Are firms and households constrained in the use of a productive input? Theoretical approaches to this question range from exogenously imposed credit allocation rules to endogenous market failures stemming from some sort of limited-commitment or moral-hazard problem. However, when testing for constraints, researchers often simply ask firms or households if they would wish to borrow more at the current interest rate and/or test for suboptimal use of inputs in production functions relative to a full-information, full-commitment benchmark. We demonstrate that if credit is part of a much larger information-constrained (or limited-commitment) incentive scheme, then input use may very well be distorted away from the first-best. Further, households and firms, in certain well-defined circumstances, may, at the true interest rate or opportunity cost of credit, desire to borrow more (or less) than the assigned level of credit. In other, more constrained, contractual regimes, firms and households would say that they do not want to borrow more (or less), but these regimes are decidedly suboptimal, although the magnitude of the loss does depend on parameter values. We conclude with empirical methods that, in principle, could allow researchers armed with enough data to estimate parameters and distinguish regimes. Researchers then could see if firms and households are truly constrained and, if so, what the welfare loss might be.

A seasonal commodity is one that either (1) is not available during certain seasons or (2) is always available but its prices or quantities fluctuate with the season or time of year. The existence of type-1 seasonal commodities in consumer preference functions means that the usual economic approach to index number theory cannot be applied to construct a short-term month-to-month or quarter-to-quarter consumer price index. We postulate various separability assumptions on intertemporal preferences that can be used to justify various seasonal index number formulas. One of our approaches leads to an index number solution to the problem of seasonal adjustment.

A simple technique for directly testing the parameters of a time-series regression model for instability across frequencies is presented. The method can be implemented easily in the time domain, so that parameter instability across frequency bands can be conveniently detected and modeled in conjunction with other econometric features of the problem at hand, such as simultaneity, cointegration, missing observations, and cross-equation restrictions. The usefulness of the new technique is illustrated with an application to a cointegrated consumption-income regression model, yielding a straightforward test of the permanent income hypothesis.

This is the second part of a two-part survey of the modern theory of nonlinear dynamical systems. We focus on the study of statistical properties of orbits generated by maps, a field of research known as ergodic theory. After introducing some basic concepts of measure theory, we discuss the notions of invariant and ergodic measures and provide examples of economic applications. The question of attractiveness and observability, already considered in Part I, is revisited and the concept of natural, or physical, measure is explained. This theoretical apparatus then is applied to the question of predictability of dynamical systems, and the notion of metric entropy is discussed. Finally, we consider the class of Bernoulli dynamical systems and discuss the possibility of distinguishing orbits of deterministic chaotic systems and realizations of stochastic processes.

This dialogue is the first to appear in Macroeconomic Dynamics. Other dialogues on topics of importance to macroeconomics will appear occasionally in this journal. Unlike interviews appearing in the MD Interview series, conversations appearing in the MD Dialogue series will not be focused on the life and work of a participant but rather on a particular research topic. Another distinction between the two series is the general format and structure. Each interview in the MD Interview series will include only one interviewee, although there may be multiple interviewers who jointly conduct an interview with a single interviewee (e.g., the interview of David Cass by Stephen Spear and Randall Wright in the preceding issue). In contrast, each dialogue will include at least two direct dialogue participants, and may or not be conducted by a third party to the conversation.

Every graduate school has its own distinctive history that makes it unique in some way, but every graduate school is also part of the broader economics profession and reflects the currents in the profession. The following dialogue focuses on the question: Is it useful to distinguish a “Yale school of macroeconomics” from other schools of economics? The idea for this dialogue came from William Barnett in a discussion with Bob Shiller. Bill suggested to Bob some names of individuals who might conduct the “dialogue” and I was selected from that list. I happily agreed because, from my knowledge of the writings of the Yale faculty, I felt that there was a uniformity of ideas with which I was sympathetic, and which might deserve to be called a “Yale School”—a view shared with Bob Shiller.

Exploring the issue further, I found that there was far less agreement on whether the macroeconomics work that currently goes on at Yale can be classified meaningfully as “the Yale school.” The objections to specifying a separate Yale school were the following: (1) The term, Yale school, had been used in the 1960's to describe Jim Tobin's position in a debate with monetarists. Some felt it would be confusing to use the Yale school classification to describe a broader set of works that are not connected to that earlier, more narrow, use. (2) Calling the work in macroeconomics currently done at Yale a “school” distinguishes it too much. The work that goes on in Yale is similar to the work that goes on in any top graduate economics program. It is not so clear how the work at Yale differs from, for example, MIT or Princeton. It would need to be more distinct to warrant calling it a “school.” (3) There is a diversity of approaches that are used at Yale, and it is not clear that they actually fit together. For example, Chris Sims's work follows from a time-series statistics tradition with influences from real-business-cycle and calibration work; Shiller's work follows from a Keynesian tradition. Fitting them together requires a bit of a stretch. (4) The degree of continuity in the Yale school over time is not as great as I had first imagined. There was little linkage at Yale from Irving Fisher to Jim Tobin; thus the historical continuity needed for specifying a Yale school does not exist. These objections are elaborated in the dialogues below. After discussing these issues with a number of Yale faculty, I decided that there probably wasn't a Yale school of economics, but that there was a Yale tradition. We also decided to have a conversation with only two individuals—Jim Tobin and Bob Shiller—because they are major figures in maintaining what I believe is a Yale tradition. The conversations were held separately, although I asked many of the same questions to both, and focused much of the conversation on the issue of whether it is useful to distinguish a Yale school. Thus, the conversations discuss the work of other individuals at Yale more than a dialogue with another focus would have, and do not cover Tobin's or Shiller's current work as much as conversations with an alternative focus would have. The results are, I believe, interesting. They provide some useful insight into both the Yale tradition and current thinking and debates in macro.