Add example3 that uses steady_state_model block to call fsolve

examples/example3.mod

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+/*
+ * 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

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+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);
+
+