/* * This file implements the Baseline New Keynesian DSGE model described in * much detail in Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez (2006): "A Baseline DSGE * Model", available at http://economics.sas.upenn.edu/~jesusfv/benchmark_DSGE.pdf * * The parametrization is based on the estimated version of this model in * Jesús Fernández-Villaverde (2010): "The econometrics of DSGE models", * SERIEs, Vol. 1, pp. 3-49, DOI 10.1007/s13209-009-0014-7 * * This implementation was written by Benjamin Born and Johannes Pfeifer. In * case you spot mistakes, email us at jpfeifer@gmx.de * * This mod-file implements a non-linearized version of the New Keynesian * model based on a recursive formulation of the price and wage setting * equations. Moreover, it makes use of a steady state file to i) set * parameters that depend on other parameters that are potentially estimated * and ii) solve a nonlinear equation using a numerical solver to find the steady * state of labor. It provides an example on how the steady state file can be used * to circumvent some of the limitation of Dynare mod-file by accessing an external * file that allows calling general Matlab routines. These capacities will mostly be * interesting for power users. If one just wants to provide analytical steady state * values and update parameters, the steady_state_model-block allows an easy and convenient * alternative. It even allows calling numerical solvers like fsolve. For an example, see * example3.mod * * The model is written in the beginning of period stock notation. To make the model * conform with Dynare's end of period stock notation, we use the * predetermined_variables-command. * * Please note that the following copyright notice only applies to this Dynare * implementation of the model. */ /* * Copyright (C) 2013-2016 Dynare Team * * This file is part of Dynare. * * Dynare is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * Dynare is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with Dynare. If not, see . */ 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 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 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 LambdaA //steady state neutral technology growth 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 =0.998; h=0.97; varpsi =8.92; gammma = 1.17; kappa =9.51; alppha =0.21; thetap =0.82; chi = 0.63; thetaw =0.68; chiw =0.62; gammmaR =0.77; gammmay =0.19; gammmaPI =1.29; 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=3.4e-3; LambdaA = 2.8e-3; /* The following parameters are set in the steady state file as they depend on other deep parameters (some 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=mu_z*mu_I/betta-(1-delta); R=1+(PIbar*mu_z/betta-1); Lambdax=exp(LambdaYd); LambdaYd= (LambdaA+alppha*Lambdamu)/(1-alppha); */ /* The following model equations are the stationary model equations, taken from FV(2006), p. 20, section 3.2. */ model; //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; shocks; var epsd; stderr exp(sigma_d); var epsphi; stderr exp(sigma_phi); var epsmu_I; stderr exp(sigma_mu); var epsA; stderr exp(sigma_A); var epsm; stderr exp(sigma_m); end; steady; check; stoch_simul(order=1,irf=20) yd c R PI;