266 lines
11 KiB
Modula-2
266 lines
11 KiB
Modula-2
/*
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* This file implements the Baseline New Keynesian DSGE model described in
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* much detail in Jesús Fernández-Villaverde and Juan F. Rubio-Ramírez (2006): “A Baseline DSGE
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* Model”, available at http://economics.sas.upenn.edu/~jesusfv/benchmark_DSGE.pdf
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*
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* The parametrization is based on the estimated version of this model in
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* Jesús Fernández-Villaverde (2010): “The econometrics of DSGE models”,
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* SERIEs, Vol. 1, pp. 3-49, DOI 10.1007/s13209-009-0014-7
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*
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* This implementation was written by Benjamin Born and Johannes Pfeifer. In
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* case you spot mistakes, email us at jpfeifer@gmx.de
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*
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* This mod-file implements a non-linearized version of the New Keynesian
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* model based on a recursive formulation of the price and wage setting
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* equations. Moreover, it makes use of a steady state file to i) set
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* parameters that depend on other parameters that are potentially estimated
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* and ii) solve a nonlinear equation using a numerical solver to find the steady
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* state of labor. It provides an example on how the steady state file can be used
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* to circumvent some of the limitation of Dynare mod-file by accessing an external
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* file that allows calling general MATLAB routines. These capacities will mostly be
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* interesting for power users. If one just wants to provide analytical steady state
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* values and update parameters, the steady_state_model-block allows an easy and convenient
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* alternative. It even allows calling numerical solvers like fsolve. For an example, see
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* example3.mod
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*
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* The model is written in the beginning of period stock notation. To make the model
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* conform with Dynare’s end of period stock notation, we use the
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* predetermined_variables-command.
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*
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* The model has been implemented in detrended form, i.e. the \mu_{i,t} are actually
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* the the growth rates of the original \mu_{i,t}^{orig} in the paper, i.e.
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* log(\mu_{i,t})=log(\mu_{i,t}^{orig}/\mu_{i,t-1}^{orig})
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*
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* Please note that the following copyright notice only applies to this Dynare
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* implementation of the model.
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*/
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/*
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* Copyright © 2013-2023 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Dynare is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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*/
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var d (long_name='preference shock')
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c (long_name='consumption')
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mu_z (long_name='trend growth rate of the economy (from neutral and investment specific technology)')
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mu_I (long_name='growth rate of investment-specific technology growth')
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mu_A (long_name='growth rate of neutral technology')
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lambda (long_name='Lagrange multiplier')
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R (long_name='Nominal Interest rate')
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PI (long_name='Inflation')
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r (long_name='rental rate of capital')
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x (long_name='investment')
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u (long_name='capacity utilization')
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q (long_name='Tobin marginal q')
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f (long_name='variable for recursive formulation of wage setting')
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ld (long_name='aggregate labor demand')
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w (long_name='real wage')
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wstar (long_name='optimal real wage')
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PIstarw (long_name='optimal wage inflation')
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PIstar (long_name='optimal price inflation')
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g1 (long_name='variable 1 for recursive formulation of price setting')
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g2 (long_name='variable 2 for recursive formulation of price setting')
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yd (long_name='aggregate output')
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mc (long_name='marginal costs')
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k (long_name='capital')
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vp (long_name='price dispersion term')
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vw (long_name='wage dispersion term')
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l (long_name='aggregate labor bundle')
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phi (long_name='labor disutility shock')
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F (long_name='firm profits')
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;
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varexo epsd (long_name='Innovation preference shock')
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epsphi (long_name='Innovation labor disutility shock')
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epsmu_I (long_name='Innovation investment-specific technology')
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epsA (long_name='Innovation neutral technology')
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epsm (long_name='Innovation monetary policy shock')
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;
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predetermined_variables k;
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parameters h (long_name='consumption habits')
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betta (long_name='discount factor')
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gammma1 (long_name='capital utilization, linear term')
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gammma2 (long_name='capital utilization, quadratic term')
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delta (long_name='depreciation rate')
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kappa (long_name='capital adjustment costs parameter')
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eta (long_name='elasticity of substitution between labor varieties')
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epsilon (long_name='elasticity of substitution between goods varieties')
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varpsi (long_name='labor disutility parameter')
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gammma (long_name='inverse Frisch elasticity')
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chiw (long_name='wage indexation parameter')
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chi (long_name='price indexation')
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thetap (long_name='Calvo parameter prices')
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thetaw (long_name='Calvo parameter wages')
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alppha (long_name='capital share')
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Rbar (long_name='steady state interest rate')
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PIbar (long_name='steady state inflation')
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gammmaR (long_name='interest smoothing coefficient Taylor rule')
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gammmaPI (long_name='feedback coefficient to inflation monetary policy rule')
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gammmay (long_name='feedback coefficient to output growth deviation in monetary policy rule')
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Phi (long_name='firms fixed costs')
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rhod (long_name='autocorrelation preference shock')
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rhophi (long_name='autocorrelation labor disutility shock')
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Lambdamu (long_name='steady state growth rate of investmentment-specific technology')
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LambdaA (long_name='steady state neutral technology growth')
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Lambdax (long_name='steady state growth rate of investment')
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LambdaYd (long_name='steady state growth rate of output')
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sigma_d (long_name='standard deviation preference shock')
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sigma_phi (long_name='standard deviation labor disutility shock')
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sigma_mu (long_name='standard deviation investment-specific technology')
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sigma_A (long_name='standard deviation neutral technology')
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sigma_m (long_name='standard deviation monetary policy shock')
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;
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//Note that the parameter naming in FV(2010) differs from FV(2006)
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//Fixed parameters, taken from FV(2010), Table 2, p. 37
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delta=0.025;
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epsilon=10;
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eta= 10;
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Phi=0;
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gammma2=0.001;
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//Estimated parameters, taken from FV(2010), Table 3, p. 38, median estimate parameters
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betta =0.998;
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h=0.97;
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varpsi =8.92;
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gammma = 1.17;
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kappa =9.51;
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alppha =0.21;
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thetap =0.82;
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chi = 0.63;
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thetaw =0.68;
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chiw =0.62;
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gammmaR =0.77;
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gammmay =0.19;
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gammmaPI =1.29;
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PIbar = 1.01;
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rhod = 0.12;
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rhophi = 0.93;
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sigma_A = exp(-3.97);
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sigma_d = exp(-1.51);
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sigma_phi =exp(-2.36);
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sigma_mu =exp(-5.43);
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sigma_m =exp(-5.85);
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Lambdamu=3.4e-3;
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LambdaA = 2.8e-3;
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/*
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The following parameters are set in the steady state file as they depend on other
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deep parameters (some were estimated in the original study). Setting them in the
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steady state file means they are updated for every parameter draw in the MCMC
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algorithm, while the parameters initialized here are only set once for the initial
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values of the parameters they depend on:
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gammma1=mu_z*mu_I/betta-(1-delta);
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Rbar=1+(PIbar*mu_z/betta-1);
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Lambdax=exp(LambdaYd);
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LambdaYd= (LambdaA+alppha*Lambdamu)/(1-alppha);
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*/
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/*
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The following model equations are the stationary model equations, taken from
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FV(2006), p. 20, section 3.2.
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*/
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model;
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[name='FOC consumption']
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d*(c-h*c(-1)*mu_z^(-1))^(-1)-h*betta*d(+1)*(c(+1)*mu_z(+1)-h*c)^(-1)=lambda;
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[name='Euler equation']
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lambda=betta*lambda(+1)*mu_z(+1)^(-1)/PI(+1)*R;
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[name='FOC capital utilization']
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r=gammma1+gammma2*(u-1);
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[name='FOC capital']
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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));
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[name='FOC investment']
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1=q*(1-(kappa/2*(x/x(-1)*mu_z-Lambdax)^2)-(kappa*(x/x(-1)*mu_z-Lambdax)*x/x(-1)*mu_z))
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+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;
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[name='Wage setting 1']
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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);
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[name='Wage setting 2']
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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);
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[name='Firm price setting 1']
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g1=lambda*mc*yd+betta*thetap*(PI^chi/PI(+1))^(-epsilon)*g1(+1);
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[name='Firm price setting 2']
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g2=lambda*PIstar*yd+betta*thetap*(PI^chi/PI(+1))^(1-epsilon)*PIstar/PIstar(+1)*g2(+1);
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[name='Firm price setting 3']
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epsilon*g1=(epsilon-1)*g2;
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[name='Optimal capital labor ratio']
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u*k/ld=alppha/(1-alppha)*w/r*mu_z*mu_I;
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[name='Marginal costs']
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mc=(1/(1-alppha))^(1-alppha)*(1/alppha)^alppha*w^(1-alppha)*r^alppha;
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[name='law of motion wages']
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1=thetaw*(PI(-1)^chiw/PI)^(1-eta)*(w(-1)/w*mu_z^(-1))^(1-eta)+(1-thetaw)*PIstarw^(1-eta);
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[name='law of motion prices']
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1=thetap*(PI(-1)^chi/PI)^(1-epsilon)+(1-thetap)*PIstar^(1-epsilon);
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[name='Taylor Rule']
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R/Rbar=(R(-1)/Rbar)^gammmaR*((PI/PIbar)^gammmaPI*((yd/yd(-1)*mu_z)/exp(LambdaYd))^gammmay)^(1-gammmaR)*exp(sigma_m*epsm);
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[name='Resource constraint']
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yd=c+x+mu_z^(-1)*mu_I^(-1)*(gammma1*(u-1)+gammma2/2*(u-1)^2)*k;
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[name='Aggregate production']
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yd=(mu_A*mu_z^(-1)*(u*k)^alppha*ld^(1-alppha)-Phi)/vp;
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[name='Aggregate labor market']
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l=vw*ld;
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[name='LOM Price dispersion term']
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vp=thetap*(PI(-1)^chi/PI)^(-epsilon)*vp(-1)+(1-thetap)*PIstar^(-epsilon);
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[name='LOM Wage dispersion term']
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vw=thetaw*(w(-1)/w*mu_z^(-1)*PI(-1)^chiw/PI)^(-eta)*vw(-1)+(1-thetaw)*(PIstarw)^(-eta);
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[name='Law of motion for capital']
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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;
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[name='Profits']
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F=yd-1/(1-alppha)*w*ld;
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[name='definition optimal wage inflation']
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PIstarw=wstar/w;
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//exogenous processes
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[name='Preference Shock']
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log(d)=rhod*log(d(-1))+sigma_d*epsd;
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[name='Labor disutility Shock']
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log(phi)=rhophi*log(phi(-1))+sigma_phi*epsphi;
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[name='Investment specific technology']
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log(mu_I)=Lambdamu+sigma_mu*epsmu_I;
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[name='Neutral technology']
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log(mu_A)=LambdaA+sigma_A*epsA;
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[name='Defininition composite technology']
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mu_z=mu_A^(1/(1-alppha))*mu_I^(alppha/(1-alppha));
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end;
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shocks;
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var epsd; stderr 1;
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var epsphi; stderr 1;
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var epsmu_I; stderr 1;
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var epsA; stderr 1;
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var epsm; stderr 1;
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end;
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steady;
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check;
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stoch_simul(order=1,irf=20) yd c R PI;
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