Modifications for 2019

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}