164 lines
6.8 KiB
Modula-2
164 lines
6.8 KiB
Modula-2
/*
|
|
* This file implements the baseline New Keynesian model of Jordi Galí (2015): Monetary Policy, Inflation,
|
|
* and the Business Cycle, Princeton University Press, Second Edition, Chapter 3
|
|
*
|
|
* THIS MOD-FILE REQUIRES DYNARE 4.5 OR HIGHER
|
|
*
|
|
* Notes:
|
|
* - all model variables are expressed in deviations from steady state, i.e. in contrast to
|
|
* to the chapter, both the nominal interest rate and natural output are not in log-levels, but rather mean 0
|
|
*
|
|
* This implementation was written by Johannes Pfeifer. In case you spot mistakes,
|
|
* email me at jpfeifer@gmx.de
|
|
*
|
|
* Please note that the following copyright notice only applies to this Dynare
|
|
* implementation of the model.
|
|
*/
|
|
|
|
/*
|
|
* Copyright © 2016-20 Johannes Pfeifer
|
|
* Copyright © 2020 Dynare Team
|
|
*
|
|
* This 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.
|
|
*
|
|
* It 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.
|
|
*
|
|
* For a copy of the GNU General Public License,
|
|
* see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
|
|
var pi ${\pi}$ (long_name='inflation')
|
|
y_gap ${\tilde y}$ (long_name='output gap')
|
|
y_nat ${y^{nat}}$ (long_name='natural output') //(in contrast to the textbook defined in deviation from steady state)
|
|
y ${y}$ (long_name='output')
|
|
yhat ${\hat y}$ (long_name='output deviation from steady state')
|
|
r_nat ${r^{nat}}$ (long_name='natural interest rate')
|
|
r_real ${r^r}$ (long_name='real interest rate')
|
|
i ${i}$ (long_name='nominal interrst rate')
|
|
n ${n}$ (long_name='hours worked')
|
|
m_real ${m-p}$ (long_name='real money stock')
|
|
m_growth_ann ${\Delta m}$ (long_name='money growth annualized')
|
|
m_nominal ${m}$ (long_name='nominal money stock')
|
|
a ${a}$ (long_name='AR(1) technology shock process')
|
|
r_real_ann ${r^{r,ann}}$ (long_name='annualized real interest rate')
|
|
i_ann ${i^{ann}}$ (long_name='annualized nominal interest rate')
|
|
r_nat_ann ${r^{nat,ann}}$ (long_name='annualized natural interest rate')
|
|
pi_ann ${\pi^{ann}}$ (long_name='annualized inflation rate')
|
|
z ${z}$ (long_name='AR(1) preference shock process')
|
|
p ${p}$ (long_name='price level')
|
|
w ${w}$ (long_name='nominal wage')
|
|
c ${c}$ (long_name='consumption')
|
|
w_real ${\frac{w}{p}}$ (long_name='real wage')
|
|
mu ${\mu}$ (long_name='markup')
|
|
mu_hat ${\hat \mu}$ (long_name='markup gap')
|
|
;
|
|
|
|
varexo eps_a ${\varepsilon_a}$ (long_name='technology shock')
|
|
eps_z ${\varepsilon_z}$ (long_name='preference shock innovation')
|
|
;
|
|
|
|
parameters alppha ${\alpha}$ (long_name='capital share')
|
|
betta ${\beta}$ (long_name='discount factor')
|
|
rho_a ${\rho_a}$ (long_name='autocorrelation technology shock')
|
|
rho_z ${\rho_{z}}$ (long_name='autocorrelation monetary demand shock')
|
|
siggma ${\sigma}$ (long_name='inverse EIS')
|
|
varphi ${\varphi}$ (long_name='inverse Frisch elasticity')
|
|
phi_pi ${\phi_{\pi}}$ (long_name='inflation feedback Taylor Rule')
|
|
phi_y ${\phi_{y}}$ (long_name='output feedback Taylor Rule')
|
|
eta ${\eta}$ (long_name='semi-elasticity of money demand')
|
|
epsilon ${\epsilon}$ (long_name='demand elasticity')
|
|
theta ${\theta}$ (long_name='Calvo parameter')
|
|
;
|
|
%----------------------------------------------------------------
|
|
% Parametrization, p. 67 and p. 113-115
|
|
%----------------------------------------------------------------
|
|
siggma = 1;
|
|
varphi=5;
|
|
phi_pi = 1.5;
|
|
phi_y = 0.125;
|
|
theta=3/4;
|
|
rho_z = 0.5;
|
|
rho_a = 0.9;
|
|
betta = 0.99;
|
|
eta =3.77; %footnote 11, p. 115
|
|
alppha=1/4;
|
|
epsilon=9;
|
|
|
|
%----------------------------------------------------------------
|
|
% First Order Conditions
|
|
%----------------------------------------------------------------
|
|
|
|
model(linear);
|
|
//Composite parameters
|
|
#Omega=(1-alppha)/(1-alppha+alppha*epsilon); %defined on page 60
|
|
#psi_n_ya=(1+varphi)/(siggma*(1-alppha)+varphi+alppha); %defined on page 62
|
|
#lambda=(1-theta)*(1-betta*theta)/theta*Omega; %defined on page 61
|
|
#kappa=lambda*(siggma+(varphi+alppha)/(1-alppha)); %defined on page 63
|
|
[name='New Keynesian Phillips Curve eq. (22)']
|
|
pi=betta*pi(+1)+kappa*y_gap;
|
|
[name='Dynamic IS Curve eq. (23)']
|
|
y_gap=-1/siggma*(i-pi(+1)-r_nat)+y_gap(+1);
|
|
[name='Definition natural rate of interest eq. (24)']
|
|
r_nat=-siggma*psi_n_ya*(1-rho_a)*a+(1-rho_z)*z;
|
|
[name='Definition real interest rate']
|
|
r_real=i-pi(+1);
|
|
[name='Definition natural output, eq. (20)']
|
|
y_nat=psi_n_ya*a;
|
|
[name='Definition output gap']
|
|
y_gap=y-y_nat;
|
|
[name='TFP shock']
|
|
a=rho_a*a(-1)+eps_a;
|
|
[name='Production function (eq. 14)']
|
|
y=a+(1-alppha)*n;
|
|
[name='Preference shock, p. 54']
|
|
z = rho_z*z(-1) - eps_z;
|
|
[name='Money growth (derived from eq. (4))']
|
|
m_growth_ann=4*(y-y(-1)-eta*(i-i(-1))+pi);
|
|
[name='Real money demand (eq. 4)']
|
|
m_real=y-eta*i;
|
|
[name='Annualized nominal interest rate']
|
|
i_ann=4*i;
|
|
[name='Annualized real interest rate']
|
|
r_real_ann=4*r_real;
|
|
[name='Annualized natural interest rate']
|
|
r_nat_ann=4*r_nat;
|
|
[name='Annualized inflation']
|
|
pi_ann=4*pi;
|
|
[name='Output deviation from steady state']
|
|
yhat=y-steady_state(y);
|
|
[name='Definition price level']
|
|
pi=p-p(-1);
|
|
[name='resource constraint, eq. (12)']
|
|
y=c;
|
|
[name='FOC labor, eq. (2)']
|
|
w-p=siggma*c+varphi*n;
|
|
[name='definition real wage']
|
|
w_real=w-p;
|
|
[name='definition nominal money stock']
|
|
m_nominal=m_real+p;
|
|
[name='average price markup, eq. (18)']
|
|
mu=-(siggma+(varphi+alppha)/(1-alppha))*y+(1+varphi)/(1-alppha)*a;
|
|
[name='average price markup, eq. (20)']
|
|
mu_hat=-(siggma+(varphi+alppha)/(1-alppha))*y_gap;
|
|
end;
|
|
|
|
|
|
%----------------------------------------------------------------
|
|
% define shock variances
|
|
%---------------------------------------------------------------
|
|
shocks;
|
|
var eps_a = 0.5^2; //unit shock to preferences
|
|
end;
|
|
|
|
planner_objective 0.5*((siggma+(varphi+alppha)/(1-alppha))*yhat^2+epsilon/0.0215*pi^2)/100;
|
|
discretionary_policy(instruments=(i),irf=20,planner_discount=betta, periods=0) y_gap pi_ann y n w_real p yhat;
|
|
|
|
|