Recursive Methods in Economic Dynamics
608
Recursive Methods in Economic Dynamics
608eBook
Available on Compatible NOOK devices, the free NOOK App and in My Digital Library.
Related collections and offers
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
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 IndexWhat 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.
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
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
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