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ISBN 978-0-367-28501-2
www.routledge.com aninformabusiness
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Rational Expectations
Econometrics
UNDERGROUND CLASSICS IN ECONOMICS
Consulting Editors
Kenneth Arrow, James Heckman,
Thomas Sargent, and Robert Solow
~ in economics takes place in many different forums. Many of
these forums are not "above ground," in the sense of published work
freely available. They are in the form of unpublished notes, dissertations,
government reports, and lectures. This series is dedicated to making the
best of this underground literature more widely available to libraries,
scholars, and their students. In so doing it will serve to fill a large gap
in the contemporary economic literature.
Entries in this series can be on any topic of interest to economists,
and they may occasionally be in rough or unfinished form. The only
criteria are that the works have been influential, widely cited, of exceptional
excellence, and, for whatever reason, never before published.
Other Titles in This Series
Behind the Diffusion Curve: Theoretical and Applied Contributions to the
Microeconomics of Technology Adoption, Paul A. David
The Allocation of Scarce Resources: Experimental Economics and the
Problem of Allocating Airport Slots, David M. Grether, R. Mark Isaac
and Charles R. Plott
Lectures on Game Theory, Robert J. Aumann
Notes on the Theory of Choice, David M: Kreps
Functional Form and Utility: A Review of Consumer Demand Theory,
Arthur S. Goldberger
Rational Expectations
Econometrics
Lars Peter Hansen
•
and Thomas J. Sargent
WITH CONTRIBUTIONS BY
John Heaton, Albert Marcet
and William Roberds
~l Routledge
~ ~
Taylor & Francis Group
L0f',JLJON AND NEW
First published 1991 by Westview Press
Published 2019 by Routledge
52 Vanderbilt Avenue, New York, NY 10017
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN
Routledge is an imprint of the Taylor & Francis Group, an informa business
Copyright © 1991 by Taylor & Francis
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or
by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or retrieval system, without permission
in writing from the publishers.
Notice:
Product or corporate names may be trademarks or registered trademarks, and are used only for
identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Hansen, Lars Peter.
Rational expectations econometrics / by Lars Peter Hansen and
Thomas J. Sargent.
p. cm.-(Underground classics in economics)
ISBN 0-8133-7800-1
1. Rational expectations (Economic theory). 2. Econometrics.
I. Sargent, Thomas J. II. Title. III. Series.
HB3730.H284 1991
330'.01'5195-dc20 89-16674
CIP
ISBN 13: 978-0-367-28501-2 (hbk)
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
by Lars Peter HANSEN and Thomas J. SARGENT
2. Lecture Notes on Least Squares Prediction Theory 13
by Lars Peter HANSEN and Thomas J. SARGENT
3. Exact Linear Rational Expectations Models:
Specification and Estimation . . . . . . . . 45
by Lars Peter HANSEN and Thomas J. SARGENT
4. Two Difficulties in Interpreting Vector Autoregressions 77
by Lars Peter HANSEN and Thomas J. SARGENT
5. Time Series Implications of Present Value Budget Balance
and of Martingale Models of Consumption and Taxes . . . . 121
by Lars Peter HANSEN, William ROBERDS and Thomas J. SARGENT
6. Implications of Expected Present Value Budget Balance:
Application to Postwar U.S. Data . . . . . . . . . . . . . . 163
by William ROBERDS
7. Faster Methods for Solving Continuous Time Recursive
Linear Models of Dynamic Economies . . . . . . . . . . 177
by Lars Peter HANSEN, John HEATON and Thomas J. SARGENT
vii
viii
8. Prediction Formulas for Continuous Time Linear Rational
Expectations Models . . . . . . . . . . . . . . . . . . . . 209
by Lars Peter HANSEN and Thomas J. SARGENT
9. Identification of Continuous Time Rational Expectations
Models from Discrete Time Data .............. 219
by Lars Peter HANSEN and Thomas J. SARGENT
10. Temporal Aggregation of Economic Time Series . . . . . . 237
by Albert MARCET
References . . . . . 283
List of Contributors 294
Acknowledgments
We are very grateful to Maria Bharwada for typesetting this manu-
script in '!EX· She did a wonderful job in converting our scribblings
into the forms that appear in this book. Several of the chapters in
this volume originally appeared as Working Papers or Staff Reports of
the Research Department of the Federal Reserve Bank of Minneapo-
lis. We would like to thank the Minneapolis Fed for supporting much
of the research that led to these papers. Some of the more recent re-
search was funded by grants from the National Science Foundation to
Hansen and Sargent. We used earlier versions of Chapter 2 in classes
and benefited from comments from students in those classes. Philip
Braun and Narayana Kocherlakota provided some particularly helpful
remarks. For computational assistance in Chapter 4 we thank Danny
Quah and Ravi Jagannathan. A lqng time has passed since we could
afford to hire either of them. We thank Andy Atkeson, John Heaton,
Hsin Chang Lu, Robert E. Lucas, Jr., Preston Miller and Chi Wa Yuen
for valuable comments on earlier drafts of Chapter 5. In addition, we
are grateful to Hsin Chang Lu and Alex Taber for expert research as-
sistance. Robin Lumsdaine read an earlier version of Chapter 7 and
made some useful suggestions. Alex Taber was a big help in proof
reading and criticizing the entire manuscript. Clark Burdick, Gregory
Cumber, Kathy Glover and Fran~ois Velde also assisted in preparing
the manuscript and in helping write some '!EX code.
Lars Hansen and Thomas Sargent
ix
