The aims of this Journal, and of the Society of which it is to be the organ, have been stated above by the Editor with that brevity and precision which are characteristic of every statement of a sound case. What I have to add, by way of comment and amplification, will, I hope, confirm the impression that there is nothing startling or paradoxical about our venture, but that it grows naturally out of the present situation of our science. We do not wish to revive controversies about general questions of ‘method’, but simply to present and discuss the results of our work. We do not impose any credo – scientific or otherwise – and we have no common credo beyond holding: first, that economics is a science, and, secondly, that this science has one very important quantitative aspect. We are no sect. Nor are we a ‘school’. For all possible differences of opinion on individual problems, which can at all exist among economists, do, and I hope always will, exist among us.

Like everything else, economic life may be looked at from a great, strictly speaking an infinite, number of standpoints. Only some of these belong to the realm of science, still fewer admit of, or require, the use of quantitative methods. Many non-quantitative aspects are, and always have been, more interesting to most minds. Fruitful work can be done on entirely non-quantitative lines. Much of what we want to know about economic phenomena can be discovered and stated without any technical, let alone mathematical, refinements upon ordinary modes of thought, and without elaborate treatment of statistical figures.

I have been researching the inadequacies of conventional approaches to the modeling of time since 1968. My dissatisfaction with treatments of tatonnement stability led me to think about price adjustments in real time, with individuals aware that they are partaking in a process in real time. This approach to modeling equilibrium resulted first in my 1971 analysis of search equilibrium in a single market. Reading Mortensen (1978) made me realize the power of Poisson processes for developing tractable models of real time activities and moved my concern for real time allocation processes into a more productive phase. These lectures represent an attempt to express the image of the workings of an economy that lies behind much of my research. Being invited to give these lectures pushed me into a reflection on modeling that would not have occurred otherwise.

The book is divided into two lectures; each lecture is divided into two chapters. In the lecture about individual industries, I begin by considering explicit modeling of time in a competitive setting where investment and production are the only decisions by firms; the Walrasian auctioneer handles prices. The thrust of the lecture is how atemporal modeling is (and must be) informed by explicittime thinking and modeling. This is illustrated by a model with uncertainty about the production costs of individual firms and is argued by consideration of data on gross and net employment flows. The second chapter moves beyond this structure by recognizing price setting as a control variable of individual suppliers, dropping the fiction of the Walrasian auctioneer.

In the Preface to the first edition of his Principles of Economics, Alfred Marshall refers to the “element of Time” as “the centre of the chief difficulty of almost every economic problem” (1948, p. ii). I share Marshall's view of time as a source of difficulty. The picture of Harold Lloyd conveys my image of a theorist grappling with the modeling of time. In these lectures, I will examine how time is modeled in various economic analyses. My focus will be on the modeling of equilibrium, particularly equilibrium with many economic agents. I will present a leisurely tour through some economic analyses, with an eye on their treatment of time. The first lecture considers models of a single industry; the second, models of an entire economy. My hope is that economic analyses will improve from awareness of the link between how time is modeled and some of the conclusions reached by the models.

Short run and long run

In Book V of his Principles, Marshall considers equilibrium. Let me quote a summary paragraph:

In the first lecture, I examined equilibrium in a single market. I examined the distinction between short run and long run in Marshallian analysis, proposing an explicit modeling of time in place of Marshall's implicit modeling with different atemporal models for different time frames. The lecture was made easier by the common core of modeling shared by so much of the writing on partial equilibrium. It does not much matter what textbook one picks up in looking for examples. It does not matter whether one uses introductory, intermediate or advanced texts. One can look to Marshall for a presentation that is a widely shared antecedent.

When considering models of an entire economy, the story is very different. To begin, there are two very different traditions of modeling an entire economy. Both microand macroeconomists engage in this activity. The Arrow- Debreu general equilibrium model looks very different from the Hicksian ISLM model. Within microeconomics, there is considerable uniformity. But, not within macroeconomics. Compare Robert Barro's (1990) intermediate text with that of N. Gregory Mankiw (1992) and one sees significant differences in the modeling techniques thought to be important. The legacy of Keynes is treated differently in the two. Graduate texts such as Olivier Jean Blanchard and Stanley Fischer (1989) or Thomas J. Sargent (1987) do not resemble undergraduate texts, or each other. Thus my task here is more difficult.

In the first lecture, I tried to portray a rich picture of the modeling of individual markets, based on models that consider different expansion paths for different firms and price competition with incomplete information.

In thinking about an entire economy, one of the critical research choices is how to relate the way that one models entire economies to the way that one models individual markets. One approach has each of these research activities proceeding independently of the other, with industry studies focusing on individual firm and household data and economy studies focusing on aggregate data. An alternative approach attempts to develop a consistent way of addressing both classes of issues. I have been part of this second group, working in what has been called the micro foundations of macro. This lecture will continue in this mode.

There are three broad categories of approaches for modeling purchasing power. Some models focus on income (with or without a role for interest rates), some models focus on money (again, with or without a role for interest rates), and some models focus on credit. It is hard to use a model that addresses all three sources at once.

I will proceed by considering the Hicksian ISLM model, and then turning to explicit-time models. In the first lecture, I contrasted a single explicit-time model with atemporal models to illustrate the importance of paying more attention to time. For this lecture, I use several explicit-time models, each with some of the properties we would like such a model to have.

Short run and long run

As in the first lecture, I want to start with the contrast between the short run and the long run. Maiinvaud draws this distinction as follows:

Both the atemporal Marshallian analysis and the explicittime entry–exit model discussed in chapter 1 had the same interaction between demand and supply within a period. With the time structure implicit in this modeling, any attempt to charge more than the “market price” fails completely, while the entire market can be taken by a price below the market price. Thus an instant response by demanders to any variation in pricing behavior is implicitly assumed. This is a common strategy for model simplification: one action happens infinitely more rapidly than another. Once we start paying attention to how long it takes to learn things and to do things, this assumption becomes implausible for many markets.

Marshall identified both space and time as issues in the analysis of a market. In his analysis of sticky prices, Robert Gordon (1981) has argued that some commodity allocations have an important tradeoff between space and time. In markets with a single location for transactions (or a small number), prices seem to react very quickly to imbalances in desired trades. But the use of a single location makes examination and collection of physical commodities prohibitively expensive. In contrast with stock markets, grocery stores have their products available for both examination and collection at a widely dispersed set of locations. Moreover, prices within a grocery store do not behave like prices on a stock exchange. Some prices (e.g., produce) are changed frequently, but not continuously; other prices are changed infrequently. Some items are “on sale.” The strategic intent of stores, along with the costs of different items are important in understanding pricing.

The results of the foregoing chapters are intended to provide empirical researchers with an appreciation of the dangers of taking one's explanatory models too literally, and with tools for coping with the necessity of using models, which by their very nature as human artifacts, may be misspecified to greater or lesser extent.

Chapter 2 of this book motivates use of the method of maximum likelihood in the presence of misspecification and establishes the existence of the quasi-maximum likelihood estimator. We see in Chapter 3 how misspecification can cause quasi-maximum likelihood estimators to fail to be consistent for parameters of interest, but that the QMLE θ generally retains an information theoretic interpretation: it is consistent for a parameter vector θ* that minimizes Kullback-Leibler information. As such,θ depends generally on the specification generating ,θ as well as on the data generation process. In Chapters 4 and 5 we see that in certain special cases, specification correct to a limited extent can allow consistent estimation of parameters of interest. For example, use of exponential family quasi-likelihood functions yields consistent estimators for the parameters of a correctly specified model of the conditional expectation of the dependent variables given the explanatory variables.