/*
* 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 .
*/
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;