% \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ % \\\\\\\\\\\\\\\\\\\\\\\\\\\THE MODEL-2country-RBC: \\\\\\\\\\\\\\\\\\\\ %\\\International trade in goods,home bonds and home&foreign equities\\\\\\ % \\\\\\\\\\Capital and labour in the production function- NO Adj cost\\\\\\\\\ close all % af1, af2, af3 etc are the zero-order portfolio holdings calculated with the % Devereux-Sutherland (DS) method.Code taken from his website. var A1 A2 Y1 Y2 C1 C2 W1 W2 N1 N2 beta_fun1 beta_fun2 Div1 Div2 I1 I2 K1 K2 rk1 rk2 cd cg NFA re1 re2 Z1 Z2 NX RER dER rb1 rb2 NR1 NR2 M1 M2 RP RPSTAR PI_CPI1 PI_CPISTAR PI_P1 PI_P2 ; % CPI1 CPISTAR P1 P2 varexo ep1 ep2 ep3 ep4 zeta; parameters consigma PSI PSI2 phi1 alpha epsilon theta tau tau2 rhoa rhoa2 rhoMP mudf Kdelta upsilon mupi muy eta mcss PI1bar; % Parameter values: PI1bar=0; consigma=1.5; % Intertemporal substitution elasticity of consumption PSI=19.563468957119511; % Parameter in the labour function PSI2=19.563468957119511; phi1=2; % Implies labour supply elasticity of 1/3(G&M, 2005). Disutility from work alpha=0.4; % Share of domestic consumption allocated to imported goods (G&M, 2005) epsilon=6; % E.S b/varieties within same country. Implies SS mark-up of 1.2 ( G&M2005) theta=1.5; % E.S b/varieties produced at Home and Foreign country. Bakus et al(1994), Beningno and Thoenissen (2008), Corsetti et al use 0.85!! tau=0.36; % Capital share in DOMESTIC(developed) production function: (D&S,2009 JDE) tau2=0.36; % Capital share in FOREIGN (developing) production function: (D&S,2009 JDE) eta=2/3; mcss=0.833333333333333; % Real marginal cost is constant due to flexible pricing. So, set as a parameter. mudf=0.015971441225614; % Paramenter used in the endogenous discount factor. See D&S(2009) Kdelta=0.025; % annual capital depreciation rate. Standard literature. upsilon=15; %Shocks parameters rhoa=0.99; % Domestic Productivity persistance (D&S,2009 JDE) (0.66 Estimation G&M 2005) rhoa2=0.99; % Foreign Productivity persistance (D&S,2009 JDE) rhoMP=0.75; % Domestic Money persistance (DS1 dynare code) % Weights mupi=1.5; % Weight of inflation HOME ( Taylor Rule) %mur=0.8; % Weight of interest rate HOME ( Taylor Rule) muy=0.5/4; % Weight of output rate HOME ( Taylor Rule) % Standard deviations of the innovation of the shocks sta=0.01; % Std deviation of the innovation of DOMESTIC technology shock (0,007 G&M, 2005) (D&S,2009 JDE Annual 2% => 2%*1/sqr(4)=1% quarterly) sta2=0.01; % Std deviation of the innovation of FOREIGN technology shock About double size of home (D&S,2009 JDE Annual 5% => 5%*1/sqr(4)=2.5% quarterly) dr={'re1','re2','rb1','rb2'}; parameters af1 af2 af3; af1 = 0; af2 = 0; af3=0; model; NFA = rb1*NFA(-1)+(W1*N1)+(rk1*K1(-1))-C1-I1+(Div1)+ (STEADY_STATE(K1))*((STEADY_STATE(beta_fun1)*af1*((re1) -(rb1)))+(STEADY_STATE(beta_fun1)*af2*((re2) -(rb1))) +(STEADY_STATE(beta_fun1)*af3*((rb2) -(rb1))) + zeta); end; % Main model equations model; cd = C1 - C2; cg = (1/2)*(C1 + C2); A1=rhoa*A1(-1) + ep1; % 4.Domestic Productivity shock A2=rhoa2*A2(-1) + ep2; % 5.Foreign Productivity shock % HOME and FOREIGN SET OF EQUATIONS %6 7 Endogenous discount factor withOUT internalization. S.Schmitt-Grohe and Uribe (JIE2003) P.169 (beta_fun1)=(1+(C1))^(-mudf); (beta_fun2)=(1+(C2))^(-mudf); % 8 9 Euler equation C : rt is the interest rate KNOWN at t that pays off in period t + 1 (C1)^(-consigma)= (beta_fun1)*(C1(+1))^(-consigma)*(rb1(+1)); (C2)^(-consigma)= (beta_fun2)*(C2(+1))^(-consigma)*(rb1(+1))*(RER/RER(+1)); %10 11 12 Rest of portfolio eulers (C1)^(-consigma)= (beta_fun1)*(C1(+1))^(-consigma)*(re1(+1)); (C1)^(-consigma)= (beta_fun1)*(C1(+1))^(-consigma)*(re2(+1)); (C1)^(-consigma)= (beta_fun1)*(C1(+1))^(-consigma)*(rb2(+1)); %13 Resources contraint Y1+Y2=(RP)^(-theta)*((1-alpha)*C1+alpha*RER^theta*C2)+I1+(RPSTAR)^(-theta)*((1-alpha)*C2+alpha*(1/RER)^theta*C1)+I2; %14 15 Labour Supply N (W1)=(PSI)*((C1)^(consigma))*(N1)^phi1; (W2)=(PSI)*((C2)^(consigma))*(N2)^phi1; %16 17 Production Function: y (Y1)=exp(A1)*((N1)^(1-tau))*(K1(-1))^tau; (Y2)=exp(A2)*((N2)^(1-tau))*(K2(-1))^tau; %18 19 Labour Demand: W (W1)= exp(A1)*mcss*(1-tau)*((N1)^(-tau))*(K1(-1))^(tau); (W2)= exp(A2)*mcss*(1-tau)*((N2)^(-tau))*(K2(-1))^(tau); %20 net exports NX=((alpha)*((RP/RER)^(-theta))*C2)-((alpha)*((RPSTAR*RER)^(-theta))*C1); %21 22 Real Dividends.Note that W and K are real variables ( divided by CPIt) %(P1/CPI1)*(Div1)=(Y1*(P1/CPI1))-(W1)*(N1)-(rk1)*(K1(-1)); %UNIT ROOT %(P2/CPISTAR)*(Div2)=(Y2*(P2/CPISTAR))-(W2)*(N2)-(rk2)*(K2(-1)); %UNIT ROOT (RP)*(Div1)=(Y1*RP)-(W1)*(N1)-(rk1)*(K1(-1)); (RPSTAR)*(Div2)=(Y2*RPSTAR)-(W2)*(N2)-(rk2)*(K2(-1)); %23 24 Capital supply rk (re1(+1))=(rk1(+1))+(1-Kdelta); (re1(+1))*(RER/RER(+1))=(rk2(+1))+(1-Kdelta); %25 26 Gross Investment I (I1)=(K1)-(1-Kdelta)*(K1(-1)); (I2)=(K2)-(1-Kdelta)*(K2(-1)); %27 28 Capital Demand:K1(-1) K (rk1)= mcss*exp(A1)*tau*((N1)^(1-tau))*(K1(-1))^(tau-1); (rk2)= mcss*exp(A2)*tau*((N2)^(1-tau))*(K2(-1))^(tau-1); %29 30 Gross rate of returns on financial assets. Z1 Z2 are REAL PRICES %re1=((Div1+Z1)*P1*CPI1(-1))/(Z1(-1)*P1(-1)*CPI1); %UNIT ROOT %re2=((Div2+Z2)*P2*ER*CPISTAR(-1))/(Z2(-1)*CPISTAR*ER(-1)*P2(-1)); %UNIT ROOT re1=((Div1+Z1)*RP)/(Z1(-1)*RP(-1)); re2=((Div2+Z2)*RPSTAR*dER)/(Z2(-1)*RPSTAR(-1)); % NOMINAL VARIABLES AND EQUATIONS 31 32 %NR1/(STEADY_STATE(NR1))=(((CPI1/CPI1(-1))/(1+PI1bar))^mupi)*(((Y1)/(STEADY_STATE(Y1)))^mupi)+ep3; %UNIT ROOT %NR2/(STEADY_STATE(NR2))=(((CPISTAR/CPISTAR(-1))/(1+PI1bar))^mupi)*(((Y2)/(STEADY_STATE(Y2)))^mupi)+ep4; %UNIT ROOT NR1/(STEADY_STATE(NR1))=(((PI_CPI1)/(1+PI1bar))^mupi)*(((Y1)/(STEADY_STATE(Y1)))^mupi)+ep3; NR2/(STEADY_STATE(NR2))=(((PI_CPISTAR)/(1+PI1bar))^mupi)*(((Y2)/(STEADY_STATE(Y2)))^mupi)+ep4; % Money demand equations: FOC w.r.t to money.33 34 %(M1/CPI1)=((C1^consigma)/(1-(1/NR1)))^(1/mupi); % NOMINAL MONEY %(M2/CPISTAR)=((C2^consigma)/(1-(1/NR2)))^(1/mupi); (M1)=((C1^consigma)/(1-(1/NR1)))^(1/mupi); % REAL MONEY (M2)=((C2^consigma)/(1-(1/NR2)))^(1/mupi); %35 36 rb1=(NR1(-1))/PI_CPI1; rb2=(NR2(-1)*dER)/(PI_CPISTAR); %37 38 %(CPI1)=(((1-alpha)*(P1)^(1-theta))+(alpha)*(P2*ER)^(1-theta))^(1/(1-theta));%UNIT ROOT %(CPISTAR)=(((1-alpha)*(P2)^(1-theta))+(alpha)*(P1/ER)^(1-theta))^(1/(1-theta));%UNIT ROOT 1=(((1-alpha)*(RP)^(1-theta))+(alpha)*(RPSTAR*RER)^(1-theta))^(1/(1-theta)); 1=(((1-alpha)*(RPSTAR)^(1-theta))+(alpha)*(RP/RER)^(1-theta))^(1/(1-theta)); % 39 40 RELATIVE PRICES RP/RP(-1)=PI_P1/PI_CPI1; RPSTAR/RPSTAR(-1)=PI_P2/PI_CPISTAR; % 41 42 %ER=M2/M1; % UNIT ROOT %dER(+1)=NR1/NR2; dER=PI_P2/PI_P1; %RER=(CPISTAR*ER)/CPI1; %dER=(M2/M2(-1))/(M1/M2(-1)); RER/RER(-1)=(dER*PI_CPISTAR)/PI_CPI1; end; initval; cd = 0; cg =0.876238900469134; NFA=0; A1=0; A2=0; NX=0; dER=1; RER=1; RP=1; RPSTAR=1; PI_CPI1=1; PI_CPISTAR=1; PI_P1=1; PI_P2=1; %CPI1=1; %CPISTAR=1; %P1=1; %P2=1; M1=18.877994839260968; NR1=1.010101010101010; M2=18.877994839260968; NR2=1.010101010101010; N1=(0.3333333333333333); N2=(0.3333333333333333); Y1=(1.114338583396246); Y2=(1.114338583396246); C1=(0.876238900469134); C2=(0.876238900469134); I1=(0.238099682927112); I2=(0.238099682927112); K1= (9.523987317084471); K2=(9.523987317084471); rk1=(0.035101010101010); rk2=(0.035101010101010); W1= (1.782941733433994); W2= (1.782941733433994); beta_fun1=(0.990000000000000); beta_fun2=(0.990000000000000); re1=(1.010101010101010); re2=(1.010101010101010); rb1=(1.010101010101010); rb2=(1.010101010101010); Div1=(0.185723097232708); Div2=(0.185723097232708); Z1=(18.386586626038042); Z2=(18.386586626038042); end; resid(1); steady; resid(1); check; model_diagnostics; shocks; var ep1; stderr 0.01; var ep2; stderr 0.01; var ep3; stderr 0.01; var ep4; stderr 0.01; end; %-------------------------------------------------------------------------- % Stage 1: calculate zero-order asset holdings %-------------------------------------------------------------------------- stoch_simul(order=1,noprint,nomoments,irf=0); BB=oo_.dr.ghu; nvar=M_.endo_nbr; nu=M_.exo_nbr-1; ordo=oo_.dr.order_var; for i=1:nvar varo{i,1} = M_.endo_names(ordo(i),:); end SIGMA=M_.Sigma_e(1:nu,1:nu); icd=inx('cd',varo); [dm,na]=size(dr); for i=1:na ia(i)=inx(dr{i},varo); end D1=BB(icd,nu+1); D2=BB(icd,1:nu); for k=1:na-1 R1(k,:)=BB(ia(k),nu+1)-BB(ia(na),nu+1); R2(k,:)=BB(ia(k),1:nu)-BB(ia(na),1:nu); end alpha_tilde=inv(R2*SIGMA*D2'*R1'-R2*SIGMA*R2'*D1)*R2*SIGMA*D2'; % Set af1, af2 etc to calculated values npr=M_.param_nbr-na+1; for i=1:na-1 alval{i,1}=['M_.params( ' num2str(i+npr) ' )=alpha_tilde(' num2str(i) ',1);']; alval{i,2}=['af' num2str(i) '=alpha_tilde(' num2str(i) ',1);']; end for i=1:na-1 eval(alval{i,1}); eval(alval{i,2}); end