Merge pull request #548 from JohannesPfeifer/master
Clean up steady state file examples/NK_baseline_steadystate.m to make it...time-shift
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@ -10518,8 +10518,12 @@ Two examples of a small RBC model in a stochastic setup, presented in
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@cite{Collard (2001)} (see the file @file{guide.pdf} which comes with
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Dynare).
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@item example3.mod
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A small RBC model in a stochastic setup, presented in
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@cite{Collard (2001)}. The steady state is solved analytically using the @code{steady_state_model} block (@pxref{steady_state_model}).
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@item fs2000.mod
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A cash in advance model, estimated by @cite{Schorfheide (2000)}.
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A cash in advance model, estimated by @cite{Schorfheide (2000)}. The file shows how to use Dynare for estimation.
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@item fs2000_nonstationary.mod
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The same model than @file{fs2000.mod}, but written in non-stationary
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@ -10527,12 +10531,15 @@ form. Detrending of the equations is done by Dynare.
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@item bkk.mod
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Multi-country RBC model with time to build, presented in @cite{Backus,
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Kehoe and Kydland (1992)}.
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Kehoe and Kydland (1992)}. The file shows how to use Dynare's macro-processor.
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@item agtrend.mod
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Small open economy RBC model with shocks to the growth trend, presented
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in @cite{Aguiar and Gopinath (2004)}.
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@item NK_baseline.mod
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Baseline New Keynesian Model estimated in @cite{Fernández-Villaverde (2010)}. It demonstrates how to use an explicit steady state file to update parameters and call a numerical solver.
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@end table
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@node Dynare misc commands
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@ -10699,6 +10706,10 @@ Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2005): ``Estimating
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Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood,''
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@i{Journal of Applied Econometrics}, 20, 891--910
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@item
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Fernández-Villaverde, Jesús (2010): ``The econometrics of DSGE models,''
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@i{SERIEs}, 1, 3--49
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@item
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Geweke, John (1992): ``Evaluating the accuracy of sampling-based approaches
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to the calculation of posterior moments'', in J.O. Berger, J.M. Bernardo,
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@ -15,7 +15,14 @@
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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.
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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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@ -1,14 +1,27 @@
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function [ys,check] = NK_baseline_steadystate(ys,exe)
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global M_ lgy_
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function [ys,check] = NK_baseline_steadystate(ys,exo)
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% function [ys,check] = NK_baseline_steadystate(ys,exo)
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% computes the steady state for the NK_baseline.mod and uses a numerical
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% solver to do so
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% Inputs:
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% - ys [vector] vector of initial values for the steady state of
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% the endogenous variables
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% - exo [vector] vector of values for the exogenous variables
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%
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% Output:
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% - ys [vector] vector of steady state values fpr the the endogenous variables
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% - check [scalar] set to 0 if steady state computation worked and to
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% 1 of not (allows to impos restriction on parameters)
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if isfield(M_,'param_nbr') == 1
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global M_
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% read out parameters to access them with their name
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NumberOfParameters = M_.param_nbr;
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for i = 1:NumberOfParameters
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paramname = deblank(M_.param_names(i,:));
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eval([ paramname ' = M_.params(' int2str(i) ');']);
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for ii = 1:NumberOfParameters
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paramname = deblank(M_.param_names(ii,:));
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eval([ paramname ' = M_.params(' int2str(ii) ');']);
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end
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% initialize indicator
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check = 0;
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end
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%% Enter model equations here
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@ -32,6 +45,11 @@ Lambdax=mu_z;
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%set the parameter gammma1
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gammma1=mu_z*mu_I/betta-(1-delta);
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if gammma1<0 % parameter violates restriction; Preventing this cannot be implemented via prior restriction as it is a composite of different parameters and the valid prior region has unknown form
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check=1; %set failure indicator
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return; %return without updating steady states
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end
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r=1*gammma1;
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R=1+(PI*mu_z/betta-1);
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@ -49,9 +67,17 @@ vp=(1-thetap)/(1-thetap*PI^((1-chi)*epsilon))*PIstar^(-epsilon);
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vw=(1-thetaw)/(1-thetaw*PI^((1-chiw)*eta)*mu_z^eta)*PIstarw^(-eta);
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tempvaromega=alppha/(1-alppha)*w/r*mu_z*mu_I;
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ld=fsolve(@(ld)(1-betta*thetaw*mu_z^(eta-1)*PI^(-(1-chiw)*(1-eta)))/(1-betta*thetaw*mu_z^(eta*(1+gammma))*PI^(eta*(1-chiw)*(1+gammma)))...
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[ld,fval,exitflag]=fsolve(@(ld)(1-betta*thetaw*mu_z^(eta-1)*PI^(-(1-chiw)*(1-eta)))/(1-betta*thetaw*mu_z^(eta*(1+gammma))*PI^(eta*(1-chiw)*(1+gammma)))...
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-(eta-1)/eta*wstar/(varpsi*PIstarw^(-eta*gammma)*ld^gammma)*((1-h*mu_z^(-1))^(-1)-betta*h*(mu_z-h)^(-1))*...
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((mu_A*mu_z^(-1)*vp^(-1)*tempvaromega^alppha-tempvaromega*(1-(1-delta)*(mu_z*mu_I)^(-1)))*ld-vp^(-1)*Phi)^(-1),0.25,options);
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if exitflag <1
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%indicate the SS computation was not sucessful; this would also be detected by Dynare
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%setting the indicator here shows how to use this functionality to
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%filter out parameter draws
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check=1; %set failure indicator
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return; %return without updating steady states
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end
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l=vw*ld;
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k=tempvaromega*ld;
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@ -68,27 +94,12 @@ g2=epsilon/(epsilon-1)*g1;
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%% end own model equations
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for iter = 1:length(M_.params)
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for iter = 1:length(M_.params) %update parameters set in the file
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eval([ 'M_.params(' num2str(iter) ') = ' M_.param_names(iter,:) ';' ])
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end
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if isfield(M_,'param_nbr') == 1
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if isfield(M_,'orig_endo_nbr') == 1
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NumberOfEndogenousVariables = M_.orig_endo_nbr;
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else
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NumberOfEndogenousVariables = M_.endo_nbr;
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end
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ys = zeros(NumberOfEndogenousVariables,1);
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for i = 1:NumberOfEndogenousVariables
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varname = deblank(M_.endo_names(i,:));
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eval(['ys(' int2str(i) ') = ' varname ';']);
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end
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else
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ys=zeros(length(lgy_),1);
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for i = 1:length(lgy_)
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ys(i) = eval(lgy_(i,:));
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end
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check = 0;
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NumberOfEndogenousVariables = M_.orig_endo_nbr; %auxiliary variables are set automatically
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for ii = 1:NumberOfEndogenousVariables
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varname = deblank(M_.endo_names(ii,:));
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eval(['ys(' int2str(ii) ') = ' varname ';']);
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end
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@ -0,0 +1,88 @@
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/*
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* Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
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* A practical guide" (see "guide.pdf" in the documentation directory).
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*
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* This file uses the steady_state_model-block to provide analytical steady state values.
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* To do so, the equations of the model have been transformed into a non-linear equation in
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* labor h. Within the steady_state_model-block, a helper function is called that uses fsolve
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* to solve this non-linear equation. The use of the helper function is necessary to avoid
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* interference of the Matlab syntax with Dynare's preprocessor. A more complicated alternative
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* that provides more flexibility in the type of commands executed and functions called is the use
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* of an explicit steady state file. See the NK_baseline.mod in the Examples Folder.
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*
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* This mod-file also shows how to use Dynare's capacities to generate TeX-files of the model equations.
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* If you want to see the model equations belonging to this mod-file, run it using Dynare
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* and then use a TeX-editor to compile the TeX-files generated.
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*/
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/*
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* Copyright (C) 2013 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 <http://www.gnu.org/licenses/>.
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*/
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var y, c, k, a, h, b;
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varexo e, u;
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parameters beta $\beta$
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rho $\rho$
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alpha $\alpha$
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delta $\delta$
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theta $\theta$
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psi $\psi$
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tau $\tau$;
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alpha = 0.36;
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rho = 0.95;
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tau = 0.025;
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beta = 0.99;
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delta = 0.025;
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psi = 0;
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theta = 2.95;
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phi = 0.1;
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model;
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c*theta*h^(1+psi)=(1-alpha)*y;
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k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
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*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
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y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
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k = exp(b)*(y-c)+(1-delta)*k(-1);
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a = rho*a(-1)+tau*b(-1) + e;
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b = tau*a(-1)+rho*b(-1) + u;
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end;
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steady_state_model;
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h=example3_steady_state_helper(alpha,beta,delta,psi,theta);
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k=((1/beta-(1-delta))/alpha)^(1/(alpha-1))*h;
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y = k^alpha*h^(1-alpha);
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c=(1-alpha)*y/(theta*h^(1+psi));
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a=0;
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b=0;
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end;
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shocks;
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var e; stderr 0.009;
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var u; stderr 0.009;
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var e, u = phi*0.009*0.009;
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end;
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//use command to generate TeX-Files with dynamic and static model equations
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write_latex_dynamic_model;
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write_latex_static_model;
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stoch_simul;
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@ -0,0 +1,5 @@
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function h=example3_steady_state_helper(alpha,beta,delta,psi,theta)
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options=optimset('Display','Final','TolX',1e-10,'TolFun',1e-10);
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h=fsolve(@(h)1- ((((((1/beta-(1-delta))/alpha)^(1/(alpha-1))*h)^(alpha-1))*(h^(1-alpha))-(((1-alpha)*((((1/beta-(1-delta))/alpha)^(1/(alpha-1)))^alpha))/(theta*h^psi))/(((1/beta-(1-delta))/alpha)^(1/(alpha-1))*h))+(1-delta)),0.2,options);
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