Recursive Macroeconomic Theory

by Lars Ljungqvist and Thomas J. Sargent

• ISBN13: 9780262194518
• ISBN10: 0262194511
• Format: Hardcover
• Copyright: 2000-09-01
• Publisher: Mit Pr

Summary

Recursive methods offer a powerful approach in dynamic macroeconomics. This book contains both an introduction to recursive tools, including standard applications such as asset pricing, and advanced material, including analyses of reputational mechanisms and contract design. The tools are presented with enough technical sophistication to get the reader started working on practical problems. When numerical simulations are called for, the book provides suggestions for how to proceed, as well as references for further reading. The applications cover many substantive issues in macroeconomics, such as equilibrium asset prices, market incompleteness, wealth distribution, fiscal-monetary theories of inflation, government debt, optimal labor and capital taxation, time consistency and credible government policies, optimal social insurance, economic growth, and labor market dynamics.

Table of Contents

Acknowledgments	xxi
Preface	xxiii
Time Series	1	(28)
Two workhorses	1	(1)
Markov chains	1	(6)
Stationary distributions	3	(1)
Asymptotic stationarity	4	(1)
Expectations	5	(1)
Forecasting functions	5	(1)
Simulating a Markov chain	6	(1)
The likelihood function	6	(1)
Stochastic linear difference equations	7	(12)
Moments	8	(2)
Impulse response function	10	(1)
Prediction and discounting	11	(1)
Stochastic discount factor	11	(1)
Population regression	12	(2)
The spectrum	14	(1)
Examples	15	(3)
Estimation	18	(1)
Concluding remarks	19	(1)
Appendix: A linear difference equation	20	(1)
Exercises	21	(8)
Dynamic Programming	29	(10)
Sequential problems	29	(6)
Three computational methods	31	(2)
Cobb-Douglas transition, logarithmic preferences	33	(2)
Euler equations	35	(1)
A sample Euler equation	35	(1)
Stochastic control problems	35	(2)
Concluding remarks	37	(1)
Exercise	37	(2)
Practical Dynamic Programming	39	(14)
The curse of dimensionality	39	(1)
Discretization of state space	39	(1)
Discrete-state dynamic programming	40	(2)
Application of Howard improvement algorithm	42	(1)
Numerical implementation	43	(2)
Modified policy iteration	44	(1)
Sample Bellman equations	45	(2)
Calculating expected utility	45	(1)
Risk-sensitive preferences	45	(1)
Costs of business cycles	46	(1)
Polynomial approximations	47	(4)
Recommended computational strategy	48	(1)
Chebyshev polynomials	48	(1)
Algorithm: summary	49	(1)
Shape preserving splines	50	(1)
Concluding remarks	51	(2)
Linear Quadratic Dynamic Programming	53	(22)
Introduction	53	(1)
The optimal linear regulator problem	53	(3)
Value function iteration	55	(1)
Discounted linear regulator problem	55	(1)
Policy improvement algorithm	55	(1)
The stochastic optimal linear regulator problem	56	(2)
Discussion of certainty equivalence	58	(1)
Shadow prices in the linear regulator	58	(3)
Stability	59	(2)
A Lagrangian formulation	61	(4)
The Kalman filter	65	(6)
Muth's example	67	(2)
Jovanovic's example	69	(2)
Concluding remarks	71	(1)
Appendix A: Matrix formulas	71	(1)
Appendix B: Linear-quadratic approximations	72	(3)
An example: the stochastic growth model	72	(1)
Kydland and Prescott's method	73	(1)
Determination of z	74	(1)
Log linear approximation	74	(1)
Trend removal	75	(1)
Exercises	75