Skip to content
GitLab
Explore
Sign in
Register
Primary navigation
Search or go to…
Project
P
perfect-foresight-slides
Manage
Activity
Members
Labels
Plan
Issues
Issue boards
Milestones
Wiki
Code
Merge requests
Repository
Branches
Commits
Tags
Repository graph
Compare revisions
Snippets
Build
Pipelines
Jobs
Pipeline schedules
Artifacts
Deploy
Releases
Container registry
Model registry
Operate
Environments
Monitor
Incidents
Analyze
Value stream analytics
Contributor analytics
CI/CD analytics
Repository analytics
Model experiments
Help
Help
Support
GitLab documentation
Compare GitLab plans
GitLab community forum
Contribute to GitLab
Provide feedback
Keyboard shortcuts
?
Snippets
Groups
Projects
Show more breadcrumbs
Sébastien Villemot
perfect-foresight-slides
Commits
c7160a40
Verified
Commit
c7160a40
authored
Jun 3, 2019
by
Sébastien Villemot
Browse files
Options
Downloads
Patches
Plain Diff
Modifications for 2019
parent
73579ccf
No related branches found
No related tags found
No related merge requests found
Changes
2
Show whitespace changes
Inline
Side-by-side
Showing
2 changed files
deterministic.pdf
+0
-0
0 additions, 0 deletions
deterministic.pdf
deterministic.tex
+27
-13
27 additions, 13 deletions
deterministic.tex
with
27 additions
and
13 deletions
deterministic.pdf
+
0
−
0
View file @
c7160a40
No preview for this file type
This diff is collapsed.
Click to expand it.
deterministic.tex
+
27
−
13
View file @
c7160a40
...
...
@@ -14,7 +14,7 @@
\author
{
Sébastien Villemot
}
\pgfdeclareimage
[height=0.6cm]
{
logo
}{
cepremap
}
\institute
[CEPREMAP]
{
\pgfuseimage
{
logo
}}
\date
{
June
12
, 201
8
}
\date
{
June
4
, 201
9
}
\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 w
as
deterministic.
$
\Rightarrow
$
the model behaves as if it w
ere
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 model
s
}
\begin{frame}
{
Approximating infinite horizon problem
s
}
\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 © 2015-201
8
Dynare Team
\\
Copyright © 2015-201
9
Dynare Team
\\
License:
\href
{
http://creativecommons.org/licenses/by-sa/4.0/
}{
Creative
Commons Attribution-ShareAlike 4.0
}
\end{columns}
...
...
This diff is collapsed.
Click to expand it.
Preview
0%
Loading
Try again
or
attach a new file
.
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Save comment
Cancel
Please
register
or
sign in
to comment