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Add example3 that uses steady_state_model block to call fsolve
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Johannes Pfeifer
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Dec 3, 2013
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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. | ||
*/ | ||
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/* | ||
* 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/>. | ||
*/ | ||
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var y, c, k, a, h, b; | ||
varexo e, u; | ||
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parameters beta $\beta$ | ||
rho $\rho$ | ||
alpha $\alpha$ | ||
delta $\delta$ | ||
theta $\theta$ | ||
psi $\psi$ | ||
tau $\tau$; | ||
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alpha = 0.36; | ||
rho = 0.95; | ||
tau = 0.025; | ||
beta = 0.99; | ||
delta = 0.025; | ||
psi = 0; | ||
theta = 2.95; | ||
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phi = 0.1; | ||
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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; | ||
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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; | ||
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shocks; | ||
var e; stderr 0.009; | ||
var u; stderr 0.009; | ||
var e, u = phi*0.009*0.009; | ||
end; | ||
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//use command to generate TeX-Files with dynamic and static model equations | ||
write_latex_dynamic_model; | ||
write_latex_static_model; | ||
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stoch_simul; |
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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); | ||
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