Knowledge that Transforms

We consider the question, “Under what conditions is the extremum of a random function over a random set itself a random object?” The answer is relevant to problems in both game theory and econometrics, as we illustrate with examples. Our purpose here is to bring the powerful tools of the theory of analytic sets as developed by Dellacherie and Meyer (1978) to the wider attention of the economics profession and to distill Dellacherie and Meyer's work in such a way as to provide some readily accessible theoretical results that will permit relatively easy treatment of economically or econometrically relevant applications.

We develop an empirical model of labour supply that is consistent with on-the-job search and which is identified and estimated by combining two data sets: the U.K. Family Expenditure Survey which contains information on income and expenditure and the U.K. Labour Force Survey, which has data on hours and job search behaviour. We provide statistical evidence on the compatibility of the two samples for the purposes of estimating our model. We find that search has a direct negative effect on hours of work and we establish a strong positive effect of wages on hours.

Despite the significance of limited labor mobility across sectors, few attempts have been made to produce dynamic models of sectoral adjustment that are consistent with perfect foresight and, yet, flexible enough to allow for a variety of dynamic experiments. This paper proposes a simple perfect-foresight model of two-sector economies in which aggregate sectoral movement of labor takes place through the process of demographic change. The model is tractable enough that one can easily examine the effects of intertemporally complicated relative price shocks (both exogenous and endogenous) under a variety of assumptions on technology. Copyright 1992 by The Review of Economic Studies Limited.

Multiplicity of sequential equilibria is a common problem in bargaining models with incomplete information in which the informed player makes an offer. Most of these equilibria are supported by optimistic conjectures by the uninformed player. This paper reexamines the bargaining model in Rubinstein (1953). Monotonicity restrictions are placed on off-the-equilibrium-path beliefs to exclude equilibria supported by optimistic conjectures. Sequential equilibria that survive these restrictions are characterized. Copyright 1992 by The Review of Economic Studies Limited.

This paper presents a microeconometric model of capital utilization and retirement. Estimates of a firm's discrete decision problem with regard to an existing piece of capital--whether to operate, hold idle, or retire it--are obtained, in the context of the U.S. cement industry, by solving a discrete-choice stochastic dynamic programming model. The estimates are then used to simulate the effects of product and input price changes, and changes in the size and age of a cement kiln on a firm's propensity to operate, hold idle, and retire a kiln. Copyright 1992 by The Review of Economic Studies Limited.

Profit rates differ across industries. Explanations have often relied on static models of imperfect competition. This paper develops a dynamic model of perfect competition to demonstrate that long-run average profit rates differ even across competitive industries when the effects of sunk costs on entry and exit are considered. The hypothesis that firms maximize their present expected values has few empirical implications for long-run average profit rates, but it does have implications for the behaviour of variables over time; for example, industries with high variability in the number of firms should exhibit low variability in firm values.

This paper motivates a financial propagation mechanism in the context of an intertemporal production economy with asymmetric information, and with borrowers and lenders who enter multi-period financial relationships. A key feature is that aggregate output and borrowers' "financial capacity" —the maximum overhang of past debt they may feasibly carry—are determined jointly, much in the spirit of Gurley and Shaw (1955). Expectations of future economic conditions govern financial capacity which in turn may constrain current production, especially in bad times. A small but persistent shift in aggregate conditions may have a large impact on financial capacity, making the framework capable of motivating large endogenous fluctuations in financial constraints.

This paper describes several learning processes which converge, with probability one, to the rational expectations (Bayesian-Nash) equilibrium of a stationary linear game. The learning processes include a test for convergence to equilibrium, and a method for changing the parameters of the process when non-convergence is indicated. This self-stabilization property eliminates the need to impose stability conditions on the economic environment. Convergence to equilibrium is proved for two types of self-stabilizing learning mechanisms: a centralized forecasting mechanism and a decentralized strategy adjustment process.

The author considers a Bertrand-Edgeworth model of price competition. Firms have identical and constant marginal costs and finite exogenous capacities. Firms choose prices. The author's interest is in the set of those prices which are left over after the iterated elimination of dominated strategies. The author shows that in two circumstances this set will be close to the set containing only the market-clearing (Walrasian) price: (1) if any n - 1 out of n firms assumed to be in the market have sufficient capacity to cover demand at marginal costs; (2) if any given total capacity is owned by a very large number of very small firms. Copyright 1992 by The Review of Economic Studies Limited.

We consider a principal-agent contracting problem under incomplete information where some of the agent's actions are imperfectly observable. Contracts take the form of reward schedules based on the noisy observation of the agent's action. We first review situations where the principal can reach the same utility as in the absence of noise. Then we focus on the use of linear reward schedules, which allow universal implementation, i.e. implementation of a given mechanism for any unbiased noise of observation, and on quadratic reward schedules, which only require the knowledge of the variance of the noise. We exhibit sufficient conditions under which linear reward schedules implement a given mechanism. Finally, we characterize necessary conditions for a mechanism to be implementable under noisy observation by a linear schedule, and by quadratic schedules. We give the geometric intuition behind all results.