Handbook of Computational Economics, Volume 3

Contributors

Acknowledgments

Introduction to the Series

Introduction for Volume 3 of the Handbook of Computational Economics

Chapter 1. Learning About Learning in Dynamic Economic Models

Abstract

1 Introduction

2 The Framework

3 What We Have Learned

4 What We Hope to Learn

5 Algorithms and Codes

6 A Showcase on Active Learning

7 Learning with Forward Looking Variables

8 Other Applications of Active Learning

9 Summary

References

Chapter 2. On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm

Abstract

1 Motivation and Introduction

2 Theoretical Model

3 Primer on Relevant Numerical Strategies

4 Previous Research Concerning Numerical Solutions

5 Some Examples

6 Comparisons of Relative Performance and Potential Improvements

7 Summary and Conclusions

Acknowledgments

References

Chapter 3. Analyzing Fiscal Policies in a Heterogeneous-Agent Overlapping-Generations Economy

Abstract

1 Introduction

2 Existing Literature

3 Stylized Model Economy

4 Computational Algorithm

5 Calibration to the US Economy

6 Policy Experiments

7 Concluding Remarks

References

Chapter 4. On Formulating and Solving Portfolio Decision and Asset Pricing Problems

Abstract

1 Introduction

2 Discrete Time Portfolio Decision Making

3 Discrete Time Asset Pricing

4 Continuous Time Portfolio Decision Problem

5 Continuous Time Asset Pricing

6 Conclusion

Acknowledgments

References

Chapter 5. Computational Methods for Derivatives with Early Exercise Features

Abstract

1 General Introduction

2 The Problem Statement—In the Case of Stochastic Volatility and Poisson Jump Dynamics

3 American Call Options Under Jump-Diffusion Processes

4 American Call Options under Jump-Diffusion and Stochastic Volatility Processes

5 Conclusion

References

Chapter 6. Solving and Simulating Models with Heterogeneous Agents and Aggregate Uncertainty

Abstract

1 Introduction

2 Example Economy

3 Algorithms—Overview

4 Models with Nontrivial Market Clearing

5 Approximate Aggregation

6 Simulation with a Continuum of Agents

7 Accuracy

8 Comparison

9 Other Types of Heterogeneity

10 Concluding Comments

Acknowledgments

References

Chapter 7. Numerical Methods for Large-Scale Dynamic Economic Models

Abstract

1 Introduction

2 Literature Review

3 The Chapter at a Glance

4 Nonproduct Approaches to Representing, Approximating, and Interpolating Functions

5 Approximation of Integrals

6 Derivative-Free Optimization Methods

7 Dynamic Programming Methods for High-Dimensional Problems

8 Precomputation Techniques

9 Local (Perturbation) Methods

10 Parallel Computation

11 Numerical Analysis of a High-Dimensional Model

12 Numerical Results for the Multicountry Model

13 Conclusion

Acknowledgments

References

Chapter 8. Advances in Numerical Dynamic Programming and New Applications

Abstract

1 Introduction

2 Theoretical Challenges

3 Numerical Methods for Dynamic Programming

4 Tools from Numerical Analysis

5 Shape-preserving Dynamic Programming

6 Parallelization

7 Dynamic Portfolio Optimization with Transaction Costs

8 Dynamic Stochastic Integration of Climate and Economy

9 Conclusions

Acknowledgments

References

Chapter 9. Analysis of Numerical Errors

Abstract

1 Introduction

2 Dynamic Stochastic Economies

3 Numerical Solution of Simple Markov Equilibria

4 Recursive Methods for Non-optimal Economies

5 Numerical Experiments

6 Concluding Remarks

References

Chapter 10. GPU Computing in Economics

Abstract

1 Introduction

2 Basics of GPGPU Computing

3 A Simple GPGPU Example

4 Example: Value Function Iteration

5 Example: A General Equilibrium Asset Pricing Model with Heterogeneous Beliefs

6 The Road Ahead

7 Conclusion

References

Chapter 11. Computing All Solutions to Polynomial Equations in Economics

Abstract

1 Introduction

2 Gröbner Bases and Polynomial Equations

3 Applying Gröbner Bases to Economic Models

4 All-Solution Homotopy Methods

5 Applying Homotopy Methods

6 Conclusion

Acknowledgments

References

Index

Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing.

Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential.

• Samples different styles and approaches, reflecting the breadth of computational economics as practiced today
• Focuses on problems with few well-developed solutions in the literature of other disciplines
• Emphasizes the potential for increasing the value of computational modeling in economics

Upper-division undergraduates, graduate students, and professionals worldwide working on economic analyses.