/*My estimation*/ var d //preference shock c //consumption mu_z //trend growth rate of the economy (from neutral and investment specific technology) mu_I //growth rate of investment-specific technology growth mu_A //growth rate of neutral technology lambda //Lagrange multiplier R //Nominal Interest rate PI //Inflation r //rental rate of capital x //investment u //capacity utilization q //Tobin's marginal q f //variable for recursive formulation of wage setting ld //aggregate labor demand w //real wage wstar //optimal real wage PIstarw //optimal wage inflation PIstar //optimal price inflation g1 //variable 1 for recursive formulation of price setting g2 //variable 2 for recursive formulation of price setting yd //aggregate output mc //marginal costs k //capital vp //price dispersion term vw //wage dispersion term l //aggregate labor bundle phi //labor disutility shock F; //firm profits varexo epsd epsphi epsmu_I epsA epsm; predetermined_variables k; parameters h //consumption habits betta // discount factor betta_transform //discount factor (transformed) gammma1 //capital utilization, linear term gammma2 //capital utilization, quadratic term delta //depreciation rate kappa //capital adjustment costs parameter eta //elasticity of substitution between labor varieties epsilon //elasticity of substitution between goods varieties varpsi //labor disutility parameter gammma //inverse Frisch elasticity chiw //wage indexation parameter chi //price indexation thetap //Calvo parameter prices thetaw //Calvo parameter wages alppha //capital share Rbar //steady state interest rate PIbar //steady state inflation PIbar_transform // steady state inflation (transformed) gammmaR //interest smoothing coefficient Taylor rule gammmaPI //feedback coefficient to inflation monetary policy rule gammmay //feedback coefficient to output growth deviation in monetary policy rule Phi //firms fixed costs rhod //autocorrelation preference shock rhophi //autocorrelation labor disutility shock Lambdamu //steady state growth rate of investmentment-specific technology Lambdamu_transform LambdaA //steady state neutral technology growth LambdaA_transform Lambdax //steady state growth rate of investment LambdaYd //steady state growth rate of output sigma_d //standard deviation preference shock sigma_phi //standard deviation labor disutility shock sigma_mu //standard deviation investment-specific technology sigma_A //standard deviation neutral technology sigma_m; //standard deviation preference shock //Note that the parameter naming in FV(2010) differs from FV(2006) //Fixed parameters, taken from FV(2010), Table 2, p. 37 delta=0.025; epsilon=10; eta= 10; Phi=0; gammma2=0.001; //Estimated parameters, taken from FV(2010), Table 3, p. 38, median estimate parameters betta_transform = 0.2004; // 100*((1/0.998)-1) betta = ((betta_transform/100)+1)^(-1); h=0; varpsi =8.92; gammma = 1.17; kappa =9.51; alppha =0.21; thetap =0.82; chi = 0.63; thetaw =0.68; chiw =1; gammmaR =0.77; gammmay =0.19; gammmaPI =1.29; PIbar_transform = 1; PIbar = (PIbar_transform/100)+1; //PIbar = 1.01; rhod = 0.12; rhophi = 0.93; sigma_A = -3.97; sigma_d = -1.51; sigma_phi =-2.36; sigma_mu =-5.43; sigma_m =-5.85; Lambdamu_transform = 0.34; Lambdamu = Lambdamu_transform/100; //Lambdamu=3.4e-3; LambdaA_transform = 0.28; LambdaA = LambdaA_transform/100; //LambdaA = 2.8e-3; LambdaYd= (LambdaA+alppha*Lambdamu)/(1-alppha); /* The following parameters are set in the steady state file as they depend on other deep parameters that were estimated in the original study. Setting them in the steady state file means they are updated for every parameter draw in the MCMC algorithm, while the parameters initialized here are only set once for the initial values of the parameters they depend on: gammma1 as it depends on LambdaA, alppha, Lambdamu, betta, and delta Rbar =0 as it depends on PI, LambdaA, alppha, Lambdamu, and betta Lambdax */ /* The following model equations are the stationary model equations, taken from FV(2006), p. 20, section 3.2. */ model; //# betta = ((betta_transform/100)+1)^(-1); //1. FOC consumption d*(c-h*c(-1)*mu_z^(-1))^(-1)-h*betta*d(+1)*(c(+1)*mu_z(+1)-h*c)^(-1)=lambda; //2. Euler equation lambda=betta*lambda(+1)*mu_z(+1)^(-1)/PI(+1)*R; //3. FOC capital utilization r=gammma1+gammma2*(u-1); //4. FOC capital q=betta*lambda(+1)/lambda*mu_z(+1)^(-1)*mu_I(+1)^(-1)*((1-delta)*q(+1)+r(+1)*u(+1)-(gammma1*(u(+1)-1)+gammma2/2*(u(+1)-1)^2)); //5. FOC investment 1=q*(1-(kappa/2*(x/x(-1)*mu_z-Lambdax)^2)-(kappa*(x/x(-1)*mu_z-Lambdax)*x/x(-1)*mu_z)) +betta*q(+1)*lambda(+1)/lambda*mu_z(+1)^(-1)*kappa*(x(+1)/x*mu_z(+1)-Lambdax)*(x(+1)/x*mu_z(+1))^2; //6-7. Wage setting f=(eta-1)/eta*wstar^(1-eta)*lambda*w^eta*ld+betta*thetaw*(PI^chiw/PI(+1))^(1-eta)*(wstar(+1)/wstar*mu_z(+1))^(eta-1)*f(+1); f=varpsi*d*phi*PIstarw^(-eta*(1+gammma))*ld^(1+gammma)+betta*thetaw*(PI^chiw/PI(+1))^(-eta*(1+gammma))*(wstar(+1)/wstar*mu_z(+1))^(eta*(1+gammma))*f(+1); //8-10. firm's price setting g1=lambda*mc*yd+betta*thetap*(PI^chi/PI(+1))^(-epsilon)*g1(+1); g2=lambda*PIstar*yd+betta*thetap*(PI^chi/PI(+1))^(1-epsilon)*PIstar/PIstar(+1)*g2(+1); epsilon*g1=(epsilon-1)*g2; //11-12. optimal inputs u*k/ld=alppha/(1-alppha)*w/r*mu_z*mu_I; mc=(1/(1-alppha))^(1-alppha)*(1/alppha)^alppha*w^(1-alppha)*r^alppha; //13. law of motion wages 1=thetaw*(PI(-1)^chiw/PI)^(1-eta)*(w(-1)/w*mu_z^(-1))^(1-eta)+(1-thetaw)*PIstarw^(1-eta); //14. law of motion prices 1=thetap*(PI(-1)^chi/PI)^(1-epsilon)+(1-thetap)*PIstar^(1-epsilon); //15. Taylor Rule R/Rbar=(R(-1)/Rbar)^gammmaR*((PI/PIbar)^gammmaPI*((yd/yd(-1)*mu_z)/exp(LambdaYd))^gammmay)^(1-gammmaR)*exp(epsm); //16-17. Market clearing yd=c+x+mu_z^(-1)*mu_I^(-1)*(gammma1*(u-1)+gammma2/2*(u-1)^2)*k; yd=(mu_A*mu_z^(-1)*(u*k)^alppha*ld^(1-alppha)-Phi)/vp; //18-20. Price and wage dispersion terms l=vw*ld; vp=thetap*(PI(-1)^chi/PI)^(-epsilon)*vp(-1)+(1-thetap)*PIstar^(-epsilon); vw=thetaw*(w(-1)/w*mu_z^(-1)*PI(-1)^chiw/PI)^(-eta)*vw(-1)+(1-thetaw)*(PIstarw)^(-eta); //21. Law of motion for capital k(+1)*mu_z*mu_I-(1-delta)*k-mu_z*mu_I*(1-kappa/2*(x/x(-1)*mu_z-Lambdax)^2)*x=0; //22. Profits F=yd-1/(1-alppha)*w*ld; //23. definition optimal wage inflation PIstarw=wstar/w; //exogenous processes //24. Preference Shock log(d)=rhod*log(d(-1))+epsd; //25. Labor disutility Shock log(phi)=rhophi*log(phi(-1))+epsphi; //26. Investment specific technology log(mu_I)=Lambdamu+epsmu_I; //27. Neutral technology log(mu_A)=LambdaA+epsA; //28. Defininition composite technology mu_z=mu_A^(1/(1-alppha))*mu_I^(alppha/(1-alppha)); end; estimated_params; // PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE // crhoa,.9676 ,.01,.9999,BETA_PDF,0.5,0.20; stderr epsA , inv_gamma_pdf, 0.018873433 , 10; stderr epsd , inv_gamma_pdf, 0.220909978 , 10; stderr epsphi , inv_gamma_pdf, 0.094420223 , 10; stderr epsmu_I , inv_gamma_pdf, 0.004383096 , 10; stderr epsm , inv_gamma_pdf, 0.002879899 , 10; betta_transform, gamma_pdf, 0.25, 0.1; // h, 0.97, 0.95, 0.98, beta_pdf, 0.7, 0.1; varpsi, normal_pdf, 9, 3; gammma, normal_pdf, 1, 0.25; kappa, normal_pdf, 4, 1.5; alppha, normal_pdf, 0.3, 0.025; thetap, beta_pdf, 0.5, 0.1; chi, beta_pdf, 0.5, 0.15; thetaw, beta_pdf, 0.5, 0.1; // chiw, 0.68, 0.62, 0.73, beta_pdf, 0.5, 0.1; gammmaR, beta_pdf, 0.75, 0.1; gammmay, normal_pdf, 0.12, 0.05; gammmaPI, normal_pdf, 1.5, 0.125; PIbar_transform, gamma_pdf, 0.95, 0.1; rhod, beta_pdf, 0.5, 0.2; rhophi, beta_pdf, 0.5, 0.2; Lambdamu_transform, normal_pdf, 0.34, 0.1; LambdaA_transform, normal_pdf, 0.178, 0.075; end; estimated_params_init(use_calibration); end; varobs PI R mu_I mu_z w; estimation(datafile='arti_NK',conf_sig =.95,first_obs=51,nobs=300,mode_check,mode_compute=1,mh_replic=600,mh_jscale=0.5,mh_nblocks=1) PI R mu_I mu_z w;