Merge pull request #548 from JohannesPfeifer/master

Clean up steady state file examples/NK_baseline_steadystate.m to make it...

doc/dynare.texi

@@ -10518,8 +10518,12 @@ Two examples of a small RBC model in a stochastic setup, presented in
 @cite{Collard (2001)} (see the file @file{guide.pdf} which comes with
 Dynare).
 
+@item example3.mod
+A small RBC model in a stochastic setup, presented in
+@cite{Collard (2001)}. The steady state is solved analytically using the  @code{steady_state_model} block (@pxref{steady_state_model}). 
+
 @item fs2000.mod
-A cash in advance model, estimated by @cite{Schorfheide (2000)}.
+A cash in advance model, estimated by @cite{Schorfheide (2000)}. The file shows how to use Dynare for estimation.
 
 @item fs2000_nonstationary.mod
 The same model than @file{fs2000.mod}, but written in non-stationary
@@ -10527,12 +10531,15 @@ form. Detrending of the equations is done by Dynare.
 
 @item bkk.mod
 Multi-country RBC model with time to build, presented in @cite{Backus,
-Kehoe and Kydland (1992)}.
+Kehoe and Kydland (1992)}. The file shows how to use Dynare's macro-processor.
 
 @item agtrend.mod
 Small open economy RBC model with shocks to the growth trend, presented
 in @cite{Aguiar and Gopinath (2004)}.
 
+@item NK_baseline.mod
+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.
+
 @end table
 
 @node Dynare misc commands
@@ -10699,6 +10706,10 @@ Fernández-Villaverde, Jesús and Juan Rubio-Ramírez (2005): ``Estimating
 Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood,''
 @i{Journal of Applied Econometrics}, 20, 891--910
 
+@item
+Fernández-Villaverde, Jesús (2010): ``The econometrics of DSGE models,''
+@i{SERIEs}, 1, 3--49
+
 @item
 Geweke, John (1992): ``Evaluating the accuracy of sampling-based approaches 
 to the calculation of posterior moments'', in J.O. Berger, J.M. Bernardo, 

examples/NK_baseline.mod

@@ -15,7 +15,14 @@
  * equations. Moreover, it makes use of a steady state file to i) set 
  * parameters that depend on other parameters that are potentially estimated
  * and ii) solve a nonlinear equation using a numerical solver to find the steady
- * state of labor.
+ * state of labor. It provides an example on how the steady state file can be used
+ * to circumvent some of the limitation of Dynare mod-file by accessing an external
+ * file that allows calling general Matlab routines. These capacities will mostly be 
+ * interesting for power users. If one just wants to provide analytical steady state 
+ * values and update parameters, the steady_state_model-block allows an easy and convenient
+ * alternative. It even allows calling numerical solvers like fsolve. For an example, see
+ * example3.mod
+ * 
  * The model is written in the beginning of period stock notation. To make the model
  * conform with Dynare's end of period stock notation, we use the 
  * predetermined_variables-command.

examples/NK_baseline_steadystate.m

-function [ys,check] = NK_baseline_steadystate(ys,exe)
-global M_ lgy_
-
-if isfield(M_,'param_nbr') == 1
+function [ys,check] = NK_baseline_steadystate(ys,exo)
+% function [ys,check] = NK_baseline_steadystate(ys,exo)
+% computes the steady state for the NK_baseline.mod and uses a numerical
+% solver to do so
+% Inputs: 
+%   - ys        [vector] vector of initial values for the steady state of
+%                   the endogenous variables
+%   - exo       [vector] vector of values for the exogenous variables
+%
+% Output: 
+%   - ys        [vector] vector of steady state values fpr the the endogenous variables
+%   - check     [scalar] set to 0 if steady state computation worked and to
+%                    1 of not (allows to impos restriction on parameters)
+
+global M_ 
+
+% read out parameters to access them with their name
 NumberOfParameters = M_.param_nbr;
-for i = 1:NumberOfParameters
-  paramname = deblank(M_.param_names(i,:));
-  eval([ paramname ' = M_.params(' int2str(i) ');']);
+for ii = 1:NumberOfParameters
+  paramname = deblank(M_.param_names(ii,:));
+  eval([ paramname ' = M_.params(' int2str(ii) ');']);
 end
+% initialize indicator
 check = 0;
-end
 
 
 %% Enter model equations here
@@ -32,6 +45,11 @@ Lambdax=mu_z;
 
 %set the parameter gammma1
 gammma1=mu_z*mu_I/betta-(1-delta);
+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
+    check=1; %set failure indicator
+    return; %return without updating steady states
+end
+
 
 r=1*gammma1;
 R=1+(PI*mu_z/betta-1);
@@ -49,9 +67,17 @@ vp=(1-thetap)/(1-thetap*PI^((1-chi)*epsilon))*PIstar^(-epsilon);
 vw=(1-thetaw)/(1-thetaw*PI^((1-chiw)*eta)*mu_z^eta)*PIstarw^(-eta);
 tempvaromega=alppha/(1-alppha)*w/r*mu_z*mu_I;
 
-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)))...
+[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)))...
 -(eta-1)/eta*wstar/(varpsi*PIstarw^(-eta*gammma)*ld^gammma)*((1-h*mu_z^(-1))^(-1)-betta*h*(mu_z-h)^(-1))*...
 ((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);
+if exitflag <1
+    %indicate the SS computation was not sucessful; this would also be detected by Dynare
+    %setting the indicator here shows how to use this functionality to
+    %filter out parameter draws
+    check=1; %set failure indicator
+    return; %return without updating steady states
+end
+
 
 l=vw*ld;
 k=tempvaromega*ld;
@@ -68,27 +94,12 @@ g2=epsilon/(epsilon-1)*g1;
 
 %% end own model equations
 
-
-for iter = 1:length(M_.params)
+for iter = 1:length(M_.params) %update parameters set in the file
   eval([ 'M_.params(' num2str(iter) ') = ' M_.param_names(iter,:) ';' ])
 end
 
-if isfield(M_,'param_nbr') == 1
-
-if isfield(M_,'orig_endo_nbr') == 1
-NumberOfEndogenousVariables = M_.orig_endo_nbr;
-else
-NumberOfEndogenousVariables = M_.endo_nbr;
-end
-ys = zeros(NumberOfEndogenousVariables,1);
-for i = 1:NumberOfEndogenousVariables
-  varname = deblank(M_.endo_names(i,:));
-  eval(['ys(' int2str(i) ') = ' varname ';']);
-end
-else
-ys=zeros(length(lgy_),1);
-for i = 1:length(lgy_)
-    ys(i) = eval(lgy_(i,:));
-end
-check = 0;
+NumberOfEndogenousVariables = M_.orig_endo_nbr; %auxiliary variables are set automatically
+for ii = 1:NumberOfEndogenousVariables
+  varname = deblank(M_.endo_names(ii,:));
+  eval(['ys(' int2str(ii) ') = ' varname ';']);
 end

examples/example3.mod

+/*
+ * Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
+ * A practical guide" (see "guide.pdf" in the documentation directory).
+ * 
+ * This file uses the steady_state_model-block to provide analytical steady state values.
+ * To do so, the equations of the model have been transformed into a non-linear equation in 
+ * labor h. Within the steady_state_model-block, a helper function is called that uses fsolve
+ * to solve this non-linear equation. The use of the helper function is necessary to avoid 
+ * interference of the Matlab syntax with Dynare's preprocessor. A more complicated alternative 
+ * that provides more flexibility in the type of commands executed and functions called is the use 
+ * of an explicit steady state file. See the NK_baseline.mod in the Examples Folder.
+ * 
+ * This mod-file also shows how to use Dynare's capacities to generate TeX-files of the model equations. 
+ * If you want to see the model equations belonging to this mod-file, run it using Dynare 
+ * and then use a TeX-editor to compile the TeX-files generated.
+ */
+
+/*
+ * Copyright (C) 2013 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/>.
+ */
+
+
+var y, c, k, a, h, b;
+varexo e, u;
+
+parameters beta $\beta$
+     rho $\rho$
+     alpha $\alpha$
+     delta $\delta$
+     theta $\theta$
+     psi $\psi$
+     tau $\tau$;
+
+alpha = 0.36;
+rho   = 0.95;
+tau   = 0.025;
+beta  = 0.99;
+delta = 0.025;
+psi   = 0;
+theta = 2.95;
+
+phi   = 0.1;
+
+model;
+c*theta*h^(1+psi)=(1-alpha)*y;
+k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
+    *(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
+y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
+k = exp(b)*(y-c)+(1-delta)*k(-1);
+a = rho*a(-1)+tau*b(-1) + e;
+b = tau*a(-1)+rho*b(-1) + u;
+end;
+
+steady_state_model;
+h=example3_steady_state_helper(alpha,beta,delta,psi,theta);
+k=((1/beta-(1-delta))/alpha)^(1/(alpha-1))*h;
+y = k^alpha*h^(1-alpha);
+c=(1-alpha)*y/(theta*h^(1+psi));
+a=0;
+b=0;
+end;
+
+shocks;
+var e; stderr 0.009;
+var u; stderr 0.009;
+var e, u = phi*0.009*0.009;
+end;
+
+//use command to generate TeX-Files with dynamic and static model equations
+write_latex_dynamic_model;
+write_latex_static_model;
+
+stoch_simul;

examples/example3_steady_state_helper.m

+function h=example3_steady_state_helper(alpha,beta,delta,psi,theta)
+options=optimset('Display','Final','TolX',1e-10,'TolFun',1e-10);
+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);
+
+