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}