Bayesian Economics Through Numerical Methods A Guide to Econometrics

The aim of this book is to provide researchers in economics, finance, and statistics with an up-to-date introduction to applying Bayesian techniques to empirical studies. It covers the full range of the new numerical techniques which have been developed o

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Springer New York Berlin Heidelberg Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo

Jeffrey H. Dorfman

Bayesian Economics Through Numerical Methods A Guide to Econometrics and Decision-Making with Prior Information

Springer

Jeffrey H. Dorfman Department of Agricultural and Applied Economics University of Georgia Athens, GA 30602-7509 USA

Library of Congress Cataloging-in-Publication Data Dorfman, Jeffrey H. Bayesian economics through numerical methods : a guide to econometrics and decision-making with prior information / Jeffrey H. Dorfman. p. cm. Includes bibliographical references and index. ISBN 0-387-98233-7 (he : alk. paper) 1. Econometrics. 2. Bayesian statistical decision theory. I. Title. HB139.D674 1997 330'.01'5195—dc21 97-12147

© 1997 Springer-Verlag N ew York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag N ew York, Inc., 175 Fifth Avenue, N ew York, N Y 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not esnecjallv identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

ISBN 0-387-98233-7 Springer-Verlag N ew York Berlin Heidelberg

SPIN

10574679

To Melody, for too many reasons to list.

Contents

Chapter 1

Introduction

1

Part I Theory and Basics Chapter 2 Chapter 3

A Quick Course in Bayesian Statistics and Decision Theory New Advances in Numerical Bayesian Techniques

6 19

Part II Applications in Econometrics Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9

Imposing Economic Theory Studying Parameters of Interest Unit Root and Cointegration Tests Model Specification Uncertainty Forecasting More Realistic Models Through Numerical Methods

30 41 49 64 72 82

Part III Applications to Economic Decision Making Chapter 10 Bibliography Index

Decision Theory Applications

88 97 109

vii

1 Introduction

Bayesian statistics at its most basic level is an approach to statistical problems that seeks to optimally combine information from two sources: the information the researcher believes at the start of the research process and the information contained in the data. Bayes’ theorem is essentially a rule for how to combine these two sources of information into a single set of (updated) information concerning the parameters or hypotheses of interest. There are a number of advantages to this approach as opposed to the alternative, sampling theory, approach to statistics. First, by formalizing the researcher’s advance beliefs, through a mathematical construct called the prior distribution, underlying assu