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Add example for user-defined steady state file 

Closes https://git.dynare.org/Dynare/dynare/-/issues/1576
time-shift
Johannes Pfeifer 2020-11-13 14:29:12 +01:00
parent e6c8daf922
commit 1ce2ad22c5
3 changed files with 205 additions and 1 deletions
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8
doc/manual/source/examples.rst
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@ -61,4 +61,10 @@ description, please refer to the comments inside the files themselves.
File demonstrating how to conduct optimal policy experiments in a
simple New Keynesian model either under commitment (Ramsey) or using
optimal simple rules (OSR)
optimal simple rules (OSR)
``Ramsey_steady_file.mod``
File demonstrating how to conduct optimal policy experiments in a
simple New Keynesian model under commitment (Ramsey) with a user-defined
conditional steady state file

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examples/Ramsey_steady_file.mod Normal file
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/*
* This file replicates the model studied in:
* Lawrence J. Christiano, Roberto Motto and Massimo Rostagno (2007):
* "Notes on Ramsey-Optimal Monetary Policy", Section 2
* The paper is available at http://faculty.wcas.northwestern.edu/~lchrist/d16/d1606/ramsey.pdf
*
* Notes:
* - This mod-files allows to simulate a simple New Keynesian Model with Rotemberg price
* adjustment costs under fully optimal monetary under commitment (Ramsey)
*
* - This files shows how to use a userd-defined conditional steady state file in the Ramsey case. It takes
* the value of the defined instrument R as given and then computes the rest of the steady
* state, including the steady state inflation rate, based on this value. The initial value
* of the instrument for steady state search must then be defined in an initval-block.
*
* This implementation was written by Johannes Pfeifer.
*
* If 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) 2019 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')
pi $\pi$ (long_name='Gross inflation')
h $h$ (long_name='hours worked')
Z $Z$ (long_name='TFP')
R $R$ (long_name='Net nominal interest rate')
log_C ${\ln C}$ (long_name='Log Consumption')
log_h ${\ln h}$ (long_name='Log hours worked')
pi_ann ${\pi^{ann}}$ (long_name='Annualized net inflation')
R_ann ${R^{ann}}$ (long_name='Annualized net nominal interest rate')
r_real ${r^{ann,real}}$ (long_name='Annualized net real interest rate')
y_nat ${y^{nat}}$ (long_name='Natural (flex price) output')
y_gap ${r^{gap}}$ (long_name='Output gap')
;
varexo epsilon ${\varepsilon}$ (long_name='TFP shock')
;
parameters beta ${\beta}$ (long_name='discount factor')
theta ${\theta}$ (long_name='substitution elasticity')
tau ${\tau}$ (long_name='labor subsidy')
chi ${\chi}$ (long_name='labor disutility')
phi ${\phi}$ (long_name='price adjustment costs')
rho ${\rho}$ (long_name='TFP autocorrelation')
;
beta=0.99;
theta=5;
phi=100;
rho=0.9;
tau=0;
chi=1;
model;
[name='Euler equation']
1/(1+R)=beta*C/(C(+1)*pi(+1));
[name='Firm FOC']
(tau-1/(theta-1))*(1-theta)+theta*(chi*h*C/(exp(Z))-1)=phi*(pi-1)*pi-beta*phi*(pi(+1)-1)*pi(+1);
[name='Resource constraint']
C*(1+phi/2*(pi-1)^2)=exp(Z)*h;
[name='TFP process']
Z=rho*Z(-1)+epsilon;
[name='Definition log consumption']
log_C=log(C);
[name='Definition log hours worked']
log_h=log(h);
[name='Definition annualized inflation rate']
pi_ann=4*log(pi);
[name='Definition annualized nominal interest rate']
R_ann=4*R;
[name='Definition annualized real interest rate']
r_real=4*log((1+R)/pi(+1));
[name='Definition natural output']
y_nat=exp(Z)*sqrt((theta-1)/theta*(1+tau)/chi);
[name='output gap']
y_gap=log_C-log(y_nat);
end;
initval;
R=1/beta-1;
end;
shocks;
var epsilon = 0.01^2;
end;
//use Ramsey optimal policy
//define planner objective, which corresponds to utility function of agents
planner_objective log(C)-chi/2*h^2;
//set up Ramsey optimal policy problem with interest rate R as the instrument,...
// defining the discount factor in the planner objective to be the one of private agents
ramsey_model(instruments=(R),planner_discount=beta,planner_discount_latex_name=$\beta$);
//conduct stochastic simulations of the Ramsey problem
stoch_simul(order=1,irf=20,periods=500) pi_ann log_h R_ann log_C Z r_real;
evaluate_planner_objective;

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examples/Ramsey_steady_file_steadystate.m Normal file
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function [ys,params,check] = Ramsey_steady_file_steadystate(ys,exo,M_,options_)
% function [ys,params,check] = Ramsey_steady_file_steadystate(ys,exo,M_,options_)
% computes the steady state for the Ramsey_steady_file.mod, conditional on
% the instrument value provided
%
% Inputs:
% - ys [vector] vector of initial values for the steady state of
% the endogenous variables
% - exo [vector] vector of values for the exogenous variables
% - M_ [structure] Dynare model structure
% - options [structure] Dynare options structure
%
% Output:
% - ys [vector] vector of steady state values for the the endogenous variables
% - params [vector] vector of parameter values
% - check [scalar] set to 0 if steady state computation worked and to
% 1 of not (allows to impose restrictions on parameters)
% Copyright (C) 2020 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 <http://www.gnu.org/licenses/>.
% read out parameters to access them with their name
beta=NaN; %make parameter known to Matlab function, prevents crashes due to Matlab function with same name;
%will be overwritten next
NumberOfParameters = M_.param_nbr;
for ii = 1:NumberOfParameters
paramname = M_.param_names{ii};
eval([ paramname ' = M_.params(' int2str(ii) ');']);
end
% read in instrument values
for ii = 1:size(options_.instruments,1)
eval([options_.instruments{ii} ' = ys(strmatch(options_.instruments{ii},M_.endo_names,''exact'')) ;']);
end
% initialize indicator
check = 0;
%% Enter model equations here
Z=0;
pi=(R+1)*beta;
C=sqrt((1+1/theta*((1-beta)*(pi-1)*pi-(tau-1/(theta-1))*(1-theta)))/(chi*(1+phi/2*(pi-1)^2)));
h=C*(1+phi/2*(pi-1)^2);
log_C=log(C);
log_h=log(h);
pi_ann=4*log(pi);
R_ann=4*R;
r_real=4*log((1+R)/pi);
y_nat=sqrt((theta-1)/theta*(1+tau)/chi);
y_gap=log_C-log(y_nat);
%% end own model equations
params=NaN(NumberOfParameters,1);
for iter = 1:length(M_.params) %update parameters set in the file
eval([ 'params(' num2str(iter) ') = ' M_.param_names{iter} ';' ])
end
NumberOfEndogenousVariables = M_.orig_endo_nbr; %auxiliary variables are set automatically
for ii = 1:NumberOfEndogenousVariables
varname = M_.endo_names{ii};
eval(['ys(' int2str(ii) ') = ' varname ';']);
end