Commit c7160a40 authored by Sébastien Villemot's avatar Sébastien Villemot

Modifications for 2019

parent 73579ccf
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......@@ -14,7 +14,7 @@
\author{Sébastien Villemot}
\pgfdeclareimage[height=0.6cm]{logo}{cepremap}
\institute[CEPREMAP]{\pgfuseimage{logo}}
\date{June 12, 2018}
\date{June 4, 2019}
\AtBeginSection[]
{
......@@ -48,7 +48,7 @@
\item since there is shared knowledge of the model and of future shocks,
agents can compute their optimal plans for all future periods;
\item optimal plans are not adjusted in periods 2 and later \\
$\Rightarrow$ the model behaves as if it was deterministic.
$\Rightarrow$ the model behaves as if it were deterministic.
\end{itemize}
\item Cost of this approach: the effect of future uncertainty is not taken
into account (\textit{e.g.} no precautionary motive)
......@@ -254,21 +254,35 @@ f(\bar y, \bar y, \bar y, \bar u) = 0
where $Y =
\left[\begin{array}{llll}y_1'&y_2'&\ldots&y_T'\end{array}\right]'$ \\
and $y_0$, $y_{T+1}$, $u_1\ldots u_T$ are implicit
\item Resolution uses a Newton-type method on the stacked system
\end{itemize}
\end{frame}
\begin{frame}{Solution of perfect foresight models}
\begin{frame}{Approximating infinite horizon problems}
\begin{itemize}
\item This technique numerically computes trajectories for given shocks over a
finite number of periods
\item No possibility of computing a recursive policy function (as with
perturbation methods), because
future shock paths are
state variables, and those are infinite-dimensional objects
\item However, it is possible to approximate the asymptotic return to
equilibrium with $y_{T+1}=\bar y$ and a large enough $T$
\item Resolution uses a Newton-type method on the stacked system
\item The above technique numerically computes trajectories for given shocks over a
\emph{finite} number of periods
\item Suppose you are rather interested in solving an \emph{infinite} horizon
problem
\item One option consists in computing the recursive policy function (as with
perturbation methods), but this is challenging
\begin{itemize}
\item in the general case, this function is defined over an infinite-dimensional space
(because all future shocks are state variables)
\item in the particular case of a return to equilibrium, the state-space
is finite (starting from the date where all shocks are zero), but a
projection method would still be needed
\item in any case, Dynare does not do that
\end{itemize}
\item An easier solution, in the case of a return to equilibrium, is to
approximate it by a finite horizon problem
\begin{itemize}
\item consists in computing the trajectory with $y_{T+1}=\bar y$ and $T$
large enough
\item drawback compared to the policy function approach: the
solution is specific to a given sequence of shock, and not generic
\end{itemize}
\end{itemize}
\end{frame}
......@@ -1379,7 +1393,7 @@ plot(oo_.endo_simul(ic, 1:21));
\ccbysa
\column{0.71\textwidth}
\tiny
Copyright © 2015-2018 Dynare Team \\
Copyright © 2015-2019 Dynare Team \\
License: \href{http://creativecommons.org/licenses/by-sa/4.0/}{Creative
Commons Attribution-ShareAlike 4.0}
\end{columns}
......
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