diff --git a/examples/NK_baseline.mod b/examples/NK_baseline.mod
index 800bc1f02d2bf2feab2375b419bf0e577dec0b8a..805f19e86e73154cc27040f469fbea2e6a7fcdd2 100644
--- a/examples/NK_baseline.mod
+++ b/examples/NK_baseline.mod
@@ -29,11 +29,10 @@
*
* Please note that the following copyright notice only applies to this Dynare
* implementation of the model.
-
*/
/*
- * Copyright (C) 2013-2016 Dynare Team
+ * Copyright (C) 2013-2020 Dynare Team
*
* This file is part of Dynare.
*
@@ -51,72 +50,78 @@
* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
*/
-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
+var d (long_name='preference shock')
+ c (long_name='consumption')
+ mu_z (long_name='trend growth rate of the economy (from neutral and investment specific technology)')
+ mu_I (long_name='growth rate of investment-specific technology growth')
+ mu_A (long_name='growth rate of neutral technology')
+ lambda (long_name='Lagrange multiplier')
+ R (long_name='Nominal Interest rate')
+ PI (long_name='Inflation')
+ r (long_name='rental rate of capital')
+ x (long_name='investment')
+ u (long_name='capacity utilization')
+ q (long_name='Tobin marginal q')
+ f (long_name='variable for recursive formulation of wage setting')
+ ld (long_name='aggregate labor demand')
+ w (long_name='real wage')
+ wstar (long_name='optimal real wage')
+ PIstarw (long_name='optimal wage inflation')
+ PIstar (long_name='optimal price inflation')
+ g1 (long_name='variable 1 for recursive formulation of price setting')
+ g2 (long_name='variable 2 for recursive formulation of price setting')
+ yd (long_name='aggregate output')
+ mc (long_name='marginal costs')
+ k (long_name='capital')
+ vp (long_name='price dispersion term')
+ vw (long_name='wage dispersion term')
+ l (long_name='aggregate labor bundle')
+ phi (long_name='labor disutility shock')
+ F (long_name='firm profits')
+ ;
-varexo epsd epsphi epsmu_I epsA epsm;
+varexo epsd (long_name='Innovation preference shock')
+ epsphi (long_name='Innovation labor disutility shock')
+ epsmu_I (long_name='Innovation investment-specific technology')
+ epsA (long_name='Innovation neutral technology')
+ epsm (long_name='Innovation monetary policy shock')
+ ;
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
-
+parameters h (long_name='consumption habits')
+ betta (long_name='discount factor')
+ gammma1 (long_name='capital utilization, linear term')
+ gammma2 (long_name='capital utilization, quadratic term')
+ delta (long_name='depreciation rate')
+ kappa (long_name='capital adjustment costs parameter')
+ eta (long_name='elasticity of substitution between labor varieties')
+ epsilon (long_name='elasticity of substitution between goods varieties')
+ varpsi (long_name='labor disutility parameter')
+ gammma (long_name='inverse Frisch elasticity')
+ chiw (long_name='wage indexation parameter')
+ chi (long_name='price indexation')
+ thetap (long_name='Calvo parameter prices')
+ thetaw (long_name='Calvo parameter wages')
+ alppha (long_name='capital share')
+ Rbar (long_name='steady state interest rate')
+ PIbar (long_name='steady state inflation')
+ gammmaR (long_name='interest smoothing coefficient Taylor rule')
+ gammmaPI (long_name='feedback coefficient to inflation monetary policy rule')
+ gammmay (long_name='feedback coefficient to output growth deviation in monetary policy rule')
+ Phi (long_name='firms fixed costs')
+ rhod (long_name='autocorrelation preference shock')
+ rhophi (long_name='autocorrelation labor disutility shock')
+ Lambdamu (long_name='steady state growth rate of investmentment-specific technology')
+ LambdaA (long_name='steady state neutral technology growth')
+ Lambdax (long_name='steady state growth rate of investment')
+ LambdaYd (long_name='steady state growth rate of output')
+ sigma_d (long_name='standard deviation preference shock')
+ sigma_phi (long_name='standard deviation labor disutility shock')
+ sigma_mu (long_name='standard deviation investment-specific technology')
+ sigma_A (long_name='standard deviation neutral technology')
+ sigma_m (long_name='standard deviation monetary policy shock')
+ ;
//Note that the parameter naming in FV(2010) differs from FV(2006)
//Fixed parameters, taken from FV(2010), Table 2, p. 37
@@ -177,60 +182,67 @@ FV(2006), p. 20, section 3.2.
*/
model;
-//1. FOC consumption
+[name='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
+[name='Euler equation']
lambda=betta*lambda(+1)*mu_z(+1)^(-1)/PI(+1)*R;
-//3. FOC capital utilization
+[name='FOC capital utilization']
r=gammma1+gammma2*(u-1);
-//4. FOC capital
+[name='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
+[name='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
+[name='Wage setting 1']
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);
+[name='Wage setting 2']
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
+[name='Firm price setting 1']
g1=lambda*mc*yd+betta*thetap*(PI^chi/PI(+1))^(-epsilon)*g1(+1);
+[name='Firm price setting 2']
g2=lambda*PIstar*yd+betta*thetap*(PI^chi/PI(+1))^(1-epsilon)*PIstar/PIstar(+1)*g2(+1);
+[name='Firm price setting 3']
epsilon*g1=(epsilon-1)*g2;
-//11-12. optimal inputs
+[name='Optimal capital labor ratio']
u*k/ld=alppha/(1-alppha)*w/r*mu_z*mu_I;
+[name='Marginal costs']
mc=(1/(1-alppha))^(1-alppha)*(1/alppha)^alppha*w^(1-alppha)*r^alppha;
-//13. law of motion wages
+[name='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
+[name='law of motion prices']
1=thetap*(PI(-1)^chi/PI)^(1-epsilon)+(1-thetap)*PIstar^(1-epsilon);
-//15. Taylor Rule
+[name='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
+[name='Resource constraint']
yd=c+x+mu_z^(-1)*mu_I^(-1)*(gammma1*(u-1)+gammma2/2*(u-1)^2)*k;
+[name='Aggregate production']
yd=(mu_A*mu_z^(-1)*(u*k)^alppha*ld^(1-alppha)-Phi)/vp;
-//18-20. Price and wage dispersion terms
+[name='Aggregate labor market']
l=vw*ld;
+[name='LOM Price dispersion term']
vp=thetap*(PI(-1)^chi/PI)^(-epsilon)*vp(-1)+(1-thetap)*PIstar^(-epsilon);
+[name='LOM Wage dispersion term']
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
+[name='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
+[name='Profits']
F=yd-1/(1-alppha)*w*ld;
-//23. definition optimal wage inflation
+[name='definition optimal wage inflation']
PIstarw=wstar/w;
//exogenous processes
-//24. Preference Shock
+[name='Preference Shock']
log(d)=rhod*log(d(-1))+epsd;
-//25. Labor disutility Shock
+[name='Labor disutility Shock']
log(phi)=rhophi*log(phi(-1))+epsphi;
-//26. Investment specific technology
+[name='Investment specific technology']
log(mu_I)=Lambdamu+epsmu_I;
-//27. Neutral technology
+[name='Neutral technology']
log(mu_A)=LambdaA+epsA;
-//28. Defininition composite technology
+[name='Defininition composite technology']
mu_z=mu_A^(1/(1-alppha))*mu_I^(alppha/(1-alppha));
end;