Knowledge that Transforms

Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and Knoer [1], we show that equilibrium in such markets exists and is stable, in spite of workers' discrete choices among jobs, provided that all workers are gross substitutes from each firm's standpoint. We also generalize Gale and Shapley's [3] result that the equilibrium to which the adjustment process converges is biased in favor of agents on the side of the market that makes offers, beyond the class of economies to which it was extended by Crawford and Knoer [1]. Finally, we use our techniques to establish the existence of equilibrium in a wider class of markets, and some sensible comparative statics results about the effects of adding agents to the market are obtained. THE ARROW-DEBREU THEORY of general economic equilibrium has long been recognized as a powerful and elegant tool for the analysis of resource allocation in market economies. Not all markets fit equally well into the Arrow-Debreu framework, however. Consider, for example, the labor market-or the housing market, which provides an equally good example for most of our purposes. Essential features of the labor market are pervasive uncertainty about market opportunities on the part of participants, extensive heterogeneity, in the sense that job satisfaction and productivity generally differ (and are expected to differ) interactively and significantly across workers and jobs, and large set-up costs and returns to specialization that typically limit workers to one job. All of these features can be fitted formally into the Arrow-Debreu framework. State-contingent general equilibrium theory, for example, provides a starting point for studying the effects of uncertainty. But this analysis has been made richer and its explanatory power broadened by the examination of equilibrium with incomplete markets, search theory, and market signaling theory. The purpose of this paper is to attempt some improvements in another dimension: we study the outcome of competitive sorting processes in markets where complete heterogeneity prevails (or may prevail). To do this, we take as given the implications of set-up costs and returns to specialization by assuming that, while firms can hire any number of workers, workers can take at most one job. We also return to the simplification of perfect information. In the customary view of competitive markets, agents take market prices as given and respond noncooperatively to them. In this framework equilibrium cannot exist in general unless the goods traded in each market are truly homogeneous; heterogeneity therefore generally requires a very large number of markets. And since these markets are necessarily extremely thin-in many cases containing only a single agent on each side-the traditional stories supporting the plausibility of price-taking behavior are quite strained.

This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Receiver (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standard assumptions, and show that equilibrium signaling always takes a strikingly simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise into his signal by reporting, in effect, only which element of the partition his observation actually lies in. We show under further assumptions that before S observes his private information, the equilibrium whose partition has the greatest number of elements is Pareto-superior to all other equilibria, and that if agents coordinate on this equilibrium, R's equilibrium expected utility rises when agents' preferences become more similar. Since R bases his choice of action on rational expectations, this establishes a sense in which equilibrium signaling is more informative when agents' preferences are more similar.

In this paper we analyze the solutions of linear econometric models with rational expectations. More precisely, we describe in detail the set of all the solutions; in particular this set is shown to be much larger than the sets previously considered. We also study various criteria of selection in this set of solutions and we examine to what extent these criteria redtiuce the set of the solutions.

[This paper describes a method for estimating and testing nonlinear rational expectations models directly from stochastic Euler equations. The estimation procedure makes sample counterparts to the population orthogonality conditions implied by the economic model close to zero. An attractive feature of this method is that the parameters of the dynamic objective functions of economic agents can be estimated without explicitly solving for the stochastic equilibrium.]

THIS PAPER PRESENTS a simple model of the manner in which person-specific information on productive capabilities is put to use in the firm. The analysis is then employed to examine the impact of improved information quality on equilibrium output, wage rates, and degree of specialization. Much effort has been devoted to studying the process through which personspecific information is accumulated. Burdett-Mortensen [1], MacDonald [8], Prescott-Visscher [10], Hartog [3], and Johnson [5] examine the process of learning about person-specific parameters through investment of resources in activities that yield information. Jovanovic [6] analyses the more specific problem of inferring the quality of a particular job-worker match. Little attention has been given to the question of just how the firm utilizes this kind of information. For information to play an interesting role in production, two things are necessary. One is that workers be heterogeneous in a meaningful sense. That is, in the space of productive characteristics, workers must not all be simply scalar multiples of one another. Second, the firm must have some choice about the kind of activities in which workers are engaged. If either of these conditions fails, the optimal assignment of workers is not a problem.2

Equilibria in stochastic economic models are often time series which fluctuate in complex ways. But it is sometimes possible to summarize the long run, characteristics of these fluctuations. For example, if the law of motion determined by economic interactions is Markovian and if the equilibrium time series converges in a specific probabilistic sense then the long run behavior is completely determined by an invariant probability distribution. This paper develops and unifies a number of results found in the probability literature which enable one to prove, under very general conditions, the existence of an invariant distribution and the convergence of the corresponding Markov process. VIRTUALLY ALL OF ECONOMIC THEORY focuses upon the study of economic equilibrium. This concept has recently undergone several subtle elaborations. No longer must a system of markets in equilibrium be thought of as one at rest in a static steady state. Instead there is a growing body of literature (e.g., [4, 5, 12, 16, 20, 21]) which defines equilibrium as a stochastic process of market clearing prices and quantities which is consistent with the self-interested behavior of economic agents. Needless to say equilibrium stochastic processes can be very complex time series which fluctuate in irregular ways. For theoretical and econometric purposes it is useful to have a convenient way of summarizing the average behavior of such processes over time. This paper draws together and unifies a number of fundamental results from the probability literature which enable one to do this for discrete time, Markov processes on general state spaces. The starting point of the analysis is a set S of economic states (e.g., prices and/or quantities). The only technical restriction placed upon S is that it be a Borel subset of a complete, separable metric space. The second datum is a transition probability P(s, ) on S. The number P(s,A) records the probability that the economic system moves from the state s to some state in the Borel subset A of S during one unit of elapsed time. In economic applications the transition probability is usually derived from hypotheses about market clearing and the maximizing behavior of economic agents. The transition probability (together with an initial probability measure on S) defines a discrete time Markov process. One way of summarizing the dynamic behavior implied by P is to look for an invariant probability. A probability measure X on S is invariant for P if for all Borel subsets A of S one has the equality f P(s, A )X(ds) = X(A). An invariant probability is a kind of probabilistic steady state for the dynamics defined by P. Of course there may be no invariant probability for P at all; and even if one exists it may convey no information about the behavior of the process over time except under very special initial conditions. There is a second way of summarizing the behavior of Markov processes defined by the transition probability P. Let P (s,A) denote the n step transition

Both the class position of agents and their status as exploiters or exploited is endogenously determined as they optimize against asset constraints which limit their capacity to produce revenue. The Class Exploitation Correspondence Principle (CECP) asserts that class and exploitation status are related in a classical way. It is further shown that the class structure associated with a labor market can be generated isomorphically by a credit market, demonstrating the functional equivalence of these markets. Morever, these results hold in models of precapitalist, subsistence economy, showing that the phenomena of Marxian exploitation and class are applicable in economic mechanisms other than capitalist ones. The possibility for a general theory of exploitation is thereby suggested.

[We present a model of information acquisition in a competitive market in which traders can learn both from costly (and diverse) private enquiry and price, which costlessly (but partially) reveals the total amount of information known to all traders. Our major purpose is to show that an equilibrium exists in such a market: that is, there exists a rational expectations competitive equilibrium in which the amount of costly diverse information each trader acquires is endogenously determined. From this result we investigate the change in the informativeness of price relative to changes in the level of noise, the cost of acquiring information, and the distribution of traders' risk preferences.]

[Recent results have shown that, for bargaining over the distribution of commodities, or other riskless outcomes, Nash's solution predicts that risk aversion is a disadvantage in bargaining. Here we consider bargaining games which may concern risky outcomes as well as riskless outcomes, and we demonstrate that, in such games, risk aversion need not always be a disadvantage in bargaining. Intuitively, for bargaining games in which potential agreements involve lotteries which have a positive probability of leaving one of the players worse off than if a disagreement had occurred, the more risk averse a player, the better the terms of the agreement which had occurred, the more risk averse a player, the better the terms of agreeement which he must be offered in order to induce him to reach an agreement, and to compensate him for the risk involved. For bargaining games whose disagreement outcome involves no uncertainty, we characterize when risk aversion is advantageous, disadvantageous, or irrelevant from the point of view of Nash's solution.]

[This paper studies estimators that make sample analogues of population orthogonality conditions close to zero. Strong consistency and asymptotic normality of such estimators is established under the assumption that the observable variables are stationary and ergodic. Since many linear and nonlinear econometric estimators reside within the class of estimators studied in this paper, a convenient summary of the large sample properties of these estimators, including some whose large sample properties have not heretofore been discussed, is provided.]