Modifications for 2019

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