From 6dd8e9201b455ba59c79bc9b8f6bd2626e2b510c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?S=C3=A9bastien=20Villemot?= Date: Thu, 8 Sep 2011 18:09:37 +0200 Subject: [PATCH] =?UTF-8?q?Cosmetic=20changes=20to=20the=20documentation?= =?UTF-8?q?=20of=20BVAR=20"=C3=A0=20la=20Sims"?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- doc/bvar-a-la-sims.tex | 52 +++++++++++++++++++++++++----------------- license.txt | 10 ++++++++ 2 files changed, 41 insertions(+), 21 deletions(-) diff --git a/doc/bvar-a-la-sims.tex b/doc/bvar-a-la-sims.tex index c69ed695b..ca1621a41 100644 --- a/doc/bvar-a-la-sims.tex +++ b/doc/bvar-a-la-sims.tex @@ -1,21 +1,42 @@ -\documentclass[10pt,a4paper]{article} +\documentclass[11pt,a4paper]{article} \usepackage{amsmath} \usepackage{amssymb} -\usepackage{url} +\usepackage{hyperref} +\hypersetup{breaklinks=true,pagecolor=white,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue} +\usepackage{fullpage} +\usepackage{textcomp} \newcommand{\df}{\text{df}} \begin{document} -\title{BVAR models ``\`a la Sims'' in Dynare} -\author{S\'ebastien Villemot\thanks{CEPREMAP. E-mail: \texttt{sebastien.villemot@ens.fr}}} -\date{September 2007} +\title{BVAR models ``\`a la Sims'' in Dynare\thanks{Copyright \copyright~2007--2011 S\'ebastien + Villemot. Permission is granted to copy, distribute and/or modify + this document under the terms of the GNU Free Documentation + License, Version 1.3 or any later version published by the Free + Software Foundation; with no Invariant Sections, no Front-Cover + Texts, and no Back-Cover Texts. A copy of the license can be found + at: \url{http://www.gnu.org/licenses/fdl.txt} + \newline + \indent Many thanks to Christopher Sims for providing his BVAR + MATLAB\textregistered~routines, to St\'ephane Adjemian and Michel Juillard + for their helpful support, and to Marek Jaroci\'nski for reporting a bug. + }} + +\author{S\'ebastien Villemot\thanks{Paris School of Economics and + CEPREMAP. E-mail: + \href{mailto:sebastien.villemot@ens.fr}{\texttt{sebastien.villemot@ens.fr}}.}} +\date{First version: September 2007 \hspace{1cm} This version: September 2011} \maketitle -Dynare incorporates routines for BVAR models estimation, that can be used alone or in parallel with a DSGE estimation. -This document describes their implementation and usage. +\begin{abstract} + Dynare incorporates routines for Bayesian VAR models estimation, using a + flavor of the so-called ``Minnesota priors,''. These routines can be used + alone or in parallel with a DSGE estimation. This document describes their + implementation and usage. +\end{abstract} If you are impatient to try the software and wish to skip mathematical details, jump to section \ref{dynare-commands}. @@ -94,7 +115,7 @@ The second component of the prior is constructed from the likelihood of $T^*$ du $$p_2(\Phi, \Sigma) \propto |\Sigma|^{-T^*/2} \exp\left\{-\frac{1}{2}Tr(\Sigma^{-1}(Y^*-X^*\Phi)'(Y^*-X^*\Phi))\right\}$$ -The dummy observations are constructed according to Sims' version of the Minnesota prior\footnote{See Doan, Litterman and Sims (1984).}. +The dummy observations are constructed according to Sims' version of the Minnesota prior.\footnote{See Doan, Litterman and Sims (1984).} Before constructing the dummy observations, one needs to choose values for the following parameters: \begin{itemize} @@ -394,7 +415,7 @@ f(\Phi,\Sigma | \df,S,\hat{\Phi},\Omega) & = & |\Sigma|^{-(\df + ny + 1)/2} \exp We also note: $$F(\df,S,\hat{\Phi},\Omega) = \int f(\Phi,\Sigma | \df,S,\hat{\Phi},\Omega)d\Phi d\Sigma$$ -The function $F$ has an analytical form, which is given by the normalization constants of matrix-normal and inverse-Wishart densities\footnote{Function \texttt{matricint} of file \texttt{bvar\_density.m} implements the calculation of the log of $F$.}: +The function $F$ has an analytical form, which is given by the normalization constants of matrix-normal and inverse-Wishart densities:\footnote{Function \texttt{matricint} of file \texttt{bvar\_density.m} implements the calculation of the log of $F$.} $$F(\df,S,\hat{\Phi},\Omega) = (2\pi)^{\frac{ny\cdot k}{2}} |\Omega|^{\frac{ny}{2}} \cdot 2^{\frac{ny\cdot \df}{2}} \pi^{\frac{ny(ny-1)}{4}} |S|^{-\frac{\df}{2}} \prod_{i=1}^{ny} \Gamma\left(\frac{\df + 1 - i}{2}\right) $$ @@ -464,7 +485,7 @@ Note that option \texttt{prefilter} implies option \texttt{noconstant}. Please also note that if option \texttt{loglinear} had been specified in a previous \texttt{estimation} statement, without option \texttt{logdata}, then the BVAR model will be estimated on the log of the provided dataset, for maintaining coherence with the DSGE estimation procedure. -\emph{Restrictions related to the initialization of lags:} in DSGE estimation routines, the likelihood (and therefore the marginal density) are evaluated starting from the observation numbered \texttt{first\_obs + presample} in the datafile\footnote{\texttt{first\_obs} points to the first observation to be used in the datafile (defaults to 1), and \texttt{presample} indicates how many observations after \texttt{first\_obs} will be used to initialize the Kalman filter (defaults to 0).}. The BVAR estimation routines use the same convention (i.e. the first observation of $Y^+$ will be \texttt{first\_obs + presample}). Since we need $p$ observations to initialize the lags, and since we may also use a training sample, the user must ensure that the following condition holds (estimation will fail otherwise): +\emph{Restrictions related to the initialization of lags:} in DSGE estimation routines, the likelihood (and therefore the marginal density) are evaluated starting from the observation numbered \texttt{first\_obs + presample} in the datafile.\footnote{\texttt{first\_obs} points to the first observation to be used in the datafile (defaults to 1), and \texttt{presample} indicates how many observations after \texttt{first\_obs} will be used to initialize the Kalman filter (defaults to 0).} The BVAR estimation routines use the same convention (i.e. the first observation of $Y^+$ will be \texttt{first\_obs + presample}). Since we need $p$ observations to initialize the lags, and since we may also use a training sample, the user must ensure that the following condition holds (estimation will fail otherwise): $$\texttt{first\_obs} + \texttt{presample} > \texttt{bvar\_prior\_train} + \text{number\_of\_lags}$$ @@ -592,16 +613,5 @@ Schorfheide, Frank (2004), ``\textit{Notes on Model Evaluation}'', Department of Sims, Christopher (2003), ``\textit{Matlab Procedures to Compute Marginal Data Densities for VARs with Minnesota and Training Sample Priors}'', Department of Economics, Princeton University -\section*{Acknowledgements} - -Many thanks to Christopher Sims for his BVAR Matlab routines, and to St\'ephane Adjemian and Michel Juillard for their helpful support. - -\section*{License} - -Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. - -A copy of the license can be found at: -\url{http://www.gnu.org/licenses/fdl.txt} - \end{document} diff --git a/license.txt b/license.txt index 135eea87f..874b60608 100644 --- a/license.txt +++ b/license.txt @@ -139,6 +139,16 @@ License: GFDL-1.3+ . A copy of the license can be found at +Files: doc/bvar_a_la_sims.tex +Copyright: 2007-2011, Sébastien Villemot +License: GFDL-1.3+ + Permission is granted to copy, distribute and/or modify this document + under the terms of the GNU Free Documentation License, Version 1.3 or + any later version published by the Free Software Foundation; with no + Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. + . + A copy of the license can be found at + Files: dynare++/*.cweb, dynare++/*.hweb, dynare++/*.cpp, dynare++/*.h, dynare++/*.tex, dynare++/*.mod, dynare++/*.m, dynare++/*.web, dynare++/*.lex, dynare++/*.y