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

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.

[A tractable dynamic general equilibrium model of continuous product innovation is developed. Patents, or any imitation lag, of infinite duration may achieve too much, too little, or the socially optimum level of innovation. Most surprising, finite-life patents may induce undamped oscillations in innovation.]

Many important questions in macroeconomics concern the impact of taxation and spending policies on private resource allocation. One approach, typified by Robert Hall (1971) and William Brock and Stephen Turnovsky (1981), is to use dynamic general equilibrium models to address basic issues in fiscal and tax policy. The objective is to explicitly examine macroeconomic issues without embracing the market imperfections (fixed prices, missing markets, money illusion, etc.) found in conventional macroeconomic analysis. There is currently great interest in dynamic fiscal policy problems. This decade has already seen two major adjustments in tax policy, and many attempts to substantially alter spending patterns. The result of this tumult has been unprecedented peacetime deficits and much uncertainty about what measures will ultimately be used to bring the budget into balance. In this paper, I discuss the impact of alternative fiscal policies in a dynamic general equilibrium model. I examine the shortrun effects of fiscal policy changes, the efficiency cost of alternative dynamic tax policies, the effects of uncertain policy formation, and the redistributive effects of factor taxation.

A key feature of modern dynamic economies is imperfect competition. Some imperfect competition is due to institutions such as patents and copy-rights that allow Þrms to exercise market power over the sale of products they invent. Some imperfect competition is due to various forms of increas-ing returns to scale and product differentiation. Since market power is an essential feature of innovation and growth in the new economy (as it was in the old economy) we need to know how imperfect competition affects the conventional wisdom on tax policy. We argue that it has particularly striking implications for the taxation of capital. The current consensus among economists is that investment should be lightly taxed with most tax revenues coming from labor and consumption taxation; see Kenneth L. Judd (1999) for a discussion of this literature. These analyses assume perfect competition in all markets. Even though imperfect competition is common, economists generally prefer competitive models since analyses with imperfect competition usually get mired in strategic details

This paper examines the marginal efficiency cost of various factor taxes in a dynamic general-equilibrium model. The au thor solves for the excess burden of anticipated and unanticipated, t emporary and permanent, tax policies. Using a range of estimates for taste and technology parameters, he finds excess burdens larger than those indicated by previous studies that use static models. These exc ess burdens are sensitive to parameter values and timing. However, th e rankings of alternative tax policies turn out to be insensitive to structural parameter values.

[It is shown that wquilibria with dispersed prices exist in environments with identical and rational agents on both sides of the market. In particular, the original Stigler model of nonsequential search often has many equilibria, some with price dispersion. Also, price dispersion holds in equilibrium in general if search is "noisy," i.e., there is some chance of learning two or more prices when an agent is looking for one price.]