%%%%%%%%%%%%%%%%% Master Thesis %%%%%%%%%%%%%%%%% Hui-Lan Chang %%%%%%%%%%% %%% %%%\ %%% Title: Explaining Backus-Smith puzzle in a %%%\ %%% stochastic dynamic general equilibrium model %%%\ %%% %%%\ %%% Supervisor: Prof. Almuth Scholl %%%\ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% University of Konstanz %%%% %%%\ %%% Refenerce: G. Corsetti, L. Dedola, and S. Leduc (2008), %%% "International Risk Sharing and the Transmission of %%% Productivity Shocks", The Review of Economic Studies, %%% 75, 443-473. %%% %%% Create: 25.06.2014 %%% %%% With endogenous discount factor from average capita consumption and leisure. %%% Ref. Schmitt-Grohe and Uribe (2003) %----------------------------------------------------------------------------------------------------\ % 0. Housekeeping (close all graphic windows and clear the workspace) %----------------------------------------------------------------------------------------------------\ close all; %----------------------------------------------------------------------------------------------------\ % 1. Defining variables %----------------------------------------------------------------------------------------------------\ % list of endogenous variables var GDP1 GDP2 c1 c2 c_ht1 c_ht2 c_ft1 c_ft2 c_t1 c_t2 c_n1 c_n2 ih1 if2 bh1 bh2 k_ht1 k_ft2 k_n1 k_n2 k1 k2 y_ht1 y_ft2 y_n1 y_n2 l1 l2 l_ht1 l_ft2 l_n1 l_n2 p_wht1 p_wht2 p_wft1 p_wft2 p_ht1 p_ht2 p_ft1 p_ft2 p_n1 p_n2 p_t1 p_t2 wage_1 wage_2 R_1 R_2 r_b p1 p2 TOT RER nx1 nx2 z_ht1 z_ft2 z_n1 z_n2 discount_ONEperiod1 discount_ONEperiod2 MU1_l MU2_l MU1_c MU2_c MC1_ct MC2_ct MC1_cn MC2_cn MCT1_ch MCT1_cf MCT2_ch MCT2_cf; % the following exogenous variables are shocked varexo e_ht1 e_ft2 e_n1 e_n2; parameters sigma alpha rho elasTN aHT aFT aN aT psi diM LsT LsN KsT KsN delta ps11 ps12 ps13 ps14 ps21 ps22 ps23 ps24 ps31 ps32 ps33 ps34 ps41 ps42 ps43 ps44 vv11 vv12 vv13 vv14 vv21 vv22 vv23 vv24 vv31 vv32 vv33 vv34 vv41 vv42 vv43 vv44 u_bar l_bar r_bar p_n1_bar p_wh_bar p_h_bar c_bar c_f_bar c_n_bar c_h_bar c_t_bar y_n_bar wage1_bar R_bar K_bar y_h_bar LH_bar LN_bar KH_bar KN_bar ZH_bar ZN_bar; %----------------------------------------------------------------------------------------------------\ % 2. Calibration %----------------------------------------------------------------------------------------------------\ %% Baseline Model %% With estimate by Stockman and Tesar (1995) from U.S. relative to a set of OECD countries on annual data %% Table 2 % For Preferences and technology sigma = 2; %Risk aversion alpha = 0.34; %Consumption share rho = 1-(1/0.85); % 1/(1-rho)=0.85; Home and Foreign-traded goods of Elasticity of substitution elasTN = 1-(1/0.74); % 1/(1-elasTN)=0.74; Traded and non-traded goods of Elasticity of Substitution aHT = 0.72; %Share of Home-traded goods -->imports in steady state is 5% of aggregate output aFT = 1-aHT; %Share of Foreign-traded goods aN = 0.45; %Share of non-traded goods in consumption aT = 1-aN; %Share of traded goods in consumption psi = 0.08; %Elasticity of the discount factor with respect to C and L diM = 1.09; %Distribution margin LsT = 0.61; %Labor share in tradables KsT = 1-LsT; %Capital share in tradables LsN = 0.56; %Labor share in non-tradables KsN = 1-LsN; %Capital share in non-tradables delta = 0.1; %Depreciation rate r_bar = 0.04; %Hidden in the text real interest rate is 4% per annuam in steady state. %%DoNotFit Steady State:importshareY = 0.05; % Hidden in the text. In steady state imports is 5% of aggregate output. %%DoNotFit Steady State:l_bar = 1/3; %Hidden in the text. In steady state 1/3 of time endownment is spent working. % Steady state algorithm %*_ %%*_Approximation value_* l_bar=0.298851047; %Calibration u_bar=0.499504184; %Calibration p_wh_bar=1; %Calibrate price for Investment %*_Price of goods_* p_n1_bar=p_wh_bar/(diM/u_bar-diM); p_h_bar=diM/u_bar*p_n1_bar; p_f_bar=p_h_bar; %*_Consumption_* c_bar=((r_bar/psi)/((1-l_bar)^(1-alpha)))^(1/alpha); c_f_bar=aT*aFT*(aT+aN*(p_n1_bar/p_h_bar)^(elasTN/(elasTN-1)))^(-1/elasTN)*c_bar; c_n_bar=aN/aT/aFT*(p_n1_bar/p_h_bar)^(1/(elasTN-1))*c_f_bar; c_h_bar=aHT/aFT*c_f_bar; c_t_bar=1/aFT*c_f_bar; %*_Returns of inputs and captial stock_* wage1_bar=(1-alpha)*p_h_bar*(aT+aN*(p_n1_bar/p_h_bar)^(elasTN/(elasTN-1)))*c_f_bar/(1-l_bar)/alpha/aT/aFT; R_bar=(r_bar+delta)*p_wh_bar; %*_Total output, inputs, and productility_* y_n_bar=c_n_bar+diM*c_h_bar+diM*c_f_bar; %Total output KN_bar=KsN*p_n1_bar*y_n_bar/R_bar; LN_bar=LsN*p_n1_bar*y_n_bar/wage1_bar; KH_bar=(KN_bar+c_h_bar/delta+c_f_bar/delta)/((r_bar+delta)/KsT/delta-1); K_bar=KH_bar+KN_bar; y_h_bar=c_h_bar+c_f_bar+delta*K_bar; LH_bar=LsT*p_wh_bar*y_h_bar/wage1_bar; ZH_bar=y_h_bar/(KH_bar^KsT)/(LH_bar^LsT); ZN_bar=y_n_bar/(KN_bar^KsN)/(LN_bar^LsN); %_* % For Productivity shocks ps11 = 0.82; ps12 = -0.06; ps13 = 0.10; ps14 = 0.24; ps21 = -0.06; ps22 = 0.82; ps23 = 0.24; ps24 = 0.10; ps31 = -0.02; ps32 = 0.02; ps33 = 0.96; ps34 = 0.01; ps41 = 0.02; ps42 = -0.02; ps43 = 0.01; ps44 = 0.96; % Variance-covariance matrix (in per cent) vv11 = 0.047; vv12 = 0.022; vv13 = 0.009; vv14 = 0.004; vv21 = 0.022; vv22 = 0.047; vv23 = 0.004; vv24 = 0.009; vv31 = 0.009; vv32 = 0.004; vv33 = 0.009; vv34 = -0.001; vv41 = 0.004; vv42 = 0.009; vv43 = -0.001; vv44 = 0.009; %----------------------------------------------------------------------------------------------------\ % 3. Model--From Social Planner's perspective. %----------------------------------------------------------------------------------------------------\ model; %% CES aggregator for consumption exp(c_t1) = (aHT^(1-rho)*exp(c_ht1)^(rho)+aFT^(1-rho)*exp(c_ft1)^(rho))^(1/rho); %Traded good consumption in country 1 exp(c_t2) = (aHT^(1-rho)*exp(c_ft2)^(rho)+aFT^(1-rho)*exp(c_ht2)^(rho))^(1/rho); %Traded good consumption in country 2 exp(c1) = (aT^(1-elasTN)*exp(c_t1)^(elasTN)+aN^(1-elasTN)*exp(c_n1)^(elasTN))^(1/elasTN); %Total consumption in country 1 exp(c2) = (aT^(1-elasTN)*exp(c_t2)^(elasTN)+aN^(1-elasTN)*exp(c_n2)^(elasTN))^(1/elasTN); %Total consumption in country 2 % First order conditions with uninternalized endogenous discount factor exp(MU1_l) = ((exp(c1)^(alpha)*(1-exp(l1))^(1-alpha))^(-sigma))*(1-alpha)*exp(c1)^(alpha)*(1-exp(l1))^(-alpha); %marginal utility w.r.t. labor in country 1 exp(MU2_l) = ((exp(c2)^(alpha)*(1-exp(l2))^(1-alpha))^(-sigma))*(1-alpha)*exp(c2)^(alpha)*(1-exp(l2))^(-alpha); %marginal utility w.r.t. labor in country 2 exp(MU1_c) = ((exp(c1)^(alpha)*(1-exp(l1))^(1-alpha))^(-sigma))*alpha*exp(c1)^(alpha-1)*(1-exp(l1))^(1-alpha); %marginal utility w.r.t. consumption in country 1 exp(MU2_c) = ((exp(c2)^(alpha)*(1-exp(l2))^(1-alpha))^(-sigma))*alpha*exp(c2)^(alpha-1)*(1-exp(l2))^(1-alpha); %marginal utility w.r.t. consumption in country 2 exp(MC1_ct) = (exp(c1)^elasTN)^(-1+1/elasTN)*(aT^(1-elasTN)*exp(c_t1)^(elasTN-1)); %marginal consumption w.r.t. traded goods in country 1 exp(MC2_ct) = (exp(c2)^elasTN)^(-1+1/elasTN)*(aT^(1-elasTN)*exp(c_t2)^(elasTN-1)); %marginal consumption w.r.t. traded goods in country 2 exp(MC1_cn) = (exp(c1)^elasTN)^(-1+1/elasTN)*(aN^(1-elasTN)*exp(c_n1)^(elasTN-1)); %marginal consumption w.r.t. non-traded goods in country 1 exp(MC2_cn) = (exp(c2)^elasTN)^(-1+1/elasTN)*(aN^(1-elasTN)*exp(c_n2)^(elasTN-1)); %marginal consumption w.r.t. non-traded goods in country 2 exp(MCT1_ch) = exp(c_ht1)^(rho-1)*aHT^(1-rho)*((aHT^(1-rho)*exp(c_ht1)^rho)+(aFT^(1-rho)*exp(c_ft1)^rho))^(-1+1/rho); %marginal traded good consumption w.r.t. Home traded goods in country 1 exp(MCT2_cf) = exp(c_ft2)^(rho-1)*aHT^(1-rho)*((aHT^(1-rho)*exp(c_ft2)^rho)+(aFT^(1-rho)*exp(c_ht2)^rho))^(-1+1/rho); %marginal traded good consumption w.r.t. Foreign traded goods in country 2 exp(MCT1_cf) = exp(c_ft1)^(rho-1)*aFT^(1-rho)*((aHT^(1-rho)*exp(c_ht1)^rho)+(aFT^(1-rho)*exp(c_ft1)^rho))^(-1+1/rho); %marginal traded good consumption w.r.t. Foreign traded goods in country 1 exp(MCT2_ch) = exp(c_ht2)^(rho-1)*aFT^(1-rho)*((aHT^(1-rho)*exp(c_ft2)^rho)+(aFT^(1-rho)*exp(c_ht2)^rho))^(-1+1/rho); %marginal traded good consumption w.r.t. Home traded goods in country 2 exp(MCT1_ch)/exp(p_ht1) = exp(MCT1_cf)/exp(p_ft1); %Trade off between Home traded good and Foreign traded good in country 1 exp(MCT2_ch)/exp(p_ht2) = exp(MCT2_cf)/exp(p_ft2); %Trade off between Home traded good and Foreign traded good in country 2 exp(MC1_ct)*exp(MCT1_ch)/exp(p_ht1) = exp(MC1_cn)/exp(p_n1); %Trade off between Home traded good and non-traded good in country 1 exp(MC2_ct)*exp(MCT2_ch)/exp(p_ht2) = exp(MC2_cn)/exp(p_n2); %Trade off between Home traded good and non-traded good in country 2 exp(MU1_l)/(LsT*exp(y_ht1)*exp(p_wht1)/exp(l_ht1)) = exp(MU1_c)*exp(MC1_cn)/exp(p_n1); %Trade off between labor input in traded section and non-traded good consumption in country 1 exp(MU2_l)/(LsT*exp(y_ft2)*exp(p_wft2)/exp(l_ft2)) = exp(MU2_c)*exp(MC2_cn)/exp(p_n2); %Trade off between labor input in traded section and non-traded good consumption in country 2 exp(MU1_l)/(LsN*exp(y_n1)*exp(p_n1)/exp(l_n1)) = exp(MU1_c)*exp(MC1_cn)/exp(p_n1); %Trade off between labor input in non-traded section and non-traded good consumption in country 1 exp(MU2_l)/(LsN*exp(y_n2)*exp(p_n2)/exp(l_n2)) = exp(MU2_c)*exp(MC2_cn)/exp(p_n2); %Trade off between labor input in non-traded section and non-traded good consumption in country 2 %Euler equations exp(discount_ONEperiod1) = 1/(1+(psi*(exp(c1))^(alpha)*(1-exp(l1))^(1-alpha))); % discountF_t+1 / discountF_t exp(discount_ONEperiod2) = 1/(1+(psi*(exp(c2))^(alpha)*(1-exp(l2))^(1-alpha))); % discountF_t+1 / discountF_t exp(MU1_c)*exp(MC1_cn)*exp(p_wht1)/exp(p_n1) = exp(discount_ONEperiod1)*exp(MU1_c(+1))*exp(MC1_cn(+1))/exp(p_n1(+1))*(exp(p_wht1(+1))*KsT*exp(y_ht1(+1))/exp(k_ht1)+(1-delta)*exp(p_wht1(+1))); %Euler equation for non-traded good consumption in country 1 exp(MU2_c)*exp(MC2_cn)*exp(p_wft2)/exp(p_n2) = exp(discount_ONEperiod2)*exp(MU2_c(+1))*exp(MC2_cn(+1))/exp(p_n2(+1))*(exp(p_wft2(+1))*KsT*exp(y_ft2(+1))/exp(k_ft2)+(1-delta)*exp(p_wft2(+1))); %Euler equation for non-traded good consumption in country 2 exp(MU1_c)*exp(MC1_cn)*exp(p_wht1)/exp(p_n1) = exp(discount_ONEperiod1)*exp(MU1_c(+1))*exp(MC1_cn(+1))/exp(p_n1(+1))*(exp(p_n1(+1))*KsN*exp(y_n1(+1))/exp(k_n1)+(1-delta)*exp(p_wht1(+1))); %Euler equation for non-traded good consumption in country 1 exp(MU2_c)*exp(MC2_cn)*exp(p_wft2)/exp(p_n2) = exp(discount_ONEperiod2)*exp(MU2_c(+1))*exp(MC2_cn(+1))/exp(p_n2(+1))*(exp(p_n2(+1))*KsN*exp(y_n2(+1))/exp(k_n2)+(1-delta)*exp(p_wft2(+1))); %Euler equation for non-traded good consumption in country 2 exp(MU1_c)*exp(MC1_cn)/exp(p_n1) = exp(discount_ONEperiod1)*exp(MU1_c(+1))*exp(MC1_cn(+1))/exp(p_n1(+1))*(1+exp(r_b)); %Euler equation for non-traded good consumption in country 1 exp(MU2_c)*exp(MC2_cn)/exp(p_n2) = exp(discount_ONEperiod2)*exp(MU2_c(+1))*exp(MC2_cn(+1))/exp(p_n2(+1))*(1+exp(r_b)); %Euler equation for non-traded good consumption in country 2 % Resource budget constraints in both countries exp(p_ht1)*exp(c_ht1)+exp(p_ft1)*exp(c_ft1)+exp(p_n1)*exp(c_n1)+bh1+exp(p_wht1)*exp(ih1) = exp(p_wht1)*exp(y_ht1)+exp(p_n1)*exp(y_n1)+(1+exp(r_b(-1)))*bh1(-1); exp(p_ft2)*exp(c_ft2)+exp(p_ht2)*exp(c_ht2)+exp(p_n2)*exp(c_n2)+bh2+exp(p_wft2)*exp(if2) = exp(p_wft2)*exp(y_ft2)+exp(p_n2)*exp(y_n2)+(1+exp(r_b(-1)))*bh2(-1); % Production function of traded and non-traded goods exp(y_ht1) = exp(z_ht1)*exp(k_ht1(-1))^KsT*exp(l_ht1)^LsT; %Output of traded goods in country 1 exp(y_ft2) = exp(z_ft2)*exp(k_ft2(-1))^KsT*exp(l_ft2)^LsT; %Output of traded goods in country 2 exp(y_n1) = exp(z_n1)*exp(k_n1(-1))^KsN*exp(l_n1)^LsN; %Output of non-traded goods in country 1 exp(y_n2) = exp(z_n2)*exp(k_n2(-1))^KsN*exp(l_n2)^LsN; %Output of non-traded goods in country 2 %% Market clearing condition exp(l1) = exp(l_ht1)+exp(l_n1); %Total labor supply in country 1 exp(l2) = exp(l_ft2)+exp(l_n2); %Total labor supply in country 2 exp(k1) = exp(ih1)+(1-delta)*exp(k1(-1)); %Law of motion for captial stock in country 1 exp(k2) = exp(if2)+(1-delta)*exp(k2(-1)); %Law of motion for captial stock in country 2 exp(k1) = exp(k_ht1)+exp(k_n1); %Total capital stock in country 1 exp(k2) = exp(k_ft2)+exp(k_n2); %Total capital stock in country 2 bh1 = -bh2; %Bond market clear exp(y_n1) = exp(c_n1)+diM*exp(c_ht1)+diM*exp(c_ft1); %Non-traded goods market clear in country 1 exp(y_n2) = exp(c_n2)+diM*exp(c_ft2)+diM*exp(c_ht2); %Non-traded goods market clear in country 2 exp(y_ht1) = exp(ih1)+exp(c_ht1)+exp(c_ht2); %Traded goods market clear in country 1 exp(y_ft2) = exp(if2)+exp(c_ft2)+exp(c_ft1); %Traded goods market clear in country 2 %% Price in equilibrium exp(wage_1) = exp(p_n1)*LsN*exp(y_n1)/exp(l_n1); %Wage in country 1 exp(wage_2) = exp(p_n2)*LsN*exp(y_n2)/exp(l_n2); %Wage in country 2 exp(R_1) = exp(p_n1)*KsN*exp(y_n1)/exp(k_n1(-1)); %Return of captial in country 1 exp(R_2) = exp(p_n2)*KsN*exp(y_n2)/exp(k_n2(-1)); %Return of captial in country 2 % Law of one price hold at the wholesale level. exp(p_wht1) = exp(p_wht2); exp(p_wft1) = exp(p_wft2); % Distribution cost added for tradable goods exp(p_ht1) = exp(p_wht1) + diM*exp(p_n1); %Retrail price for Home traded good in country 1 exp(p_ft1) = exp(p_wft1) + diM*exp(p_n1); %Retrail price for Foreign traded good in country 1 exp(p_ht2) = exp(p_wht2) + diM*exp(p_n2); %Retrail price for Home traded good in country 2 exp(p_ft2) = exp(p_wft2) + diM*exp(p_n2); %Retrail price for Foreign traded good in country 2 %Utility-based CPIs exp(p_t1) = (aHT*exp(p_ht1)^(rho/(rho-1))+aFT*exp(p_ft1)^(rho/(rho-1)))^((rho-1)/rho); exp(p_t2) = (aHT*exp(p_ft2)^(rho/(rho-1))+aFT*exp(p_ht2)^(rho/(rho-1)))^((rho-1)/rho); exp(p1) = (aT*exp(p_t1)^(elasTN/(elasTN-1))+aN*exp(p_n1)^(elasTN/(elasTN-1)))^((elasTN-1)/elasTN); exp(p2) = (aT*exp(p_t2)^(elasTN/(elasTN-1))+aN*exp(p_n2)^(elasTN/(elasTN-1)))^((elasTN-1)/elasTN); %Indexes GDP1=exp(p_wht1)*exp(y_ht1)+exp(p_n1)*exp(y_n1); GDP2=exp(p_wft2)*exp(y_ft2)+exp(p_n2)*exp(y_n2); nx1=(exp(p_wft1)*exp(c_ft1)-exp(p_wht2)*exp(c_ht2))/GDP1; %net exports ratio of GDP nx2=(exp(p_wht2)*exp(c_ht2)-exp(p_wft1)*exp(c_ft1))/GDP2; %net exports ratio of GDP TOT=exp(p_ft1)/exp(p_ht2); %terms of trade: imported goods relative to exported goods RER=exp(p2)/exp(p1); %realative price of consumption: the foreign CPI in terms of home CPI %% Productivity Shocks with log form z_ht1=ps11*z_ht1(-1)+ps12*z_ft2(-1)+ps13*z_n1(-1)+ps14*z_n2(-1)+e_ht1; z_ft2=ps21*z_ht1(-1)+ps22*z_ft2(-1)+ps23*z_n1(-1)+ps24*z_n2(-1)+e_ft2; z_n1=ps31*z_ht1(-1)+ps32*z_ft2(-1)+ps33*z_n1(-1)+ps34*z_n2(-1)+e_n1; z_n2=ps41*z_ht1(-1)+ps42*z_ft2(-1)+ps43*z_n1(-1)+ps44*z_n2(-1)+e_n2; end; %----------------------------------------------------------------------------------------------------\ % 4. Computation %----------------------------------------------------------------------------------------------------\ initval; %Steady state c1 = log(c_bar); c_ht1 = log(c_h_bar); c_ft1 = log(c_f_bar); c_t1 = log(c_t_bar); c_n1 = log(c_n_bar); k_ht1 = log(KH_bar); k_n1 = log(KN_bar); k1 = log(K_bar); ih1 = log(delta*K_bar); y_ht1 = log(y_h_bar); y_n1 = log(y_n_bar); l1=log(l_bar); l_ht1 = log(LH_bar); l_n1 = log(LN_bar); p_wht1 = log(p_wh_bar); p_wft2 = log(p_wh_bar); p_ht1 = log(p_h_bar); p_ft1 = log(p_h_bar); p_n1 = log(p_n1_bar); wage_1 = log(wage1_bar); R_1 = log(R_bar); r_b = log(r_bar); bh1 = 0; p_t1 = log((aHT*exp(p_ht1)^(rho/(rho-1))+aFT*exp(p_ft1)^(rho/(rho-1)))^((rho-1)/rho)); p1 = log((aT*exp(p_t1)^(elasTN/(elasTN-1))+aN*exp(p_n1)^(elasTN/(elasTN-1)))^((elasTN-1)/elasTN)); GDP1 = exp(p_wh_bar)*exp(y_h_bar)+exp(p_n1_bar)*exp(y_n_bar); GDP2 = GDP1; c2 = c1; c_ht2 = c_ft1; c_ft2 = c_ht1; c_t2 = c_t1; c_n2 = c_n1; if2 = ih1; bh2 = -bh1; k_ft2 = k_ht1; k_n2 = k_n1; k2 = k1; y_ft2 = y_ht1; y_n2 = y_n1; l2 = l1; l_ft2 = l_ht1; l_n2 = l_n1; p_wht2 = p_wht1; p_wft1 = p_wft2; p_ft2 = p_ht1; p_ht2 = p_ft1; p_n2 = p_n1; p_t2 = p_t1; wage_2 = wage_1; R_2 = R_1; p2 = p1; TOT = exp(p_h_bar)/exp(p_f_bar); RER = exp(p2)/exp(p1); discount_ONEperiod1 = log(1/(1+(psi*(exp(c1))^(alpha)*(1-exp(l1))^(1-alpha)))); % discountF_t+1 / discountF_t MU1_l = log(((exp(c1)^(alpha)*(1-exp(l1))^(1-alpha))^(-sigma))*(1-alpha)*exp(c1)^(alpha)*(1-exp(l1))^(-alpha)); %marginal utility w.r.t. labor MU1_c = log(((exp(c1)^(alpha)*(1-exp(l1))^(1-alpha))^(-sigma))*alpha*exp(c1)^(alpha-1)*(1-exp(l1))^(1-alpha)); %marginal utility w.r.t. consumption MC1_ct = log((exp(c1)^elasTN)^(-1+1/elasTN)*(aT^(1-elasTN)*exp(c_t1)^(elasTN-1))); %marginal consumption w.r.t. traded goods MC1_cn = log((exp(c1)^elasTN)^(-1+1/elasTN)*(aN^(1-elasTN)*exp(c_n1)^(elasTN-1))); %marginal consumption w.r.t. non-traded goods MCT1_ch = log(exp(c_ht1)^(rho-1)*aHT^(1-rho)*((aHT^(1-rho)*exp(c_ht1)^rho)+(aFT^(1-rho)*exp(c_ft1)^rho))^(-1+1/rho)); %marginal traded good consumption w.r.t. Home traded goods MCT1_cf = log(exp(c_ft1)^(rho-1)*aFT^(1-rho)*((aHT^(1-rho)*exp(c_ht1)^rho)+(aFT^(1-rho)*exp(c_ft1)^rho))^(-1+1/rho)); %marginal traded good consumption w.r.t. Foreign traded goods nx1=(exp(p_wft1)*exp(c_ft1)-exp(p_wht2)*exp(c_ht2))/GDP1; nx2=(exp(p_wht2)*exp(c_ht2)-exp(p_wft1)*exp(c_ft1))/GDP2; discount_ONEperiod2= discount_ONEperiod1; MU2_l = MU1_l; MU2_c = MU1_c; MC2_ct = MC1_ct; MC2_cn = MC1_cn; MCT2_cf = MCT1_ch; MCT2_ch = MCT1_cf; z_ht1=1; z_ft2=1; z_n1=1; z_n2=1; e_ht1=0; e_ft2=0; e_n1=0; e_n2=0; end; shocks; var e_ht1 = 0.047; var e_ft2 = 0.047; var e_n1 = 0.009; var e_n2 = 0.009; var e_ht1,e_ft2 = 0.022; var e_ht1,e_n1 = 0.009; var e_ht1,e_n2 = 0.004; var e_ft2,e_n1 = 0.004; var e_ft2,e_n2 = 0.009; var e_n1,e_n2 = -0.001; end; steady; % Eigenvalue 0/0 does not pass initial threshold, Modification Line is from https://gist.github.com/stepan-a/5757263 (Date:12Jul2014) check(qz_zero_threshold=1e-12); // Need to reduce the value of the threshold option to get it work... stoch_simul(periods=20200, drop=200,hp_filter=1600,order=1, irf=40); %Use Collard & Juillard (2001) algorithm %----------------------------------------------------------------------------------------------------\ % 5. Some Results %----------------------------------------------------------------------------------------------------} % To calculate standard deviation of deviations from steady state divide by steady state % Relative standard deviations statistic1 = 100*sqrt(diag(oo_.var(1:55,1:55)))./oo_.mean(1:55); dyntable('Relative standard deviations in %',strvcat('VARIABLE','REL. S.D.'),M_.endo_names(1:53,:),statistic1,10,8,4); % Standard deviations relative to output statistic21 = statistic1./statistic1(1); dyntable('standard deviations relative to output of country 1',strvcat('VARIABLE','S.D.'),M_.endo_names(1:53,:),statistic21,10,8,4); % Standard deviations relative to output statistic22 = statistic1./statistic1(2); dyntable('standard deviations relative to output of country 2',strvcat('VARIABLE','S.D.'),M_.endo_names(1:53,:),statistic22,10,8,4); % plot the impulse responses to a productivity shock % in percentage deviations from steady state shock_GDP1 = 100* oo_.irfs.GDP1_e1/oo_.mean(1); shock_GDP2 = 100* oo_.irfs.GDP2_e1/oo_.mean(2); shock_c1 = 100* oo_.irfs.c1_e1/oo_.mean(3); shock_c2 = 100* oo_.irfs.c2_e1/oo_.mean(4); shock_c_ht1 = 100* oo_.irfs.c_ht1_e1/oo_.mean(5); shock_c_ht2 = 100* oo_.irfs.c_ht2_e1/oo_.mean(6); shock_c_ft1 = 100* oo_.irfs.c_ft1_e1/oo_.mean(7); shock_c_ft2 = 100* oo_.irfs.c_ft2_e1/oo_.mean(8); shock_c_t1 = 100* oo_.irfs.c_t1_e1/oo_.mean(9); shock_c_t2 = 100* oo_.irfs.c_t2_e1/oo_.mean(10); shock_c_n1 = 100* oo_.irfs.c_n1_e1/oo_.mean(11); shock_c_n2 = 100* oo_.irfs.c_n2_e1/oo_.mean(12); shock_ih1 = 100* oo_.irfs.ih1_e1/oo_.mean(13); shock_if2 = 100* oo_.irfs.if2_e1/oo_.mean(14); shock_bh1 = 100* oo_.irfs.bh1_e1/oo_.mean(15); shock_bh2 = 100* oo_.irfs.bh2_e1/oo_.mean(16); shock_k_ht1 = 100* oo_.irfs.k_ht1_e1/oo_.mean(17); shock_k_ft2 = 100* oo_.irfs.k_ft2_e1/oo_.mean(18); shock_k_n1 = 100* oo_.irfs.k_n1_e1/oo_.mean(19); shock_k_n2 = 100* oo_.irfs.k_n2_e1/oo_.mean(20); shock_k1 = 100* oo_.irfs.k1_e1/oo_.mean(21); shock_k2 = 100* oo_.irfs.k2_e1/oo_.mean(22); shock_y_ht1 = 100* oo_.irfs.y_ht1_e1/oo_.mean(23); shock_y_ft2 = 100* oo_.irfs.y_ft2_e1/oo_.mean(24); shock_y_n1 = 100* oo_.irfs.y_n1_e1/oo_.mean(25); shock_y_n2 = 100* oo_.irfs.y_n2_e1/oo_.mean(26); shock_l1 = 100* oo_.irfs.n1_l1/oo_.mean(27); shock_l2 = 100* oo_.irfs.n2_l2/oo_.mean(28); shock_l_ht1 = 100* oo_.irfs.l_ht1_e1/oo_.mean(29); shock_l_ft2 = 100* oo_.irfs.l_ft2_e1/oo_.mean(30); shock_l_n1 = 100* oo_.irfs.l_n1_e1/oo_.mean(31); shock_l_n2 = 100* oo_.irfs.l_n2_e1/oo_.mean(32); shock_p_wht1 = 100* oo_.irfs.p_wht1_e1/oo_.mean(33); shock_p_wht2= 100* oo_.irfs.p_wht2_e1/oo_.mean(34); shock_p_wft1 = 100* oo_.irfs.p_wft1_e1/oo_.mean(35); shock_p_wft2 = 100* oo_.irfs.p_wft2_e1/oo_.mean(36); shock_p_ht1 = 100* oo_.irfs.p_ht1_e1/oo_.mean(37); shock_p_ht2 = 100* oo_.irfs.p_ht2_e1/oo_.mean(38); shock_p_ft1 = 100* oo_.irfs.p_ft1_e1/oo_.mean(39); shock_p_ft2 = 100* oo_.irfs.p_ft2_e1/oo_.mean(40); shock_p_n1 = 100* oo_.irfs.p_n1_e1/oo_.mean(41); shock_p_n2 = 100* oo_.irfs.p_n2_e1/oo_.mean(42); shock_p_t1 = 100* oo_.irfs.p_t1_e1/oo_.mean(43); shock_p_t2 = 100* oo_.irfs.p_t2_e1/oo_.mean(44); shock_wage_1 = 100* oo_.irfs.wage_1_e1/oo_.mean(45); shock_wage_2 = 100* oo_.irfs.wage_2_e1/oo_.mean(46); shock_R_1 = 100* oo_.irfs.R_1_e1/oo_.mean(47); shock_R_2 = 100* oo_.irfs.R_2_e1/oo_.mean(48); shock_r_b = 100* oo_.irfs.r_b_e1/oo_.mean(49); shock_p1 = 100* oo_.irfs.p1_e1/oo_.mean(50); shock_p2 = 100* oo_.irfs.p2_e1/oo_.mean(51); shock_TOT = 100* oo_.irfs.TOT_e1/oo_.mean(52); shock_RER = 100* oo_.irfs.RER_e1/oo_.mean(53); shock_nx1 = 100* oo_.irfs.nx1_e1; shock_nx2 = 100* oo_.irfs.nx2_e1; time = 1:1:40; figure = plot(time,shock_GDP1,'-*k',time, shock_c1, '-g', time, shock_k1, '--r', time, shock_l1, '-s', time, shock_nx1, 'm-d', time, shock_TOT, 'c-p',time, shock_RER, 'yellow'); title('Impulse Responses to a Shock in Technology', 'FontSize',22); xlabel('quarters', 'FontSize',18); ylabel('percentage deviation from steady state', 'FontSize',18); legend( 'home output GDP1', 'home consumption', 'home capital', 'home labor', 'home net exports', 'terms of trade', 'Relative real exchange rate', 'LOCATION', 'NorthEast'); set(figure,'LineWidth',3); set(gca, 'FontSize',20); axis([time(1) time(40) -0.5 1.5]); print('-dpdf','incomp_bench'); pause; disp('Press a key to continue ...') time = 1:1:40; figure = plot(time,shock_GDP2,'-*k',time, shock_c2, '-g', time, shock_k2, '--r', time, shock_l2, '-s' ); title('Impulse Responses to a Shock in Technology', 'FontSize',22); xlabel('quarters', 'FontSize',18); ylabel('percentage deviation from steady state', 'FontSize',18); legend( 'foreign output GDP2', 'foreign consumption', 'foreign capital', 'foreign labor', 'LOCATION', 'NorthEast'); set(figure,'LineWidth',3); set(gca, 'FontSize',20); axis([time(1) time(40) -0.1 0.25]); print('-dpdf','incomp_bench_fo');