Knowledge that Transforms

THIS PAPER PROVIDES the large sample properties of two inequality indices, Atkinson's (1970) index and the generalized entropy index (Cowell and Kuga (1981), Shorrocks (1984)). The large sample properties of the equally-distributed-equivalent (e.d.e.) income measures associated with these indices are also derived. The asymptotic distributions of these inequality and welfare measures allow the construction of confidence intervals and tests for differences in the measures; these confidence intervals and tests are asymptotically distribution-free. Given the increasing availability of large micro-data sets on incomes, these results are directly applicable to empirical work on income distributions. The sampling distributions of some inequality indices, such as the Gini coefficient and Pietra index, are known.' But the ethical bases of these indices have been subject to criticism, and some researchers may prefer the Atkinson or generalized entropy indices on ethical grounds. These researchers are confronted with a choice between using an ethically unattractive index with a known sampling distribution, or using an ethically preferable index whose sampling properties are unknown. The increasing use of the Atkinson and generalized entropy indices in empirical analyses of income distributions suggests many are choosing the second option. It then becomes important to understand the sampling properties of these indices, so that statistical inference procedures may be applied. The analysis in this paper complements the recent research on sampling properties and inference for Lorenz curves. For example, Beach and Davidson (1983), and Gastwirth and Gail (1985) propose tests for equality of Lorenz curves, and Beach and Richmond (1985) provide joint confidence intervals for the Lorenz ordinate vector. Bishop, Chakraborti, and Thistle (1987, 1988a, 1988b) and Bishop, Formby, and Thistle (1989) provide a number of extensions. These papers utilize results from the theory of linear functions of order statistics.2 However, this approach is not directly applicable to the Atkinson and generalized entropy indices; these indices are not linear functions of order statistics. The Atkinson and generalized entropy indices are functions of fractional and negative moments of the distribution, and their large sample properties follow from the properties of the sample moments.

The authors analyze the principal-agent relationship when the principal has private information as a three-stage game: contract proposal, acceptance/refusal, and contract execution. They assume that the information does not directly affect the agent's payoff (private values). Equilibrium exists and is generically locally unique. Moreover, it is Pareto optimal for the different types of principal. The principal generically does strictly better than when the agent knows her information. Equilibrium allocations are the Walrasian equilibria of an "economy" where the traders are different types of principal and "exchange" the slack on the agent's individual rationality and incentive compatibility constraints. Copyright 1990 by The Econometric Society.

This paper presents a simple estimator of the shape parameter in a Weibull duration model with unobserved heterogeneity. The estimator is consistent and asymptotically normal under mild conditions, and a consistent estimator of the asymptotic variance is available. A Monte Carlo study indicates that the asymptotic distribution of the estimator provides a good approximation to the finite sample distribution. The estimation strategy can be extended to a model with regressors and to a log-logistic model with unobserved heterogeneity. The advantages of the estimator are that it is easy to calculate and that its asymptotic distribution can be derived. Copyright 1990 by The Econometric Society.

This paper tests the effects of the level and length of unemployment insurance (UI> benefits on unemployment durations.The paper particularly studies individual behavior during the weeks just prior to when benefits lapse.Higher UI benefits are found to have a strong negative effect on the probability of leaving unemployment.However, the probability of leaving unemployment rises dramatically just prior to when benefits lapse When the length of benefits is extended, the probability of a spell ending is also very high in the week benefits were previously expected to lapse.Individual data are used with accurate information on spell durations, and the level and length of benefits.Semipararnetric estimation techniques are used and compared to alternative approaches.The semiparametric approach yields more plausible estimates and provides useful diagnostics.

This paper considers a general equilibrium model of an economy where some firms may exhibit increasing returns to scale or more general types of nonconvexities. The firms are instructed to follow the standard marginal cost pricing rule or to fulfill the first-order necessary conditions for profit maximization. A general existence theorem of equilibria is proved in the case of an arbitrary number of firms. No assumption is made to imply the aggregate productive efficiency of equilibria, a condition that must be excluded in the nonconvex case. Copyright 1990 by The Econometric Society.

This paper proposes a new approach to the study of economic problems that have hitherto been modeled as games with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies in the underlying problem. The authors' point of departure from the conventional approach is to view the sharing rules that resolve these indeterminacies as part of the solution rather than as part of the description of the model. A solution to the authors' model is a sharing rule, together with a profile of (mixed) strategies that satisfies the usual (Nash) best response criterion. Their main result is that such a solution always exists. Copyright 1990 by The Econometric Society.

MCKELVEY AND PAGE (1986) proved a remarkable theorem on common knowledge. Suppose n individuals start with a common prior and then form conditional probabilities of some event of interest based on their different information. If a stochastically monotone aggregate of the n conditional probabilities is common knowledge, then the assessments must be identical. We show that the aggregation of individual assessments allowed for in the theorem admits an elementary characterization: a function is stochastically monotone if and only if it is additively separable into strictly increasing components

This paper is an empirical investigation of equilibrium restrictions on household consumption and male labor supply. It exploits a simple factor structure, rationalized by two assumptions, that household allocations are Pareto optimal and that the labor market is competitive. The paper estimates household preferences, and tests how well this parsimonious factor structure represents panel data on married couples and time series data on asset returns. Most of the estimates are roughly comparable to those found in previous work; no evidence against the simple factor representation is found and the intertemporal capital asset pricing model is not rejected. Copyright 1990 by The Econometric Society.

The authors study a rich class of noncooperative games that includes models of oligopoly competition, macroeconomic coordination failures, arms races, bank runs, technology adoption and diffusion, R&D competition, pretrial bargaining, coordination in teams, and many others. For all these games, the sets of pure strategy Nash equilibria, correlated equilibria, and rationalizable strategies have identical bounds. Also, for a class of models of dynamic adaptive choice behavior that encompasses both best-response dynamics and Bayesian learning, the players' choices lie eventually within the same bounds. These bounds are shown to vary monotonically with certain exogenous parameters. Copyright 1990 by The Econometric Society.