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discretionary_policy: allow for non-linear model to be used

time-shift
Johannes Pfeifer 2020-12-16 21:47:43 +01:00
parent 84566adac9
commit 4b793da2c3
7 changed files with 415 additions and 13 deletions
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3
matlab/discretionary_policy/discretionary_policy.m
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@ -36,6 +36,8 @@ options_.discretionary_policy = 1;
options_.order = 1;
[info, oo_, options_, M_] = stoch_simul(M_, options_, oo_, var_list);
oo_.steady_state = oo_.dr.ys;
if ~options_.noprint
disp_steady_state(M_,oo_)
for i=M_.orig_endo_nbr:M_.endo_nbr
@ -44,7 +46,6 @@ if ~options_.noprint
end
end
end
oo_.planner_objective_value = evaluate_planner_objective(M_,options_,oo_);
options_.order = origorder;

24
matlab/discretionary_policy/discretionary_policy_1.m
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@ -41,11 +41,13 @@ beta = get_optimal_policy_discount_factor(M_.params, M_.param_names);
%call steady_state_file if present to update parameters
if options_.steadystate_flag
% explicit steady state file
[~,M_.params,info] = evaluate_steady_state_file(oo_.steady_state,[oo_.exo_steady_state; oo_.exo_det_steady_state],M_, ...
[ys,M_.params,info] = evaluate_steady_state_file(oo_.steady_state,[oo_.exo_steady_state; oo_.exo_det_steady_state],M_, ...
options_,false);
if info(1)
return;
end
else
ys=zeros(M_.endo_nbr,1);
end
[U,Uy,W] = feval([M_.fname,'.objective.static'],zeros(M_.endo_nbr,1),[], M_.params);
if any(any(isnan(Uy)))
@ -73,8 +75,10 @@ W=reshape(W,M_.endo_nbr,M_.endo_nbr);
klen = M_.maximum_lag + M_.maximum_lead + 1;
iyv=M_.lead_lag_incidence';
% Find the jacobian
z = repmat(zeros(M_.endo_nbr,1),1,klen);
z = z(nonzeros(iyv)) ;
z = repmat(ys,1,klen);
iyr0 = find(iyv(:)) ;
z = z(iyr0);
it_ = M_.maximum_lag + 1 ;
if M_.exo_nbr == 0
@ -82,10 +86,10 @@ if M_.exo_nbr == 0
end
[junk,jacobia_] = feval([M_.fname '.dynamic'],z, [zeros(size(oo_.exo_simul)) ...
oo_.exo_det_simul], M_.params, zeros(M_.endo_nbr,1), it_);
if any(junk~=0)
info = 65; %the model must be written in deviation form and not have constant terms
return;
oo_.exo_det_simul], M_.params, ys, it_);
if max(abs(junk))>options_.solve_tolf
info = 65; %the model must be written in deviation form and not have constant terms or have a steady state provided
return;
end
Indices={'lag','contemp','lead'};
@ -116,10 +120,12 @@ else
end
%write back solution to dr
dr.ys =zeros(M_.endo_nbr,1);
dr.ys =ys;
dr=set_state_space(dr,M_,options_);
T=H(dr.order_var,dr.order_var);
dr.ghu=G(dr.order_var,:);
Selection=M_.lead_lag_incidence(1,dr.order_var)>0;%select state variables
if M_.maximum_endo_lag
Selection=M_.lead_lag_incidence(1,dr.order_var)>0;%select state variables
end
dr.ghx=T(:,Selection);
oo_.dr = dr;

2
matlab/get_error_message.m
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@ -122,7 +122,7 @@ switch info(1)
case 64
message = 'discretionary_policy: the derivatives of the objective function contain NaN.';
case 65
message = 'discretionary_policy: the model must be written in deviation form and not have constant terms.';
message = 'discretionary_policy: the model must be written in deviation form and not have constant terms or an analytical steady state meeds to be provided.';
case 66
message = 'discretionary_policy: the objective function must have zero first order derivatives.';
case 71

2
matlab/stoch_simul.m
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@ -79,7 +79,7 @@ oo_.dr=set_state_space(dr,M_,options_);
if PI_PCL_solver
[oo_.dr, info] = PCL_resol(oo_.steady_state,0);
elseif options_.discretionary_policy
if ~options_.linear
if ~options_.order==1
error('discretionary_policy: only linear-quadratic problems can be solved');
end
[~,info,M_,options_,oo_] = discretionary_policy_1(options_.instruments,M_,options_,oo_);

5
tests/Makefile.am
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@ -113,6 +113,8 @@ MODFILES = \
discretionary_policy/dennis_1.mod \
discretionary_policy/dennis_1_estim.mod \
discretionary_policy/Gali_discretion.mod \
discretionary_policy/Gali_2015_chapter_3.mod \
discretionary_policy/Gali_2015_chapter_3_nonlinear.mod \
histval_initval_file/ramst_initval_file.mod \
histval_initval_file/ramst_data.mod \
histval_initval_file/ramst_datafile.mod \
@ -645,7 +647,8 @@ lmmcp/sw_newton.o.trs: lmmcp/sw_lmmcp.o.trs
discretionary_policy/dennis_1_estim.m.trs: discretionary_policy/dennis_1.m.trs
discretionary_policy/dennis_1_estim.o.trs: discretionary_policy/dennis_1.o.trs
discretionary_policy/Gali_2015_chapter_3_nonlinear.m.trs: discretionary_policy/Gali_2015_chapter_3.m.trs
discretionary_policy/Gali_2015_chapter_3_nonlinear.o.trs: discretionary_policy/Gali_2015_chapter_3.o.trs
observation_trends_and_prefiltering/MCMC: m/observation_trends_and_prefiltering/MCMC o/observation_trends_and_prefiltering/MCMC
m/observation_trends_and_prefiltering/MCMC: $(patsubst %.mod, %.m.trs, $(filter observation_trends_and_prefiltering/MCMC/%.mod, $(MODFILES)))

163
tests/discretionary_policy/Gali_2015_chapter_3.mod Normal file
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@ -0,0 +1,163 @@
/*
* 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 (C) 2016-20 Johannes Pfeifer
* Copyright (C) 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 <http://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;

229
tests/discretionary_policy/Gali_2015_chapter_3_nonlinear.mod Normal file
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@ -0,0 +1,229 @@
/*
* 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
*
* Note that this mod-file implements the non-linear first order conditions and that the IRFs show the log-deviations
* from steady state.
*
* THIS MOD-FILE REQUIRES DYNARE 4.5 OR HIGHER
*
* Notes:
* - in the LOM for the discount rate shock z the shock enters with a minus sign in this mod-file to generate the
* IRF to a -0.5% shock
*
* 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 (C) 2016-20 Johannes Pfeifer
* Copyright (C) 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 <http://www.gnu.org/licenses/>.
*/
var C ${C}$ (long_name='Consumption')
W_real ${\frac{W}{P}}$ (long_name='Real Wage')
Pi ${\Pi}$ (long_name='inflation')
A ${A}$ (long_name='AR(1) technology process')
N ${N}$ (long_name='Hours worked')
R ${R^n}$ (long_name='Nominal Interest Rate')
realinterest ${R^{r}}$ (long_name='Real Interest Rate')
Y ${Y}$ (long_name='Output')
Q ${Q}$ (long_name='Bond price')
Z ${Z}$ (long_name='AR(1) preference shock process')
S ${S}$ (long_name='Price dispersion')
Pi_star ${\Pi^*}$ (long_name='Optimal reset price')
x_aux_1 ${x_1}$ (long_name='aux. var. 1 recursive price setting')
x_aux_2 ${x_2}$ (long_name='aux. var. 2 recursive price setting')
MC ${mc}$ (long_name='real marginal costs')
M_real ${M/P}$ (long_name='real money stock')
i_ann ${i^{ann}}$ (long_name='annualized nominal interest rate')
pi_ann ${\pi^{ann}}$ (long_name='annualized inflation rate')
r_real_ann ${r^{r,ann}}$ (long_name='annualized real interest rate')
P ${P}$ (long_name='price level')
log_m_nominal ${log(M)}$ (long_name='log nominal money stock')
log_y ${log(Y)}$ (long_name='log output')
log_W_real ${log(W/P)}$ (long_name='log real wage')
log_N ${log(N)}$ (long_name='log hours')
log_P ${log(P)}$ (long_name='log price level')
log_A ${log(A)}$ (long_name='log technology level')
log_Z ${log(Z)}$ (long_name='log preference shock')
y_hat
pi
;
varexo eps_a ${\varepsilon_a}$ (long_name='technology shock')
eps_z ${\varepsilon_z}$ (long_name='preference shock')
;
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')
tau ${\tau}$ (long_name='labor subsidy')
;
%----------------------------------------------------------------
% 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;
tau=0; //1/epsilon;
%----------------------------------------------------------------
% First Order Conditions
%----------------------------------------------------------------
model;
[name='FOC Wages, eq. (2)']
W_real=C^siggma*N^varphi;
[name='Euler equation eq. (3)']
Q=betta*(C(+1)/C)^(-siggma)*(Z(+1)/Z)/Pi(+1);
[name='Definition nominal interest rate), p. 22 top']
R=1/Q;
[name='Aggregate output, above eq. (14)']
Y=A*(N/S)^(1-alppha);
[name='Definition Real interest rate']
R=realinterest*Pi(+1);
% @#if money_growth_rule==0
% [name='Monetary Policy Rule, p. 26 bottom/eq. (22)']
% R=1/betta*Pi^phi_pi*(Y/steady_state(Y))^phi_y;
% @#endif
[name='Market Clearing, eq. (15)']
C=Y;
[name='Technology Shock, eq. (6)']
log(A)=rho_a*log(A(-1))+eps_a;
[name='Preference Shock, p.54']
log(Z)=rho_z*log(Z(-1))-eps_z;
[name='Definition marginal cost']
MC=W_real/((1-alppha)*Y/N*S);
[name='LOM prices, eq. (7)']
1=theta*Pi^(epsilon-1)+(1-theta)*(Pi_star)^(1-epsilon);
[name='LOM price dispersion']
S=(1-theta)*Pi_star^(-epsilon/(1-alppha))+theta*Pi^(epsilon/(1-alppha))*S(-1);
[name='FOC price setting']
Pi_star^(1+epsilon*(alppha/(1-alppha)))=x_aux_1/x_aux_2*(1-tau)*epsilon/(epsilon-1);
[name='Auxiliary price setting recursion 1']
x_aux_1=Z*C^(-siggma)*Y*MC+betta*theta*Pi(+1)^(epsilon+alppha*epsilon/(1-alppha))*x_aux_1(+1);
[name='Auxiliary price setting recursion 2']
x_aux_2=Z*C^(-siggma)*Y+betta*theta*Pi(+1)^(epsilon-1)*x_aux_2(+1);
[name='Definition log output']
log_y = log(Y);
[name='Definition log real wage']
log_W_real=log(W_real);
[name='Definition log hours']
log_N=log(N);
[name='Annualized inflation']
pi_ann=4*log(Pi);
[name='Annualized nominal interest rate']
i_ann=4*log(R);
[name='Annualized real interest rate']
r_real_ann=4*log(realinterest);
[name='Real money demand, eq. (4)']
M_real=Y/R^eta;
[name='definition nominal money stock']
log_m_nominal=log(M_real*P);
[name='Definition price level']
Pi=P/P(-1);
[name='Definition log price level']
log_P=log(P);
[name='Definition log TFP']
log_A=log(A);
[name='Definition log preference']
log_Z=log(Z);
[mcp='a']
y_hat=log(Y)-STEADY_STATE(log(Y));
pi=log(Pi)-STEADY_STATE(log(Pi));
end;
%----------------------------------------------------------------
% Steady state values
%---------------------------------------------------------------
steady_state_model;
A=1;
Z=1;
S=1;
Pi_star=1;
P=1;
MC=(epsilon-1)/epsilon/(1-tau);
R=1/betta;
Pi=1;
Q=1/R;
realinterest=R;
N=((1-alppha)*MC)^(1/((1-siggma)*alppha+varphi+siggma));
C=A*N^(1-alppha);
W_real=C^siggma*N^varphi;
Y=C;
money_growth=0;
money_growth_ann=0;
nu=0;
x_aux_1=C^(-siggma)*Y*MC/(1-betta*theta*Pi^(epsilon/(1-alppha)));
x_aux_2=C^(-siggma)*Y/(1-betta*theta*Pi^(epsilon-1));
log_y = log(Y);
log_W_real=log(W_real);
log_N=log(N);
pi_ann=4*log(Pi);
i_ann=4*log(R);
r_real_ann=4*log(realinterest);
M_real=Y/R^eta;
log_m_nominal=log(M_real*P);
log_P=log(P);
log_A=0;
log_Z=0;
end;
%----------------------------------------------------------------
% define shock variances
%---------------------------------------------------------------
shocks;
var eps_a = 0.5^2; //unit shock to preferences
end;
% steady;
% check;
% stoch_simul;
planner_objective 0.5*((siggma+(varphi+alppha)/(1-alppha))*y_hat^2+epsilon/0.0215*pi^2)/100;
discretionary_policy(order=1,instruments=(R),irf=20,planner_discount=betta, periods=0) y_hat pi_ann log_y log_N log_W_real log_P;
temp=load('Gali_2015_chapter_3_results.mat');
if abs(oo_.planner_objective_value-temp.oo_.planner_objective_value)>1e-6
warning('Planner objective does not match linear model')
end
if max(max(abs([temp.oo_.irfs.y_eps_a; temp.oo_.irfs.w_real_eps_a; temp.oo_.irfs.n_eps_a; temp.oo_.irfs.pi_ann_eps_a]-...
[oo_.irfs.log_y_eps_a; oo_.irfs.log_W_real_eps_a; oo_.irfs.log_N_eps_a; oo_.irfs.pi_ann_eps_a])))>1e-6
error('Policy is different')
end