NANCY STOKEY AND ROBERT LUCAS, JR., and Ed Prescott have produced an exceptionally useful, thorough, and timely introduction to stochastic economic dynamics. Dynamic optimization techniques developed in Operations Research, formulated initially by Richard Bellman (1957), have been used extensively in economics, particularly in macroeconomics, finance, and public finance. Economic theorists have extended dynamic programming theory in several valuable directions. Of particular note for this book is the concept of recursive equilibrium introduced in Edward Prescott and Rajnish Mehra (1980). While these techniques have been used extensively, there has been no broad, unified, and comprehensive presentation of the concepts, tools, and applications of recursive dynamic techniques that is written for economists and demands no more mathematics than a typical student is exposed to in a good graduate program. This book succeeds marvelously in filling this need. Furthermore, given the depth of development, it is also a valuable reference for researchers. Before describing the book's contents in detail, we should discuss what is distinctive and important about the recursive approach to dynamic economic problems. To do this, let's examine a simple problem and an alternative approach to its solution. The canonical problem for economic dynamics is the infinite horizon deterministic growth problem. Let k, be the capital stock at the beginning of period t, f(kt) a neoclassical production function expressing period t production as a function of kt, ct consumption in period t chosen at the end of the period, u(c) a concave utility function, and I the discount factor. Then a social planner for this infinitely lived economy will solve the problem

We examine the incentives that owners of competing firms give their managers. We show that, in equilibrium, each manager will be paid in excess of his decision's marginal profit in a Cournot-quantity game, but paid less than the marginal profit in a price game. In the Cournot case, deviations from profit maximization are reduced by ex ante cost uncertainty and increased by correlation in the firms' costs.

Estimating structural models is often viewed as computationally difficult, an impression partly due to a focus on the nested fixed-point (NFXP) approach.We propose a new constrained optimization approach for structural estimation.We show that our approach and the NFXP algorithm solve the same estimation problem, and yield the same estimates.Computationally, our approach can have speed advantages because we do not repeatedly solve the structural equation at each guess of structural parameters.Monte Carlo experiments on the canonical Zurcher bus-repair model demonstrate that the constrained optimization approach can be significantly faster.

[We analyze complex bond portfolios within the framework of a dynamic general equilibrium asset-pricing model. Equilibrium bond portfolios are nonsensical and imply a trading volume that vastly exceeds observed trading volume on financial markets. Instead, portfolios that combine bond ladders with a market portfolio of equity assets are nearly optimal investment strategies. The welfare loss of these simple investment strategies, when compared to the equilibrium portfolio, converges to zero as the length of the bond ladder increases. This article, therefore, provides a rationale for naming bond ladders as a popular bond investment strategy.]

This paper examines the impact of Social Security on national saving and individual welfare in the presence of realistic capital market imperfections--market failure in the private provision of annuities and restrictions on borrowing against anticipated future wages. The introduction of Social Security increases lifetime welfare and reduces national saving if borrowing restrictions are absent. However, the increase in individual welfare is reduced, and in some cases eliminated, when borrowing constraints are taken into consideration. The substantial difference suggests the importance of reexamining the proportional payroll tax finance of Social Security.