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Verified Commit 22ff11c9 authored by Sébastien Villemot's avatar Sébastien Villemot
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Incorporate some improvements by Johannes Pfeifer

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......@@ -206,6 +206,9 @@ rplot c;
\item Symmetric process for variables with more than one lag
\item With future uncertainty, the transformation is more elaborate
(but still possible) on variables with leads
\item \texttt{write\_latex\_original\_model} and
\texttt{write\_latex\_dynamic\_model} show model before and after
substitution
\end{itemize}
\end{frame}
......@@ -226,12 +229,37 @@ f(\bar y, \bar y, \bar y, \bar u) = 0
\item Even for a given set of exogenous and parameter values, some (nonlinear) models have
several steady states
\item The steady state is computed by Dynare with the \texttt{steady} command
\item That command internally uses a nonlinear solver
\item Two possibilities for the steady state in Dynare:
\begin{itemize}
\item If analytical steady state is known, can be given in
\texttt{steady\_state\_model} block
\item Otherwise, numerical procedure based on a nonlinear solver, with the \texttt{steady} command
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Towards a solution}
\begin{itemize}
\item In each period, agent needs to choose control variables (\textit{e.g.} consumption) today, taking into account:
\begin{itemize}
\item the known time path of the exogenous variables
\item the current endogenous states that cannot be altered anymore
(\textit{e.g.} capital)
\item the consequences of today’s actions for future decisions
\end{itemize}
\item Assume finite horizon problem that terminates in period $T$ with
\begin{itemize}
\item initial states in $y_0$ given
\item terminal choice $y_{T+1}$ known
\end{itemize}
$\Rightarrow$ problem boils down to simultaneous equations system with
$n_y\times T$ equations in $n_y \times T$ unknowns
(where $n_y$ is the number of endogenous)
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{A two-boundary value problem}
......@@ -440,7 +468,7 @@ where
\begin{frame}
\frametitle{Laffargue-Boucekkine-Juillard algorithm (3/5)}
Normal iteration:
Normal iteration of the triangularization:
\begin{small}
\begin{equation*}
\begin{pmatrix}
......@@ -664,7 +692,7 @@ $$d_T = (B_T-A_TD_{T-1})^{-1}(f(y_{T+1},y_T,y_{T-1},u_T)+A_Td_{T-1})$$
A_{t} = {A^{\star}}e^{a_{t}}\\
a_{t} = \rho\, a_{t-1} + \varepsilon_t
\end{gather*}
where $\varepsilon_t$ is an exogenous shock.
where $\varepsilon_t$ is an exogenous shock and $k_0$ given.
\end{frame}
\begin{frame}
......
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