Knowledge that Transforms

We study subgame perfect equilibria of finitely repeated games. We prove a limit "folk theorem" for these games. Under weak conditions, any feasible and individually rational payoff vector of the one-shot game can be approximated by the average payoff in a perfect equilibrium of a repeated game with a sufficiently long horizon.

This article surveys the development of nonparametric models and methods for estimation of choice models with nonlinear budget sets.The discussion focuses on the budget set regression, that is, the conditional expectation of a choice variable given the budget set.Utility maximization in a nonparametric model with general heterogeneity reduces the curse of dimensionality in this regression.Empirical results using this regression are different from maximum likelihood and give informative inference.The article also considers the information provided by kink probabilities for nonparametric utility with general heterogeneity.Instrumental variable estimation and the evidence it provides of heterogeneity in preferences are also discussed.

[A tractable dynamic general equilibrium model of continuous product innovation is developed. Patents, or any imitation lag, of infinite duration may achieve too much, too little, or the socially optimum level of innovation. Most surprising, finite-life patents may induce undamped oscillations in innovation.]

[The rational expectations hypothesis in a life cycle context asserts that agents seek to keep the marginal utility of discounted expenditure constant across time. In this paper we present estimates of a demand system that takes explicit account of this hypothesis. We show how the restrictions from demand theory enable us to identify the model despite the presence of an unobservable variable that can be interpreted as revisions to the marginal utility of discounted expenditure. This allows us to take explicit account of the different effects of anticipated and unanticipated price changes. An important check on our model is the derivation of expenditure elasticities despite the fact that the demand system does not have expenditure on the right hand side. Our estimates are "sensible" and we find that we can reject the hypothesis that revisions to the marginal utility of discounted money are orthogonal to the past values of our variables. We interpret this to be a rejection of the rational expectations hypothesis.]

[This paper finds in closed form a noisy rational expectations equilibrium for a class of economies with many risky assets and analyzes the properties of such equilibria. Because of the various interactions between the assets, phenomena appear that do not arise in models with a single risky asset. For example, an asset's equilibrium price might be decreasing in its own payoff and/or increasing in its own supply; an asset might be a Giffen good; a higher price for an asset (holding other prices fixed) might be "bad news" for the asset's payoff; and even for assets in fixed supply, uncertainty about other assets' supplies may prevent their prices from being fully revealing.]

This paper adopts a new approach to the problem of generalizing the properties of the two-by-two Heckscher-Ohlin model, asking whether we can obtain results which hold in very general models for dichotomous categories of commodities and factors. Using duality theory, some results of this kind are derived, which generalize certain properties of the Heckscher-Ohlin model to models which allow for any number of goods and factors, joint production, international factor mobility, and substitution between primary factors and intermediate inputs. The consequences of assuming sector-specific factors and equal numbers of goods and factors' are also examined.

[The paper presents a general theoretical framework for the analysis of integrated life-cycle models of consumption and family labor supply under uncertainty. Profit functions are used to represent intertemporally additive preferences and to yield convenient characterizations of "constant marginal utility of wealth" or "Frisch" demand functions. Conditions on preferences derived that allow additive fixed-effect specifications for the Frisch demands. Data from the British Family Expenditure Surveys from 1970-77 are used to derive panel-like information on male labor supply and consumption for several age cohorts over time. These data reproduce standard life-cycle patterns of hours and wages, but more detailed analysis shows that the theory is incapable of offering a satisfactory common explanation of the behavior of hours and wages over both the business cycle and the life cycle. Similarly, although the theory can explain the life-cycle behavior of hours and consumption separately, the same model cannot explain both, essentially because of a failure in symmetry.]

October 1983