//************************************************************************** // A New Comparative Approach to Macroeconomic Modeling and Policy Analysis // // Volker Wieland, Tobias Cwik, Gernot J. Mueller, Sebastian Schmidt and // Maik Wolters // // Working Paper, 2009 //************************************************************************** // Model: EA_GE10 // Further references: // Gelain, Paolo. 2010. "The external finance premium in the euro area: A dynamic stochastic general equilibrium analysis" // North american Journal of Economics and finance 21, pp. 49-71. // basically, SW + BGG // This is a version of the model with financial accelerator and // estimation with data from ECB until 2008 q3 without epi // and without S as a varobs (author's comment) // Last edited: 03/08/11 by M.Jancokova var r c l inv q k nw rk y pi z mc a x eb el S g rn wp EMP ypot cf invf qf rkf rf kf wpf lf zf mcf ug //thetae; epi y_obs p_obs c_obs inv_obs //************************************************************************** // Modelbase Variables //* interest inflation inflationq output outputgap fispol; //* //************************************************************************** varexo ux ub ul ua ur ulambdapi uw //uq; uthetae upi //************************************************************************** // Modelbase Shocks //* interest_ fiscal_; //* //************************************************************************** parameters //************************************************************************** // Modelbase Parameters //* //* cofintintb1 cofintintb2 cofintintb3 cofintintb4 cofintinf0 cofintinfb1 cofintinfb2 cofintinfb3 cofintinfb4 cofintinff1 cofintinff2 cofintinff3 cofintinff4 cofintout cofintoutb1 cofintoutb2 cofintoutb3 cofintoutb4 cofintoutf1 cofintoutf2 cofintoutf3 cofintoutf4 std_r_ std_r_quart coffispol //************************************************************************** alphaa betaa deltaa thetaa RR S_ss rhob vkappa thetae phim rhol rhox rhopi rhoa NWK KNW Rk xie rpi ry h rhog sigmal sigmac cw gammaw lambdaw gammapi pis FI phii rdeltapi rdeltay thetaest c_y gz //Xi //epsilon //thetaf //rhothetae //GY //Z_ss //KY //additional local variables defined Z_ss mc_ss abar w_ss l_k k_y inv_y GY c_kap kap_ss cons_ss inv_ss Y_ss lab_ss KY ZF_ss mcF_ss wF_ss l_kF k_yF inv_yF g_yF c_kF kapF_ss consF_ss invF_ss yF_ss labF_ss KYF; //calibrated parameters betaa=0.99; //discount factor RR=(1/betaa); deltaa=0.025; //capital depreciation rate S_ss=1+(0.02/4); //SS level of the finance premium alphaa=0.3; //capital share on output Rk=S_ss*RR; KNW=2; //capital net worth ratio NWK=1/KNW; rhopi=1; lambdaw=3; //SS wage markup //KY=8.8; //thetaf=0.00000001; //GY=0.195; //Z=0.04; thetaest=6; //goods elasticity of substitution c_y=0.68; //consumption-output ratio gz=1; //posterior means of estimated parameters vkappa=0.0267; //elasticity of external finance premium w.r.t. the leverage ratio phim=0.9075; //smooth parameter in instrument rule thetae=0.9797; //entrepreneur's rate of survival rhob=0.8969; //persistence param. preference shock rhol=0.9707; //persistence param. labor supply shock rhox=0.6941; //persistence param. invest.specific shock rhoa=0.9644; //persistence param. technology shock rhog=0.8685; //persistence param. gov.spending shock rpi=1.6633; //response of int.rate to inflation ry=0.1054; //response of int.rate to output h=0.6551; //habit formation sigmal=2.0183; //inverse of the elasticity of work effort w.r.t. real wage sigmac=1.5081; //inverse of elasticity of substitution in consumption gammaw=0.3892; //past wage indexation gammapi=0.2784; //past inflation indexation cw=0.8768; //Calvo wage thetaa=0.8618; //Calvo price pis=6.5431; //inverse of investments adjustment cost phii=0.2; //fixed cost over output FI=0.0294; //inverse elast. capital util. cost function rdeltapi=0.1417; //response of int.rate to infl. first diff. rdeltay=0.2061; //response of int.rate to output growth xie=0.7458; //Calvo employment Z_ss=S_ss*(1/betaa)-1+deltaa; mc_ss=(thetaest-1)/thetaest; abar=alphaa^alphaa*(1-alphaa)^(1-alphaa); w_ss=(mc_ss*abar/Z_ss^alphaa)^(1/(1-alphaa)); l_k=(1-alphaa)/alphaa*(Z_ss/gz)/w_ss; k_y=l_k^(alphaa-1)*(1+phii)*gz^alphaa; inv_y=deltaa*l_k^(alphaa-1)*(1+phii); //inv/y GY=1-(c_y+inv_y); c_kap=(1-GY)/(1+phii)*l_k^(1-alphaa)-deltaa; // c/k kap_ss=( w_ss*(lambdaw-1)/lambdaw*((1-h)*c_kap)^(-sigmac)*l_k^(-sigmal) )^(1/(sigmac+sigmal)); cons_ss=c_kap*kap_ss; inv_ss=deltaa*kap_ss; Y_ss=(cons_ss+inv_ss)/(1-GY); lab_ss=l_k*kap_ss; KY=kap_ss/Y_ss; ZF_ss=1/betaa-1+deltaa; mcF_ss=(thetaest-1)/thetaest; wF_ss=(mcF_ss*abar/ZF_ss^alphaa)^(1/(1-alphaa)); l_kF=(1-alphaa)/alphaa*(ZF_ss/gz)/wF_ss; k_yF=l_kF^(alphaa-1)*(1+phii)*gz^alphaa; inv_yF=deltaa*l_kF^(alphaa-1)*(1+phii); g_yF=1-(c_y+inv_yF); c_kF=(1-g_yF)/(1+phii)*l_kF^(1-alphaa)-deltaa; //c/k kapF_ss=( wF_ss*(lambdaw-1)/lambdaw*((1-h)*c_kF)^(-sigmac)*l_kF^(-sigmal) )^(1/(sigmac+sigmal)); consF_ss=c_kF*kapF_ss; invF_ss=deltaa*kapF_ss; yF_ss=(consF_ss+invF_ss)/(1-g_yF); labF_ss=l_kF*kapF_ss; KYF=kapF_ss/yF_ss; //************************************************************************** // Specification of Modelbase Parameters //* //* // Load Modelbase Monetary Policy Parameters //* thispath = cd; cd('..'); load policy_param.mat; for i=1:24 deep_parameter_name = M_.param_names(i,:); eval(['M_.params(i) = ' deep_parameter_name ' ;']) end cd(thispath); //* // Definition of Discretionary Fiscal Policy Parameter //* //* coffispol = 1/GY; //* //************************************************************************** model (linear); //************************************************************************** // Definition of Modelbase Variables in Terms of Original Model Variables//* //* interest = rn*4; //* inflation = pi+pi(-1)+pi(-2)+pi(-3); //* inflationq = pi*4; //* outputgap = y-ypot; //* output = y; //* fispol = ug; //* //************************************************************************** //************************************************************************** // Policy Rule //* //* // Monetary Policy //* //* interest = cofintintb1*interest(-1) //* + cofintintb2*interest(-2) //* + cofintintb3*interest(-3) //* + cofintintb4*interest(-4) //* + cofintinf0*inflationq //* + cofintinfb1*inflationq(-1) //* + cofintinfb2*inflationq(-2) //* + cofintinfb3*inflationq(-3) //* + cofintinfb4*inflationq(-4) //* + cofintinff1*inflationq(+1) //* + cofintinff2*inflationq(+2) //* + cofintinff3*inflationq(+3) //* + cofintinff4*inflationq(+4) //* + cofintout*outputgap //* + cofintoutb1*outputgap(-1) //* + cofintoutb2*outputgap(-2) //* + cofintoutb3*outputgap(-3) //* + cofintoutb4*outputgap(-4) //* + cofintoutf1*outputgap(+1) //* + cofintoutf2*outputgap(+2) //* + cofintoutf3*outputgap(+3) //* + cofintoutf4*outputgap(+4) //* + std_r_ *interest_; //* //* // Discretionary Government Spending //* //* fispol = coffispol*fiscal_; //* //************************************************************************** // WARNING: z IS THE MARGINAL PRODUCTIVITY OF CAPITAL AND IT IS ALSO THE RENTAL RATE OF CAPITAL // HENCE IN THE PRODCTION FUNCTION AND IN THE LABOUR DEMAND EQUATION THERE IS NOT RK, // WHICH IS THE RETURN ON CAPITAL, BUT z. (author's note) //********************************** //STICKY ECONOMY (prices and wages) //********************************** //Resource constraint y=(1-deltaa*KY-GY)*c+deltaa*KY*inv+GY*g+KY*FI*Z_ss*z+KY*(Rk-RR)*(1-NWK)*(rk+q(-1)+k); //Euler equation c=(1/(1+h))*c(+1)+(h/(1+h))*c(-1)-((1-h)/((1+h)*sigmac))*(rn-pi(+1))+ ((1-h)/((1+h)*sigmac))*(eb); //External finance premium (Financial accelerator mechanism) rk(+1)=r-vkappa*(nw-q(-1)-k); //Ex-post aggregate return to capital rk = (Z_ss*z+(1-deltaa)*q)/(1-deltaa+Z_ss)-q(-1); //Real marginal cost z=mc+y-k(-1); //Investment dynamics inv=(1/(1+betaa))*inv(-1)+(betaa/(1+betaa))*inv(+1)+((1/pis)/(1+betaa))*q+x; //Production function y/(1+phii) = alphaa*(k(-1)+FI*z)+(1-alphaa)*l+a; //Wage equation wp=(betaa/(1+betaa))*wp(+1)+(1/(1+betaa))*wp(-1)+(betaa/(1+betaa))*pi(+1)-((1+betaa*gammaw)/(1+betaa))*pi +(gammaw/(1+betaa))*pi(-1)-(1/(1+betaa))*(((1-betaa*cw)*(1-cw))/((1+(((1+lambdaw)*sigmal)/lambdaw))*cw)) *(wp-sigmal*l-(sigmac/(1-h))*(c-h*c(-1))+el)+uw; //% condition on labour supply wiht wage stickiness and time varying wage mark up //Return on capital l=-wp+(1+FI)*z+k(-1); //NK Phillips curve pi=((((1-thetaa)*(1-thetaa*betaa))/thetaa)/(1+(betaa*gammapi)))*(mc)+(betaa/ (1+(betaa*gammapi)))*(pi(+1))+(gammapi/(1+(betaa*gammapi)))*(pi(-1))+ulambdapi; //Capital's law of motion k=(1-deltaa)*k(-1)+(deltaa)*(inv+pis*x) ; //Aggregate entrepreneurial net worth nw=thetae*((KNW)*RR*(S_ss*rk(-1)-r(-1))+(KNW)*RR*(S_ss-1)*(q(-2)+k(-1))+RR*(r(-1)+nw(-1))); //Real interest rate r=rn-pi(+1); //Monetary policy rule //rn=phim*rn(-1)+(1-phim)*(rpi*(pi(-1))+ry*(y(-1)-ypot(-1)))+rdeltapi*(pi-pi(-1)) // +rdeltay*(y-ypot-(y(-1)-ypot(-1)))+ur; %%%% FOR FLEXIBLE ECONOMY without epi //log SS finance premium S=rk(+1)-r; (EMP-EMP(-1)) = betaa*(EMP(+1)-EMP)+(1-xie)*(1-xie*betaa)/(xie)*(l-EMP); //************************************ //FLEXIBLE ECONOMY (prices and wages) //************************************ ypot=(1-deltaa*KYF-g_yF)*cf+deltaa*KYF*invf+g_yF*g-KYF*FI*ZF_ss*zf; cf=(1/(1+h))*cf(+1)+(h/(1+h))*cf(-1)-((1-h)/((1+h)*sigmac))*(rf)+ ((1-h)/((1+h)*sigmac))*(eb); rkf(+1)=rf; rkf = (ZF_ss*zf+(1-deltaa)*qf)/(1-deltaa+ZF_ss)-qf(-1); zf=mcf+ypot-kf(-1); invf=(1/(1+betaa))*invf(-1)+(betaa/(1+betaa))*invf(+1)+((1/pis)/(1+betaa))*qf+x; ypot/(1+phii) = alphaa*(kf(-1)+FI*zf)+(1-alphaa)*lf+a; wpf=sigmal*lf+((sigmac)/(1-h))*cf-((sigmac)/(1-h))*cf(-1)+el; lf=-wpf+(1+FI)*zf+kf(-1); mcf=0; kf = (1-deltaa)*kf(-1)+(deltaa)*(invf+pis*x) ; //*********************** //AR(1) shock processes //*********************** eb=rhob*eb(-1)+ub; // preference shock a=rhoa*a(-1)+ua; // technology shock x=rhox*x(-1)+ux; // investment specific shock el=rhol*el(-1)+ul; // labour supply shock g=rhog*g(-1)+ug; // government expenditure shock // observed vars y_obs=(Y_ss + y-y(-1))/400; // Y_ss+y-y(-1) p_obs= (pi+3)/400; // ss inflation about 3% yoy c_obs=(Y_ss + c-c(-1))/400; inv_obs=(Y_ss + inv-inv(-1))/400; end; initval; y_obs=Y_ss/400; p_obs=3/400; c_obs=Y_ss/400; inv_obs=Y_ss/400; // the others are zeros // see resid(1) end; shocks; var ub=0.2665^2; // preference shock var ul=1.415^2; // labor supply shock var ux=0.3237^2; // inv.specific shock var ua=0.7534^2; // technology shock var ur=0.1325^2; // MP shock //var ug=1.2456^2; // gov.spending shock var uw=0.2079^2; // wage markup shock var ulambdapi=0.1743^2; // price markup shock var fiscal_=1.2456^2; //instead of ug var interest_=0; end; resid(1); steady; // always do steady since triggered anyway by estimation. check; // comment out when deal with vars without steady state /* estimated_params; phim, beta_pdf, 0.93, 0.005;// .05; //smooth parameter in instrument rule thetae, beta_pdf, 0.99, 0.001;//.01; //entrepreneur's rate of survival rhob, beta_pdf, .96, 0.005;//.1; //persistence param. preference shock rhol, beta_pdf, .95, 0.005;//.1; //persistence param. labor supply shock rhox, beta_pdf, .77, 0.005;//.1; //persistence param. invest.specific shock rhoa, beta_pdf, .96, 0.005;//.1; //persistence param. technology shock rhog, beta_pdf, .87, 0.005;//.1; //persistence param. gov.spending shock rpi, normal_pdf, 1.68, 0.005;//.1; //response of int.rate to inflation ry, normal_pdf, 0.1, 0.005;//.05; //response of int.rate to output h, beta_pdf, 0.6, 0.005;//.05; //habit formation sigmal, normal_pdf, 2.03, 0.005;//.75; //inverse of the elasticity of work effort w.r.t. real wage sigmac, normal_pdf, 1.506, 0.005;//.4; //inverse of elasticity of substitution in consumption gammaw, beta_pdf, 0.3892, 0.005;//.15; //past wage indexation gammapi, beta_pdf, 0.288, 0.005;//.15; //past inflation indexation cw, beta_pdf, 0.9, 0.005;//.05; //Calvo wage thetaa, beta_pdf, 0.81, 0.005;//.05; //Calvo price pis, normal_pdf, 6.51, 0.009;//.07; //inverse of investments adjustment cost phii, normal_pdf,0.22, 0.005;//.25; //fixed cost over output FI, normal_pdf, 0.11, 0.005;//1.5; //inverse elast. capital util. cost function rdeltapi, normal_pdf, 0.147, 0.005;//.1; //response of int.rate to infl. first diff. rdeltay, normal_pdf, 0.21, 0.005;//.05; //response of int.rate to output growth xie, beta_pdf, 0.74, 0.005;//.15; //Calvo employment //stderr vkappa, inv_gamma_pdf, 0.027, inf; // this gives trouble //elasticity of external finance premium w.r.t. the leverage ratio //stderr ub, inv_gamma_pdf, 0.2, .01; //inf; // preference shock //stderr ul, inv_gamma_pdf, 1.4, .01; //inf; // labor supply shock //stderr ux, inv_gamma_pdf, 0.3, .01; //inf; // inv.specific shock //stderr ua, inv_gamma_pdf, 0.7, .01; //inf; // technology shock //stderr ur, inv_gamma_pdf, 0.1, .01; //inf; // MP shock //stderr uw, inv_gamma_pdf, 0.2, .01; //inf; // wage markup shock //stderr ulambdapi, inv_gamma_pdf, 0.17, .01; //inf; // price markup shock //stderr fiscal_, inv_gamma_pdf, 1.25, .01; //inf; //instead of ug //stderr interest_, inv_gamma_pdf, 0, .01; //inf; //stderr ug, inv_gamma_pdf, 1.2, inf; // this is replaced by fiscal_ // gov.spending shock end; varobs y_obs p_obs c_obs inv_obs; estimation(order=1,datafile=ea_ge10data, mh_replic=2000, mh_nblocks=2, mh_jscale=0.7, mode_compute=6, forecast=40) y_obs p_obs c_obs inv_obs; model_diagnostics(M_,options_,oo_) //stoch_simul interest inflation output; */