/usr/share/doc/dynare/dynare.html/Optimal-policy.html

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996-2017, Dynare Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with no
Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

A copy of the license can be found at http://www.gnu.org/licenses/fdl.txt. -->
<!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ -->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Optimal policy (Dynare Reference Manual)</title>

<meta name="description" content="Optimal policy (Dynare Reference Manual)">
<meta name="keywords" content="Optimal policy (Dynare Reference Manual)">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="texi2any">
<link href="index.html#Top" rel="start" title="Top">
<link href="Command-and-Function-Index.html#Command-and-Function-Index" rel="index" title="Command and Function Index">
<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
<link href="The-Model-file.html#The-Model-file" rel="up" title="The Model file">
<link href="Sensitivity-and-identification-analysis.html#Sensitivity-and-identification-analysis" rel="next" title="Sensitivity and identification analysis">
<link href="Forecasting.html#Forecasting" rel="prev" title="Forecasting">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.indentedblock {margin-right: 0em}
blockquote.smallindentedblock {margin-right: 0em; font-size: smaller}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smalllisp {margin-left: 3.2em}
kbd {font-style: oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nolinebreak {white-space: nowrap}
span.roman {font-family: initial; font-weight: normal}
span.sansserif {font-family: sans-serif; font-weight: normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en">
<a name="Optimal-policy"></a>
<div class="header">
<p>
Next: <a href="Sensitivity-and-identification-analysis.html#Sensitivity-and-identification-analysis" accesskey="n" rel="next">Sensitivity and identification analysis</a>, Previous: <a href="Forecasting.html#Forecasting" accesskey="p" rel="prev">Forecasting</a>, Up: <a href="The-Model-file.html#The-Model-file" accesskey="u" rel="up">The Model file</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Command-and-Function-Index.html#Command-and-Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Optimal-policy-1"></a>
<h3 class="section">4.19 Optimal policy</h3>

<p>Dynare has tools to compute optimal policies for various types of
objectives. <code>ramsey_model</code> computes automatically the First Order
Conditions (FOC) of a model, given the <code>planner_objective</code>. You can
then use other standard commands to solve, estimate or simulate this
new, expanded model.
</p>
<p>Alternatively, you can either solve for optimal policy under commitment
with <code>ramsey_policy</code>, for optimal policy under discretion with
<code>discretionary_policy</code> or for optimal simple rule with
<code>osr</code> (also implying commitment).
</p>

<a name="osr"></a>
<dl>
<dt><a name="index-osr"></a>Command: <strong>osr</strong> <em>[<var>VARIABLE_NAME</var>&hellip;];</em></dt>
<dt><a name="index-osr-1"></a>Command: <strong>osr</strong> <em>(<var>OPTIONS</var>&hellip;) [<var>VARIABLE_NAME</var>&hellip;];</em></dt>
<dd>
<p><em>Description</em>
</p>
<p>This command computes optimal simple policy rules for
linear-quadratic problems of the form:
</p>
<blockquote>
<p><!-- MATH
 $\min_\gamma E(y'_tWy_t)$
 -->
<SPAN CLASS="MATH"><IMG
 WIDTH="111" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_117.png"
 ALT="$\min_\gamma E(y'_tWy_t)$"></SPAN>
</p></blockquote>

<p>such that:
</p><blockquote>
<p><!-- MATH
 $A_1 E_ty_{t+1}+A_2 y_t+ A_3 y_{t-1}+C e_t=0$
 -->
<SPAN CLASS="MATH"><IMG
 WIDTH="265" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_118.png"
 ALT="$A_1 E_ty_{t+1}+A_2 y_t+ A_3 y_{t-1}+C e_t=0$"></SPAN>
</p></blockquote>

<p>where:
</p>
<ul>
<li> <SPAN CLASS="MATH"><IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="dynare.html_52.png"
 ALT="$E$"></SPAN> denotes the unconditional expectations operator;

</li><li> <SPAN CLASS="MATH"><IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_119.png"
 ALT="$\gamma$"></SPAN> are parameters to be optimized. They must be elements
of the matrices <SPAN CLASS="MATH"><IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_120.png"
 ALT="$A_1$"></SPAN>, <SPAN CLASS="MATH"><IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_121.png"
 ALT="$A_2$"></SPAN>, <SPAN CLASS="MATH"><IMG
 WIDTH="24" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_122.png"
 ALT="$A_3$"></SPAN>, <i>i.e.</i> be specified as
parameters in the <code>params</code>-command and be entered in the
<code>model</code>-block;

</li><li> <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_42.png"
 ALT="$y$"></SPAN> are the endogenous variables, specified in the
<code>var</code>-command, whose (co)-variance enters the loss function;

</li><li> <SPAN CLASS="MATH"><IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="dynare.html_123.png"
 ALT="$e$"></SPAN> are the exogenous stochastic shocks, specified in the
<code>varexo</code>-command;

</li><li> <SPAN CLASS="MATH"><IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="dynare.html_124.png"
 ALT="$W$"></SPAN> is the weighting matrix;

</li></ul>

<p>The linear quadratic problem consists of choosing a subset of model
parameters to minimize the weighted (co)-variance of a specified subset
of endogenous variables, subject to a linear law of motion implied by the
first order conditions of the model. A few things are worth mentioning.
First, <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_42.png"
 ALT="$y$"></SPAN> denotes the selected endogenous variables&rsquo; deviations
from their steady state, <i>i.e.</i> in case they are not already mean 0 the
variables entering the loss function are automatically demeaned so that
the centered second moments are minimized. Second, <code>osr</code> only solves
linear quadratic problems of the type resulting from combining the
specified quadratic loss function with a first order approximation to the
model&rsquo;s equilibrium conditions. The reason is that the first order
state-space representation is used to compute the unconditional
(co)-variances. Hence, <code>osr</code> will automatically select
<code>order=1</code>. Third, because the objective involves minimizing a
weighted sum of unconditional second moments, those second moments must
be finite. In particular, unit roots in <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_42.png"
 ALT="$y$"></SPAN> are not allowed.
</p>
<p>The subset of the model parameters over which the optimal simple rule is
to be optimized, <SPAN CLASS="MATH"><IMG
 WIDTH="14" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_119.png"
 ALT="$\gamma$"></SPAN>, must be listed with <code>osr_params</code>.
</p>
<p>The weighting matrix <SPAN CLASS="MATH"><IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="dynare.html_124.png"
 ALT="$W$"></SPAN> used for the quadratic objective function
is specified in the <code>optim_weights</code>-block. By attaching weights to
endogenous variables, the subset of endogenous variables entering the
objective function, <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="dynare.html_42.png"
 ALT="$y$"></SPAN>, is implicitly specified.
</p>

<p>The linear quadratic problem is solved using the numerical optimizer specified with <a href="#opt_005falgo">opt_algo</a>.
</p>
<p><em>Options</em>
</p>
<p>The <code>osr</code> command will subsequently run <code>stoch_simul</code> and
accepts the same options, including restricting the endogenous variables
by listing them after the command, as <code>stoch_simul</code>
(see <a href="Stochastic-solution-and-simulation.html#Computing-the-stochastic-solution">Computing the stochastic solution</a>) plus
</p>
<dl compact="compact">
<dt><code>opt_algo = <var>INTEGER</var></code></dt>
<dd><a name="opt_005falgo"></a><p>Specifies the optimizer for minimizing the objective function. The same solvers as for <code>mode_compute</code> (see <a href="Estimation.html#mode_005fcompute">mode_compute</a>) are available, except for 5,6, and 10. 
</p>
</dd>
<dt><code>optim = (<var>NAME</var>, <var>VALUE</var>, ...)</code></dt>
<dd><p>A list of <var>NAME</var> and <var>VALUE</var> pairs. Can be used to set options for the optimization routines. The set of available options depends on the selected optimization routine (<i>i.e.</i> on the value of option <a href="#opt_005falgo">opt_algo</a>). See <a href="Estimation.html#optim">optim</a>.
</p>
</dd>
<dt><code>maxit = <var>INTEGER</var></code></dt>
<dd><p>Determines the maximum number of iterations used in <code>opt_algo=4</code>.  This option is now deprecated and will be 
removed in a future release of Dynare. Use <code>optim</code> instead to set optimizer-specific values. Default: <code>1000</code>
</p>
</dd>
<dt><code>tolf = <var>DOUBLE</var></code></dt>
<dd><p>Convergence criterion for termination based on the function value used in <code>opt_algo=4</code>. Iteration will cease when it proves impossible to
improve the function value by more than tolf.  This option is now deprecated and will be 
removed in a future release of Dynare. Use <code>optim</code> instead to set optimizer-specific values. Default: <code>e-7</code>
</p>
</dd>
<dt><code>silent_optimizer</code></dt>
<dd><p>see <a href="Estimation.html#silent_005foptimizer">silent_optimizer</a>
</p>
</dd>
<dt><code>huge_number = <var>DOUBLE</var></code></dt>
<dd><p>Value for replacing the infinite bounds on parameters by finite numbers. Used by some optimizers for numerical reasons (see <a href="Estimation.html#huge_005fnumber">huge_number</a>).
Users need to make sure that the optimal parameters are not larger than this value. Default: <code>1e7</code>
</p>
</dd>
</dl>

<p>The value of the objective is stored in the variable
<code>oo_.osr.objective_function</code> and the value of parameters at the
optimum is stored in <code>oo_.osr.optim_params</code>. See below for more
details.
</p>
<p>After running <code>osr</code> the parameters entering the simple rule will be
set to their optimal value so that subsequent runs of <code>stoch_simul</code>
will be conducted at these values.
</p>
</dd></dl>

<a name="osr_005fparams"></a><dl>
<dt><a name="index-osr_005fparams"></a>Command: <strong>osr_params</strong> <em><var>PARAMETER_NAME</var>&hellip;;</em></dt>
<dd><p>This command declares parameters to be optimized by <code>osr</code>.
</p></dd></dl>

<a name="optim_005fweights"></a><dl>
<dt><a name="index-optim_005fweights"></a>Block: <strong>optim_weights</strong> <em>;</em></dt>
<dd>
<p>This block specifies quadratic objectives for optimal policy problems
</p>
<p>More precisely, this block specifies the nonzero elements of the weight
matrix <SPAN CLASS="MATH"><IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="dynare.html_124.png"
 ALT="$W$"></SPAN> used in the quadratic form of the objective function in
<code>osr</code>.
</p>
<p>An element of the diagonal of the weight matrix is given by a line of the
form:
</p><div class="example">
<pre class="example"><var>VARIABLE_NAME</var> <var>EXPRESSION</var>;
</pre></div>

<p>An off-the-diagonal element of the weight matrix is given by a line of
the form:
</p><div class="example">
<pre class="example"><var>VARIABLE_NAME</var>,  <var>VARIABLE_NAME</var> <var>EXPRESSION</var>;
</pre></div>

</dd></dl>

<p><em>Example</em>
</p>
<div class="example">
<pre class="example">var y inflation r; 
varexo y_ inf_;

parameters delta sigma alpha kappa gammarr gammax0 gammac0 gamma_y_ gamma_inf_;

delta =  0.44;
kappa =  0.18;
alpha =  0.48;
sigma = -0.06;

gammarr = 0;
gammax0 = 0.2;
gammac0 = 1.5;
gamma_y_ = 8;
gamma_inf_ = 3;

model(linear); 
y  = delta * y(-1)  + (1-delta)*y(+1)+sigma *(r - inflation(+1)) + y_;
inflation  =   alpha * inflation(-1) + (1-alpha) * inflation(+1) + kappa*y + inf_;
r = gammax0*y(-1)+gammac0*inflation(-1)+gamma_y_*y_+gamma_inf_*inf_; 
end;

shocks; 
var y_; stderr 0.63; 
var inf_; stderr 0.4; 
end;

optim_weights; 
inflation 1; 
y 1; 
y, inflation 0.5; 
end;

osr_params gammax0 gammac0 gamma_y_ gamma_inf_; 
osr y; 
</pre></div>


<a name="osr_005fparams_005fbounds"></a><dl>
<dt><a name="index-osr_005fparams_005fbounds"></a>Block: <strong>osr_params_bounds</strong> <em>;</em></dt>
<dd>
<p>This block declares lower and upper bounds for parameters in the optimal simple rule. If not specified
the optimization is unconstrained.
</p>
<p>Each line has the following syntax:
</p>
<div class="example">
<pre class="example">PARAMETER_NAME, LOWER_BOUND, UPPER_BOUND;
</pre></div>

<p>Note that the use of this block requires the use of a constrained optimizer, <i>i.e.</i> setting <a href="#opt_005falgo">opt_algo</a> to 
1,2,5, or 9.
</p>
<p><em>Example</em>
</p>
<div class="example">
<pre class="example">

osr_param_bounds;
gamma_inf_, 0, 2.5;
end;

osr(solve_algo=9) y; 
</pre></div>

</dd></dl>


<dl>
<dt><a name="index-oo_005f_002eosr_002eobjective_005ffunction"></a>MATLAB/Octave variable: <strong>oo_.osr.objective_function</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this variable contains the value of
the objective under optimal policy.
</p></dd></dl>

<dl>
<dt><a name="index-oo_005f_002eosr_002eoptim_005fparams"></a>MATLAB/Octave variable: <strong>oo_.osr.optim_params</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this variable contains the value of parameters
at the optimum, stored in fields of the form
<code>oo_.osr.optim_params.<var>PARAMETER_NAME</var></code>.
</p></dd></dl>

<dl>
<dt><a name="index-M_005f_002eosr_002eparam_005fnames"></a>MATLAB/Octave variable: <strong>M_.osr.param_names</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this cell contains the names of the parameters
</p></dd></dl>

<dl>
<dt><a name="index-M_005f_002eosr_002eparam_005findices"></a>MATLAB/Octave variable: <strong>M_.osr.param_indices</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this vector contains the indices of the OSR parameters
in <var>M_.params</var>.
</p></dd></dl>

<dl>
<dt><a name="index-M_005f_002eosr_002eparam_005fbounds"></a>MATLAB/Octave variable: <strong>M_.osr.param_bounds</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this two by number of OSR parameters
matrix contains the lower and upper bounds of the parameters in the first and second
column, respectively.
</p></dd></dl>

<dl>
<dt><a name="index-M_005f_002eosr_002evariable_005fweights"></a>MATLAB/Octave variable: <strong>M_.osr.variable_weights</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this sparse matrix
contains the weighting matrix associated with the variables in the
objective function.
</p></dd></dl>

<dl>
<dt><a name="index-M_005f_002eosr_002evariable_005findices"></a>MATLAB/Octave variable: <strong>M_.osr.variable_indices</strong></dt>
<dd><p>After an execution of the <code>osr</code> command, this vector contains the 
indices of the variables entering the objective function in <code>M_.endo_names</code>.
</p></dd></dl>

<a name="Ramsey"></a>
<dl>
<dt><a name="index-ramsey_005fmodel"></a>Command: <strong>ramsey_model</strong> <em>(<var>OPTIONS</var>&hellip;);</em></dt>
<dd>
<p><em>Description</em>
</p>
<p>This command computes the First Order Conditions for maximizing the policy maker objective function subject to the
constraints provided by the equilibrium path of the private economy.
</p>
<p>The planner objective must be declared with the <code>planner_objective</code> command.
</p>
<p>This command only creates the expanded model, it doesn&rsquo;t perform any
computations. It needs to be followed by other instructions to actually
perform desired computations. Note that it is the only way to perform
perfect foresight simulation of the Ramsey policy problem.
</p>
<p>See <a href="Auxiliary-variables.html#Auxiliary-variables">Auxiliary variables</a>, for an explanation of how Lagrange multipliers are
automatically created.
</p>
<p><em>Options</em>
</p>
<p>This command accepts the following options:
</p>
<dl compact="compact">
<dd>
<a name="planner_005fdiscount"></a></dd>
<dt><code>planner_discount = <var>EXPRESSION</var></code></dt>
<dd><p>Declares or reassigns the discount factor of the central planner
<code>optimal_policy_discount_factor</code>. Default: <code>1.0</code>
</p>
</dd>
<dt><code>instruments = (<var>VARIABLE_NAME</var>,&hellip;)</code></dt>
<dd><p>Declares instrument variables for the computation of the steady state
under optimal policy. Requires a <code>steady_state_model</code> block or a
<code>&hellip;_steadystate.m</code> file. See below.
</p>
</dd>
</dl>

<p><em>Steady state</em>
<a name="Ramsey-steady-state"></a></p>
<p>Dynare takes advantage of the fact that the Lagrange multipliers appear
linearly in the equations of the steady state of the model under optimal
policy. Nevertheless, it is in general very difficult to compute the
steady state with simply a numerical guess in <code>initval</code> for the
endogenous variables.
</p>
<p>It greatly facilitates the computation, if the user provides an
analytical solution for the steady state (in <code>steady_state_model</code>
block or in a <code>&hellip;_steadystate.m</code> file). In this case, it is
necessary to provide a steady state solution CONDITIONAL on the value
of the instruments in the optimal policy problem and declared with
option <code>instruments</code>. Note that choosing the instruments is
partly a matter of interpretation and you can choose instruments that
are handy from a mathematical point of view but different from the
instruments you would refer to in the analysis of the paper. A typical
example is choosing inflation or nominal interest rate as an
instrument.
</p>

</dd></dl>

<dl>
<dt><a name="index-ramsey_005fconstraints"></a>Block: <strong>ramsey_constraints</strong></dt>
<dd><a name="ramsey_005fconstraints"></a>
<p><em>Description</em>
</p>
<p>This block lets you define constraints on the variables in the Ramsey
problem. The constraints take the form of a variable, an inequality
operator (<code>&gt;</code> or <code>&lt;</code>) and a constant.
</p>
<p><em>Example</em>
</p>
<div class="example">
<pre class="example">ramsey_constraints;
i &gt; 0;
end;
</pre></div>
</dd></dl>
 
<dl>
<dt><a name="index-ramsey_005fpolicy"></a>Command: <strong>ramsey_policy</strong> <em>[<var>VARIABLE_NAME</var>&hellip;];</em></dt>
<dt><a name="index-ramsey_005fpolicy-1"></a>Command: <strong>ramsey_policy</strong> <em>(<var>OPTIONS</var>&hellip;) [<var>VARIABLE_NAME</var>&hellip;];</em></dt>
<dd><a name="ramsey_005fpolicy"></a>
<p><em>Description</em>
</p>
<p>This command computes the first order approximation of the policy that
maximizes the policy maker&rsquo;s objective function subject to the
constraints provided by the equilibrium path of the private economy and under 
commitment to this optimal policy. The Ramsey policy is computed
by approximating the equilibrium system around the perturbation point where the 
Lagrange multipliers are at their steady state, <i>i.e.</i> where the Ramsey planner acts 
as if the initial multipliers had 
been set to 0 in the distant past, giving them time to converge to their steady 
state value. Consequently, the optimal decision rules are computed around this steady state 
of the endogenous variables and the Lagrange multipliers.
</p>
<p>This first order approximation to the optimal policy conducted by Dynare is not to be 
confused with a naive linear quadratic approach to optimal policy that can lead to 
spurious welfare rankings (see <cite>Kim and Kim (2003)</cite>). In the latter, the optimal policy 
would be computed subject to the first order approximated FOCs of the 
private economy. In contrast, Dynare first computes the FOCs of the Ramsey planner&rsquo;s problem
subject to the nonlinear constraints that are the FOCs of the private economy 
and only then approximates these FOCs of planner&rsquo;s problem to first order. Thereby, the second
order terms that are required for a second-order correct welfare evaluation are 
preserved.
</p>
<p>Note that the variables in the list after the <code>ramsey_policy</code>-command can also contain multiplier 
names. In that case, Dynare will for example display the IRFs of the respective multipliers when <code>irf&gt;0</code>.
</p>
<p>The planner objective must be declared with the <code>planner_objective</code> command.
</p>
<p>See <a href="Auxiliary-variables.html#Auxiliary-variables">Auxiliary variables</a>, for an explanation of how this operator is handled
internally and how this affects the output.
</p>
<p><em>Options</em>
</p>
<p>This command accepts all options of <code>stoch_simul</code>, plus:
</p>
<dl compact="compact">
<dt><code>planner_discount = <var>EXPRESSION</var></code></dt>
<dd><p>See <a href="#planner_005fdiscount">planner_discount</a>.
</p>
</dd>
<dt><code>instruments = (<var>VARIABLE_NAME</var>,&hellip;)</code></dt>
<dd><p>Declares instrument variables for the computation of the steady state
under optimal policy. Requires a <code>steady_state_model</code> block or a
<code>&hellip;_steadystate.m</code> file. See below.
</p>
</dd>
</dl>

<p>Note that only a first order approximation of the optimal Ramsey policy is 
available, leading to a second-order accurate welfare ranking 
(<i>i.e.</i> <code>order=1</code> must be specified).
</p>
<p><em>Output</em>
</p>
<p>This command generates all the output variables of <code>stoch_simul</code>. For specifying
the initial values for the endogenous state variables (except for the Lagrange
multipliers), see <a href="Initial-and-terminal-conditions.html#histval">histval</a>.
</p>
<a name="index-oo_005f_002eplanner_005fobjective_005fvalue"></a>
<a name="planner_005fobjective_005fvalue"></a>
<p>In addition, it stores the value of planner objective function under
Ramsey policy in <code>oo_.planner_objective_value</code>, given the initial values 
of the endogenous state variables. If not specified with <code>histval</code>, they are 
taken to be at their steady state values. The result is a 1 by 2 
vector, where the first entry stores the value of the planner objective when the initial Lagrange
multipliers associated with the planner&rsquo;s problem are set to their steady state
values (see <a href="#ramsey_005fpolicy">ramsey_policy</a>).
</p>
<p>In contrast, the second entry stores the value of the planner objective with 
initial Lagrange multipliers of the planner&rsquo;s problem set to 0, <i>i.e.</i> it is assumed 
that the planner exploits its ability to surprise private agents in the first
period of implementing Ramsey policy. This is the value of implementating
optimal policy for the first time and committing not to re-optimize in the future.
</p>
<p>Because it entails computing at least a second order approximation, this
computation is skipped with a message when the model is too large (more than 180 state
variables, including lagged Lagrange multipliers).
<em>Steady state</em>
See <a href="#Ramsey-steady-state">Ramsey steady state</a>.
</p>

</dd></dl>

<a name="discretionary_005fpolicy"></a><dl>
<dt><a name="index-discretionary_005fpolicy"></a>Command: <strong>discretionary_policy</strong> <em>[<var>VARIABLE_NAME</var>&hellip;];</em></dt>
<dt><a name="index-discretionary_005fpolicy-1"></a>Command: <strong>discretionary_policy</strong> <em>(<var>OPTIONS</var>&hellip;) [<var>VARIABLE_NAME</var>&hellip;];</em></dt>
<dd>
<p><em>Description</em>
</p>
<p>This command computes an approximation of the optimal policy under
discretion. The algorithm implemented is essentially an LQ solver, and
is described by <cite>Dennis (2007)</cite>.
</p>
<p>You should ensure that your model is linear and your objective is
quadratic. Also, you should set the <code>linear</code> option of the
<code>model</code> block.
</p>
<p><em>Options</em>
</p>
<p>This command accepts the same options than <code>ramsey_policy</code>, plus:
</p>
<dl compact="compact">
<dt><code>discretionary_tol = <var>NON-NEGATIVE DOUBLE</var></code></dt>
<dd><p>Sets the tolerance level used to assess convergence of the solution
algorithm. Default: <code>1e-7</code>.
</p>
</dd>
<dt><code>maxit = <var>INTEGER</var></code></dt>
<dd><p>Maximum number of iterations. Default: <code>3000</code>.
</p>
</dd>
</dl>

</dd></dl>


<a name="planner_005fobjective"></a><dl>
<dt><a name="index-planner_005fobjective"></a>Command: <strong>planner_objective</strong> <em><var>MODEL_EXPRESSION</var>;</em></dt>
<dd>
<p>This command declares the policy maker objective, for use with
<code>ramsey_policy</code> or <code>discretionary_policy</code>.
</p>
<p>You need to give the one-period objective, not the discounted lifetime
objective. The discount factor is given by the <code>planner_discount</code>
option of <code>ramsey_policy</code> and <code>discretionary_policy</code>. The
objective function can only contain current endogenous variables and no
exogenous ones. This limitation is easily circumvented by defining an
appropriate auxiliary variable in the model.
</p>
<p>With <code>ramsey_policy</code>, you are not limited to quadratic
objectives: you can give any arbitrary nonlinear expression.
</p>
<p>With <code>discretionary_policy</code>, the objective function must be quadratic.
</p></dd></dl>

<hr>
<div class="header">
<p>
Next: <a href="Sensitivity-and-identification-analysis.html#Sensitivity-and-identification-analysis" accesskey="n" rel="next">Sensitivity and identification analysis</a>, Previous: <a href="Forecasting.html#Forecasting" accesskey="p" rel="prev">Forecasting</a>, Up: <a href="The-Model-file.html#The-Model-file" accesskey="u" rel="up">The Model file</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Command-and-Function-Index.html#Command-and-Function-Index" title="Index" rel="index">Index</a>]</p>
</div>



</body>
</html>
dynare-doc 4.5.4-1 / usr / share / doc / dynare / dynare.html / Optimal-policy.html
