A (jump) Markov process (generalized birth-and-death process) is used to model interactions of a large number of agents subject to field-type externalities. Transition rates are (nonlinear) functions of the composition of the population of agents classified by the choices they make. The model state randomly moves from one equilibrium to another, and exhibits asymmetrical oscillations (business cycles). It is shown that the processes can have several locally stable equilibria, depending on the degree of uncertainty associated with consequences of alternative choices. There is a positive probability of transition between any pair of such basins of attraction, and mean first-passage times between equilibria can be different when different pairs of basins are calculated.

We develop a framework to study the effects of policies of uncertain duration on consumption dynamics under both complete and incomplete markets. We focus on the dynamic implications of market incompleteness, specifically on the lack of state-contingent bonds. Two policies are considered: pure output-increasing and tariff-reducing (trade liberalization). With complete markets, the output-increasing policy leads to flat consumption, whereas with no contingent assets, consumption jumps upward on the announcement of the policy, continues rising as long as the policy is in effect, and collapses when it is abandoned. A similar consumption path obtains in a trade liberalization in the realistic case of low elasticity of substitution and no rebate of tariffs. Market incompleteness rationalizes the existence of gradual changes in consumption.

This paper studies the problems of measuring economic growth under conditions of high inflation. Traditional bilateral index number theory implicitly assumes that variations in the price of a commodity within a period can be ignored. To justify this assumption under conditions of high inflation, the accounting period must be shortened to a quarter, a month, or possibly a week. However, once the accounting period is less than a year, the problem of seasonal commodities is encountered; i.e., in some subannual periods, many seasonal commodities will be unavailable and hence the usual bilateral index number theory cannot be applied. The paper systematically reviews the problems of index number construction when there are seasonal commodities and high inflation. Various index number formulas are justified from the viewpoint of the economic approach to index number theory by making separability assumptions on consumers' intertemporal preferences. We find that accurate economic measurement under conditions of high inflation is very complex.

Persistent high unemployment has fostered the employment persistency hypothesis according to which employment changes are driven by unanticipated shocks whereas anticipated shocks that potentially could change employment are absorbed by wage changes. Empirical tests of the persistency hypothesis fail to distinguish between the properties of shocks and endogenous propagation mechanism causing persistency. This paper develops a new test strategy by explicitly distinguishing between these two factors. The methodology is applied to the manufacturing sector in Denmark, and some support in favor of an endogenous propagation mechanism causing employment persistency is found.

A known result holds that capital taxes should be high in the short run and low or zero in the long-run steady state. This paper studies the dynamics of optimal capital taxation during the transition, when a high rate is no longer optimal but the economy is still in flux. The main result is that capital should be taxed whenever the sum of the elasticities of marginal utility with respect to consumption and labor supply are rising and subsidized whenever this sum is falling. If the utility function displays increasing relative risk aversion, this paradoxically implies that capital should be taxed when the capital stock is below the modified golden-rule level and subsidized whenever it exceeds this level. Thus, savings incentives sometimes can be more desirable when the capital stock is large than when it is small.

This survey article is the first to appear in Macroeconomic Dynamics. Other surveys that are relevant to the objectives of the journal and are of unusual technical sophistication will occasionally appear in this journal in its new MD Surveys section.

This paper is the first part of a two-part survey reviewing some basic concepts and methods of the modern theory of dynamical systems. The survey is introduced by a preliminary discussion of the relevance of nonlinear dynamics and chaos for economics. We then discuss the dynamic behavior of nonlinear systems of difference and differential equations such as those commonly employed in the analysis of economically motivated models. Part I of the survey focuses on the geometrical properties of orbits. In particular, we discuss the notion of attractor and the different types of attractors generated by discrete- and continuous-time dynamical systems, such as fixed and periodic points, limit cycles, quasiperiodic and chaotic attractors. The notions of (noninteger) fractal dimension and Lyapunov characteristic exponent also are explained, as well as the main routes to chaos.

David Cass is undoubtedly one of the central contributors to modern dynamic economics. His fundamental contributions include work on optimal growth problems, overlapping-generations models, sunspot equilibria, and general equilibrium models with incomplete markets. His research has shaped in profound ways the manner in which we do both micro- and macroeconomics. From laying the foundations of real business-cycle theory via the Cass-Koopmans model, to providing us with general tools and techniques to analyze dynamic economic models, to furthering our understanding of monetary economics, to making fundamental contributions to the economics of extrinsic uncertainty, Cass's work has played a major part in the development of much of modern macroeconomic theory. In addition to being a first-class scholar, Cass is also truly his own man and a free spirit of the highest order.

In this interview, we tried to gain some insights into the story of David Cass and his approach to economic theory. Also, given the title as well as the intended readership of Macroeconomic Dynamics, we made a real effort to get him to discuss modern macroeconomics and the influence his work has had on its development. We edited out some parts of the discussion in the interests of space, but what remains is essentially unedited. As most readers will know, David Cass has collaborated extensively with Karl Shell over the years. We talked to Shell a few weeks after talking to Cass, and that interview is scheduled to appear in a future issue.

We met with Dave in his office at the University of Pennsylvania's Economics Department just before noon. Amid the boxes and piles of articles, books and CD's, he sat in his standard jeans and T-shirt, looking about as disheveled as he usually does. We chatted there for a while, went out and continued over lunch, and then returned to complete the interview several hours later. It was an unseasonably warm day in February, and Friday the 13th to be exact. That is traditionally an unlucky day, but one that turned out in this case to be a real treat, at least for us! We hope that you get as much out of this conversation with Dave as we did.

This book is an ambitious effort by three well-known and well-respected scholars to fill an acknowledged void in the literature—a text covering the burgeoning field of empirical finance. As the authors note in the preface, there are several excellent books covering financial theory at a level suitable for a Ph.D. class or as a reference for academics and practitioners, but there is little or nothing similar that covers econometric methods and applications. Perhaps the closest existing text is the recent addition to the Wiley Series in Financial and Quantitative Analysis. written by Cuthbertson (1996). The major difference between the books is that Cuthbertson focuses exclusively on asset pricing in the stock, bond, and foreign exchange markets, whereas Campbell, Lo, and MacKinlay (henceforth CLM) consider empirical applications throughout the field of finance, including corporate finance, derivatives markets, and market microstructure. The level of anticipation preceding publication can be partly measured by the fact that at least three reviews (including this one) have appeared since the book arrived. Moreover, in their reviews, both Harvey (1998) and Tiso (1998) comment on the need for such a text, a sentiment that has been echoed by numerous finance academics.