Recursive Methods in Economic Dynamics

by Nancy L. Stokey, Robert E. Lucas Jr., Edward C. Prescott (Editor)

Overview

Three eminent economists provide in this book a rigorous, self-contained treatment of modern economic dynamics. Nancy L. Stokey, Robert E. Lucas, Jr., and Edward C. Prescott develop the basic methods of recursive analysis and emphasize the many areas where they can usefully be applied.

After presenting an overview of the recursive approach, the authors develop economic applications for deterministic dynamic programming and the stability theory of first-order difference equations. They then treat stochastic dynamic programming and the convergence theory of discrete-time Markov processes, illustrating each with additional economic applications. They also derive a strong law of large numbers for Markov processes. Finally, they present the two fundamental theorems of welfare economics and show how to apply the methods developed earlier to general equilibrium systems.

The authors go on to apply their methods to many areas of economics. Models of firm and industry investment, household consumption behavior, long-run growth, capital accumulation, job search, job matching, inventory behavior, asset pricing, and money demand are among those they use to show how predictions can be made about individual and social behavior. Researchers and graduate students in many areas of economics, both theoretical and applied, will find this book essential.

Product Details

ISBN-13:	9780674735194
Publisher:	Harvard University Press
Publication date:	10/10/1989
Sold by:	Barnes & Noble
Format:	eBook
Pages:	608
File size:	18 MB
Note:	This product may take a few minutes to download.

About the Author

Nancy L. Stokey is Frederick Henry Prince Distinguished Service Professor of Economics at the University of Chicago.

Robert E. Lucas, Jr., is John Dewey Distinguished Service Professor of Economics at the University of Chicago. In 1995, he was awarded the Nobel Prize in Economics.

Edward C. Prescott is Regents’ Professor and Professor of Economics at Arizona State University and Senior Monetary Advisor to the Federal Reserve Bank of Minneapolis.

Table of Contents

Contents

Symbols Used

I. The Recursive Approach

1. Introduction

2. An Overview

2.1: A Deterministic Model of Optimal Growth

2.2: A Stochastic Model of Optimal Growth

2.3: Competitive Equilibrium Growth

2.4: Conclusions and Plans

II. Deterministic Models

3. Mathematical Preliminaries

3.1: Metric Spaces and Normed Vector Spaced

3.2: The Contraction Mapping Theorem

3.3: The Theorem of the Maximum

4. Dynamic Programming under Certainty

4.1: The Principle of Optimality

4.2: Bounded Returns

4.3: Constant Returns to Scale

4.4: Unbounded Returns

4.5: Euler Equations

5.1: The One-Sector Model of Optimal Growth

5.4: Growth with Technical Progress

5.5: A Tree-Cutting Problem

5.7: Human Capital Accumulation

5.8: Growth with Human Capital

5.9: Investment with Convex Costs

5.10: Investment with Constant Returns

5.11: Recursive Preferences

5.12: Theory of the Consumer with Recursive Preferences

5.13: A Pareto Problem with Recursive Preferences

5.14: An (s, S) Inventory Problem

5.15: The Inventory Problem in Continuous Time

5.16: A Seller with Unknown Demand

5.17: A Consumption-Savings Problem

6. Deterministic Dynamics

6.1: One-Dimensional Examples

6.2: Global Stability: Liapounov Functions

6.3: Linear Systems and Linear Approximations

6.4: Euler Equations

6.5: Applications

III. Stochastic Models

7. Measure Theory and Integration

7.1: Measurable Spaces

7.2: Measures

7.3: Measurable Functions

7.4: Integration

7.5: Product Spaces

7.6: The Monotone Class Lemma

7.7: Conditional Expectation

8. Markov Processes

8.1: Transition Functions

8.2: Probability Measures on Spaces of Sequences

8.3: Iterated Integrals

8.4: Transitions Defined by Stochastic Difference Equations

9. Stochastic Dynamic Programming

9.1: The Principle of Optimality

9.2: Bounded Returns

9.3: Constant Returns to Scale

9.4: Unbounded Returns

9.5: Stochastic Euler Equations

9.6: Policy Functions and Transition Functions

10.1: The One-Sector Model of Optimal Growth

10.3: Optimal Growth with Many Goods

10.4: Industry Investment under Uncertainty

10.5: Production and Inventory Accumulation

10.6: Asset Prices in an Exchange Economy

10.7: A Model of Search Unemployment

10.8: The Dynamics of the Search Model

10.9: Variations on the Search Model

10.10: A Model of Job Matching

10.11: Job Matching and Unemployment

11. Strong Convergence of Markov Processes

11.1: Markov Chains

11.2: Convergence Concepts for Measures

11.3: Characterizations of Stong Convergence

11.4: Sufficient Conditions

12. Weak Convergence of Markov Processes

12.1: Characterizations of Weak Convergence

12.2: Distribution Functions

12.3: Weak Convergence of Distribution Functions

12.4: Monotone Markov Processes

12.5: Dependence of the Invariant Measures on a Parameter

12.6: A Loose End

13.1: A Discrete-Space (s, S) Inventory Problem

13.2: A Continuous-State (s, S) Process

13.3: The One-Sector Model of Optimal Growth

13.4: Industry Investment under Uncertainty

13.5: Equilibrium in a Pure Currency Economy

13.6: A Pure Currency Economy with Linear Utility

13.7: A Pure Credit Economy with Linear Utility

13.8: An Equilibrium Search Economy

14. Laws of Large Numbers

14.1: Definitions and Preliminaries

14.2: A Strong Law for Markov Processes

IV. Competitive Equilibrium

15. Pareto Optima and Competitive Equilibria

15.1: Dual Spaces

15.2: The First and Second Welfare Theorems

15.3: Issues in the Choice of a Commodity Space

15.4: Inner Product Representations of Prices

16. Applications of Equilibrium Theory

16.1: A One-Sector Model of Growth under Certainty

16.2: A Many-Sector Model of Stochastic Growth

16.3: An Ecomony with Sustained Growth

16.4: Industry Investment under Uncertainty

16.5: Truncation: A Generalization

16.6: A Peculiar Example

16.7: An Economy with Many Consumers

17. Fixed-Point Arguments

17.1: An Overlapping-Generations Model

17.2: An Application of the Contraction Mapping Theorem

17.3: The Brouwer Fixed-Point Theorem

17.4: The Schauder Fixed-Point Theorem

17.5: Fixed Points of Monotone Operators

17.6: Partially Observed Shocks

18. Equilibria in Systems with Distortions

18.1: An Indrect Approach

18.2: A Local Approach Based on First-Order Conditions

18.3: A Global Approach Based on First-Order Conditions

References

Index of Theorems

General Index

What People are Saying About This

This book is a wonderful collection of results on the techniques of dynamic programming with great applications to economics written by giants in the field.

Thomas J. Sargent

A magnificent work that is bound to have immense influence on the ways economists think about dynamic systems for many years to come. My own guess is that this book will eventually acquire the stature, say, of Hicks's Value and Capital or Samuelson's Foundations.
— Thomas J. Sargent, Hoover Institution

Sanford J. Grossman

This book is a wonderful collection of results on the techniques of dynamic programming with great applications to economics written by giants in the field.
— Sanford J. Grossman, University of Pennsylvania

Andrew Caplin

The book is a tour de force. The authors present a unified approach to the techniques and applications of recursive economic theory. The presentations of discrete-time dynamic programming and of Markov processes are authoritative. There is a wide-ranging series of examples drawn from all branches of the discipline, but with special emphasis on macroeconomics. In the short run, the book will be a vital reference in any advanced course in macroeconomic theory. In the long run, it may help to remove the traditional boundaries between microeconomic theory and macroeconomic theory.
— Andrew Caplin, Columbia University

Editorial Reviews

The book is a tour de force. The authors present a unified approach to the techniques and applications of recursive economic theory. The presentations of discrete-time dynamic programming and of Markov processes are authoritative. There is a wide-ranging series of examples drawn from all branches of the discipline, but with special emphasis on macroeconomics. In the short run, the book will be a vital reference in any advanced course in macroeconomic theory. In the long run, it may help to remove the traditional boundaries between microeconomic theory and macroeconomic theory.
-- Andrew Caplin, Columbia University

This book is a wonderful collection of results on the techniques of dynamic programming with great applications to economics written by giants in the field.
-- Sanford J. Grossman, University of Pennsylvania

A magnificent work that is bound to have immense influence on the ways economists think about dynamic systems for many years to come. My own guess is that this book will eventually acquire the stature, say, of Hicks’s Value and Capital or Samuelson’s Foundations.
-- Thomas J. Sargent, The Hoover Institution

From the Publisher