diff --git a/deterministic.pdf b/deterministic.pdf
index 0b48941d112f1dcdb673e63e66fceac63cd4078a..389d4980aae5894add5dad705ec9a30630a971c6 100644
Binary files a/deterministic.pdf and b/deterministic.pdf differ
diff --git a/deterministic.tex b/deterministic.tex
index 355b386782acffd1ed6fbe66463476ee265105bb..3b0f7d95f2a3203edf75e4cae285a566a6d85de5 100644
--- a/deterministic.tex
+++ b/deterministic.tex
@@ -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}