From 952503a855619ca049c5ffad4cd6973364bcd583 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
<stephane.adjemian@univ-lemans.fr>
Date: Fri, 18 Jul 2014 18:37:31 +0200
Subject: [PATCH] Changed fourth remark added by Johannes in commit
e7727ba2d3365cf5269ab718cfbed86c82243cbe.
(cherry picked from commit c13738eea774f5b4417e1f23e503db3585246056)
---
doc/dynare.texi | 34 +++++++++++++++-------------------
1 file changed, 15 insertions(+), 19 deletions(-)
diff --git a/doc/dynare.texi b/doc/dynare.texi
index 70cae7148..5d5971792 100644
--- a/doc/dynare.texi
+++ b/doc/dynare.texi
@@ -5836,8 +5836,8 @@ model by finding the structural shocks that are needed to match the
restricted paths. Consider the an augmented state space representation
that stacks both predetermined and non-predetermined variables into a
vector @math{y_{t}}:
-
-@math{y_t=Ty_{t-1}+R\varepsilon_t}
+
+@math{y_t=Ty_{t-1}+R\varepsilon_t}
Both
@math{y_t} and @math{\varepsilon_t} are split up into controlled and
@@ -5845,9 +5845,9 @@ uncontrolled ones to get:
@math{y_t(contr\_vars)=Ty_{t-1}(contr\_vars)+R(contr\_vars,uncontr\_shocks)\varepsilon_t(uncontr\_shocks)
+R(contr\_vars,contr\_shocks)\varepsilon_t(contr\_shocks)}
-
+
which can be solved algebraically for @math{\varepsilon_t(contr\_shocks)}.
-
+
Using these controlled shocks, the state-space representation can be used
for forecasting. A few things need to be noted. First, it is assumed that
controlled exogenous variables are fully under control of the policy
@@ -5863,21 +5863,17 @@ perfectly under the control of the policy-maker, they are nevertheless
random and unforeseen shocks from the perspective of the households. That is,
households are in each period surprised by the realization of a shock
that keeps the controlled endogenous variables at their respective level.
-Fourth, due to the use of the above formula to compute the controlled
-exogenous variables, only relationships between controlled exogenous
-variables embedded in the matrix @math{R} are considered. This implies
-that any correlation information embedded in the covariance matrix of the
-@math{\varepsilon} as specified in the @code{shocks}-block are via
-estimated correlations or covariances is ignored as the controlled
-exogenous variables are assumed to be perfectly controlled without any
-interdependence. Thus, if you want to specify/preserve a correlation
-structure between controlled exogenous variables, you have to embedd that
-correlation stucture directly in the model-block by e.g. having the same
-shock enter different equations.
-
-
-This
-command has to be called after @code{estimation} of @code{stoch_simul}.
+Fourth, keep in mind that if the structural innovations are correlated,
+because the calibrated or estimated covariance matrix has non zero off
+diagonal elements, the results of the conditional forecasts will depend on
+the ordering of the innovations (as declared after @code{varexo}). As in VAR
+models, a Cholesky decomposition is used to factorize the covariance matrix
+and identify orthogonal impulses. It is preferable to declare the correlations
+in the @code{model} block (explicitly imposing the identification restrictions),
+unless you are satisfied with the implicit identification restrictions implied
+by the Cholesky decomposition.
+
+This command has to be called after @code{estimation} or @code{stoch_simul}.
Use @code{conditional_forecast_paths} block to give the list of
constrained endogenous, and their constrained future path.
--
GitLab