Recursive Models of Dynamic Linear Economies (The Gorman Lectures in Economics) - Hardcover

Hansen, Lars Peter; Sargent, Thomas J.

Hardcover

ISBN 10: 0691042772 ISBN 13: 9780691042770

Verlag: Princeton University Press, 2013

Inhaltsangabe

A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. In Recursive Models of Dynamic Linear Economies, Lars Peter Hansen and Thomas Sargent use these tools to create a class of econometrically tractable models of prices and quantities. They present examples from microeconomics, macroeconomics, and asset pricing. The models are cast in terms of a representative consumer. While Hansen and Sargent demonstrate the analytical benefits acquired when an analysis with a representative consumer is possible, they also characterize the restrictiveness of assumptions under which a representative household justifies a purely aggregative analysis.

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Über die Autorinnen und Autoren

Lars Peter Hansen is the David Rockefeller Distinguished Service Professor at the University of Chicago, where he is also the research director of the Becker Friedman Institute. Thomas J. Sargent is professor of economics at New York University and a senior fellow at the Hoover Institution at Stanford University. His books include Rational Expectations and Inflation and The Conquest of American Inflation (both Princeton). Hansen and Sargent are the coauthors of Robustness (Princeton). Sargent was awarded the Nobel Prize in economics in 2011 and Hansen received it in 2013.

Thomas J. Sargent, winner of 211 Nobel Prize in Economics and William R. Berkley Professor of Economics and Business. Lars Peter Hansen, co-winner of 213 Nobel Prize in Economics.

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"This is the ideal book for those who want to study, understand, and work with linear-quadratic dynamic economies. Providing a thorough, authoritative, yet accessible treatment, it contains a superb analysis of the connections between various linear-quadratic dynamic programming problems, the general equilibrium properties of these economies, the type of aggregation applicable to them, and the time-series implications for quantities and prices. A great book by two giants of the field."--Fernando Alvarez, University of Chicago

"In this tour-de-force of modern macroeconomics, Hansen and Sargent have written the definitive text on linear-quadratic economies that illustrate the connection between preferences and technology and the appropriate time-series representation. This gem of a book not only provides a thorough review of mathematical methods and related computational issues, but also includes cutting-edge economic models. It will be the required reference for anybody who works in modern dynamic macroeconomic problems."--Rodolfo E. Manuelli, Washington University in St. Louis

"Modern macroeconomics relies on dynamic equilibrium modeling and the statistical analysis of time-series data. This superb book teaches both techniques hands-on. It guides readers towards mastering a library of computer programs that work for many practical problems, a library that readers will then build on in their own macroeconomic research."--Martin Schneider, Stanford University

"It is nearly impossible to think of a better set of coauthors for this subject. I read their superior book with great pleasure and learned much from it."--Jesus Fernandez-Villaverde, University of Pennsylvania

"Drawing strong connections between mathematics and economic intuition, this rigorous and insightful book contains an extremely broad set of applications, treated from the same consistent framework. The exposition of the benchmark model is outstanding and unique."--John Stachurski, Australian National University

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"This is the ideal book for those who want to study, understand, and work with linear-quadratic dynamic economies. Providing a thorough, authoritative, yet accessible treatment, it contains a superb analysis of the connections between various linear-quadratic dynamic programming problems, the general equilibrium properties of these economies, the type of aggregation applicable to them, and the time-series implications for quantities and prices. A great book by two giants of the field."--Fernando Alvarez, University of Chicago

"In this tour-de-force of modern macroeconomics, Hansen and Sargent have written the definitive text on linear-quadratic economies that illustrate the connection between preferences and technology and the appropriate time-series representation. This gem of a book not only provides a thorough review of mathematical methods and related computational issues, but also includes cutting-edge economic models. It will be the required reference for anybody who works in modern dynamic macroeconomic problems."--Rodolfo E. Manuelli, Washington University in St. Louis

"Modern macroeconomics relies on dynamic equilibrium modeling and the statistical analysis of time-series data. This superb book teaches both techniques hands-on. It guides readers towards mastering a library of computer programs that work for many practical problems, a library that readers will then build on in their own macroeconomic research."--Martin Schneider, Stanford University

"It is nearly impossible to think of a better set of coauthors for this subject. I read their superior book with great pleasure and learned much from it."--Jesus Fernandez-Villaverde, University of Pennsylvania

"Drawing strong connections between mathematics and economic intuition, this rigorous and insightful book contains an extremely broad set of applications, treated from the same consistent framework. The exposition of the benchmark model is outstanding and unique."--John Stachurski, Australian National University

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Recursive Models of Dynamic Linear Economies

By Lars Peter Hansen, Thomas J. Sargent

PRINCETON UNIVERSITY PRESS

Copyright © 2014 Princeton University Press
All rights reserved.

ISBN: 978-0-691-04277-0

Contents

Preface....................................................................
xiii
Acknowledgments............................................................
xv
Part I: Overview...........................................................
1. Theory and Econometrics.................................................
3
Part II: Tools.............................................................
2. Linear Stochastic Difference Equations..................................
15
3. Efficient Computations..................................................
33
Part III: Components of Economies..........................................
4. Economic Environments...................................................
61
5. Optimal Resource Allocations............................................
79
6. A Commodity Space.......................................................
125
7. Competitive Economies...................................................
131
Part IV: Representations and Properties....................................
8. Statistical Representations.............................................
153
9. Canonical Household Technologies........................................
191
10. Examples...............................................................
217
11. Permanent Income Models................................................
233
12. Gorman Heterogeneous Households........................................
253
13. Complete Markets Aggregation...........................................
269
14. Periodic Models of Seasonality.........................................
291
A. MATLAB Programs.........................................................
327
References.................................................................
379
Subject Index..............................................................
393
Author Index...............................................................
397
MATLAB Index...............................................................
399

CHAPTER 1

Theory and Econometrics

Complete market economies are all alike....— Robert E. Lucas, Jr. (1989)

1.1. Introduction

Economic theory identifies patterns that unite apparently diverse subjects. Considerthe following models:

1. Ryoo and Rosen's (2004) partial equilibrium model of the market for engineers;

2. Rosen, Murphy, and Scheinkman's (1994) model of cattle cycles;

3. Lucas's (1978) model of asset prices;

4. Brock and Mirman's (1972) and Hall's (1978) model of the permanent incometheory of consumption;

5. Time-to-build models of business cycles;

6. Siow's (1984) model of occupational choice;

7. Topel and Rosen's (1988) model of the dynamics of house prices and quantities;

8. Theories of dynamic demand curves;

9. Theories of dynamic supply curves;

10. Lucas and Prescott's (1971) model of investment under uncertainty.

These models and many more have identical structures because all describecompetitive equilibria with complete markets. This is the meaning of words ofRobert E. Lucas, Jr., with which we have chosen to begin this chapter. Lucasrefers to the fact that complete markets models are cast in terms of a commonset of objects and a common set of assumptions about how those objects fittogether, namely:

1. Descriptions of flows of information over time, of endowments of resources,and of commodities that can be traded

2. A technology for transforming endowments into commodities and an associatedset of feasible allocations

3. A list of people and their preferences over feasible allocations

4. An assignment of endowments to people, a price system, and a single budgetconstraint for each person

5. An equilibrium concept that uses prices to reconcile decisions of diverseprice-taking agents

This book is about constructing and applying competitive equilibria for aclass of linear-quadratic-Gaussian dynamic economies with complete markets.For us, an economy will consist of a list of matrices that describe people's householdtechnologies, their preferences over consumption services, their productiontechnologies, and their information sets. Competitive equilibrium allocationsand prices satisfy some equations that are easy to write down and solve. Thesecompetitive equilibrium outcomes have representations that are convenient torepresent and estimate econometrically.

Practical and analytical advantages flow from identifying an underlyingstructure that unites a class of economies. Practical advantages come from recognizingthat apparently different applications can be formulated and estimatedusing the same tools simply by replacing one list of matrices with another. Analyticaladvantages and deeper understandings come from appreciating the rolesplayed by key assumptions such as completeness of markets and structures ofheterogeneity.

1.2. A Class of Economies

We constructed our class of economies by using (1) a theory of recursive dynamiccompetitive economies, (2) linear optimal control theory, (3) methods for estimatingand interpreting vector autoregressions, and (4) a computer languagefor rapidly manipulating linear systems. Our economies have competitive equilibriawith representations in terms of vector autoregressions that can be swiftlycomputed, simulated, and estimated econometrically. The models thus mergeeconomic theory with dynamic econometrics. The computer language MATLABimplements the computations. It has a structure and vocabulary that economizetime and effort. Better yet, dynare has immensely improved, accelerated, andeased practical applications.

We formulated this class of models because practical difficulties of computingand estimating more general recursive competitive equilibrium modelscontinue to limit their use as tools for thinking about applied problems. Recursivecompetitive equilibria were developed as useful special cases of the Arrow-Debreucompetitive equilibrium model. Relative to the more general Arrow-Debreusetting, the great advantage of recursive competitive equilibria is thatthey can be computed by solving discounted dynamic programming problems.Furthermore, under some additional conditions, a competitive equilibrium canbe represented as a Markov process. When that Markov process has a uniqueinvariant distribution, there exists a vector autoregressive representation. Thus,the theory of recursive competitive equilibria holds out the promise of makingeasier contact with econometric theory than did previous formulations ofequilibrium theory.

Two computational difficulties continue to leave some of this promise unrealized.The first is a "curse of dimensionality" that makes dynamic programminga costly procedure with even small numbers of state variables. The second isthat after a...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 0691042772
• ISBN 13: 9780691042770
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 424
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar