dii=0; ddelta=0; gammaD=gammaD_ss; gammaM=gammaM_ss; Utility=Utility_ss; gammaR=gammaR_ss; end; //stoch_simul(order=1,irf=0) ii delta e d r C piC Y pii ; // FOR OPTIMAL SIMPLE RULES: ////////////////////////////////////////////// //optim_weights; //piC 100; Y 1; e 1; r 1; dii 50; ddelta 50; //Utility 1000; //end; //osr_params h_0 h_1 h_2 h_3 k_0 k_1 k_2 k_3 k_4 ; //For MER //osr_params h_0 h_1 h_2 h_3 ; //For FER //osr_params k_0 k_1 k_2 k_3 k_4 ; //For PER //Provides numerical initialization for the optimization: //For MER; //h_0=0.8; h_1=1.5; h_2=0.1; h_3=0.0; k_0=0.0; k_1=0.0; k_2=-0.0; k_3=-0.0; k_4=-0.1; //For FER: //h_0=0.33; h_1=1.25; h_2=0.02; h_3=0.12; //For PER: //k_0=-0.3; k_1=-0.07; k_2=-0.08; k_3=-0.43; k_4=-0.08; //Instructs for osr //osr(order=1,irf=0) piC Y e C gammaD ii b delta r ; /////////////////////////////////////////////////////////////////////////// // FOR OPTIMAL POLICY WITH COMMITMENT: /////////////////////////////////// planner_objective((omega_piC*(piC-piT)^2+omega_Y*(Y-Y_ss)^2+omega_e*(e-e_ss)^2+omega_r*(r-r_ss)^2+omega_dii*dii^2+omega_ddelta*ddelta^2)); //For MER: ramsey_policy(planner_discount=0.99,order=1,instruments=(ii,delta),irf=0) ii delta e d r C piC Y pii ; //For FER: //ramsey_policy(planner_discount=0.99,order=1,instruments=(ii),irf=0) ii delta e d r C piC Y pii ; //For PER: //ramsey_policy(planner_discount=0.99,order=1,instruments=(delta),irf=0) ii delta e d r C piC Y pii ;