The authors examine core convergence for economies with a large finite number of agents and an infinite number of commodities. They find a serious disconnection between economies with a large finite number of agents and economies with a continuum of agents: the authors provide examples of nonconvergence of the core for large finite economies in L[superscript 1], a commodity space for which core equivalence holds for continuum economies. In addition, they show that, if preferences exhibit uniformly vanishing marginal utility of consumption at infinity, core convergence is restored.
THE REQUIREMENT OF NO-ENVY is at the heart of recent equity theory. An allocation is free from envy if no agent strictly prefers the bundle of goods which is assigned to another agent to the one she/he gets. An allocation rule satisfies No-Envy if it only selects envy-free allocations. In this paper, we examine the relationship between No-Envy and implementability in a general model. Our main result is that in monotonically closed domains the No-Envy property is satisfied by any allocation rule which is both horizontally equitable and Nash Implementable. The requirement of horizontal equity, called Equal Treatment of Equals, simply states that two agents having the same preferences should be treated equally, i.e., should be assigned the same welfare level. The monotonic closedness condition on the domain of admissible preferences is satisfied in many private and/or public good environments, as discussed below. Quasi-linear domains, however, are examples of nonmonotonically closed domains. Our result confirms the widespread intuition that the No-Envy requirement is justified not only from an equity point of view but also from an implementation standpoint (see Hammond (1979) and Champsaur and Laroque (1981)). Moreover, it throws some light on several previous results where specific allocation rules defined over monotonically closed domains are characterized by Nash Implementability among other axioms. As a consequence of our analysis, No-Envy can be weakened into Equal Treatment of Equals in these characterizations (see, e.g., Thomson (1990) and Nagahisa and Suh (1995)). Similar arguments apply to decentralization problems where informational efficiency is the primary concern. For instance, Calsamiglia and Kirman (1993) characterized the Equal Income Walrasian rule on the basis of informational efficiency, Pareto Optimality, and No-Envy. Again, No-Envy can be replaced by Equal Treatment of Equals in this result.2 On the other hand, our result also explains why Nash Implementable allocation rules violating No-Envy over monotonically closed domains all fail to satisfy Equal Treatment of Equals. Examples include the Lindahl solution, the ratio equilibrium solution (Kaneko (1977)) and the balanced linear cost share solution (Mas-Colell and Silvestre (1989)); see Corchon (1989) and Wilkie (1990). At the end of the paper, we show that if we restrict ourselves to allocation functions (that is, allocation rules selecting one and only one allocation per economy), then a similar result holds for Strategy-Proofness, provided the Satterthwaite-Sonnenschein (1981) property of Non-Bossiness is also imposed. That is, in monotonically closed
We consider an auction in which k identical objects of unknown value are auctioned off to n bidders. The k highest bidders get an object and pay the k + 1st bid. Bidders receive a signal that provides information about the value of the object. We characterize the unique symmetric equilibrium of this auction. We then consider a sequence of auctions A r with n r bidders and k r objects. We show that price converges in probability to the true value of the object if and only if both k r → ∞ and n r - k r → ∞, i.e., both the number of objects and the number of bidders who do not receive an object go to infinity.
THIS ARTICLE EXPLAINS current editorial procedures and policies of Econometrica; it is primarily addressed to authors who plan to submit manuscripts to the journal. Section 2 deals briefly with clarity in writing and exposition. Section 3 explains our organization and how submissions are handled. Details concerning the preparation of manuscripts are covered in Section 4; Section 5 discusses the submission of Announcements and News Notes. purpose of the Econometric Society is defined in Section 1 of our Constitution: The Econometric Society is an international society for the advancement of economic theory in its relation to statistics and mathematics.... Its main object is to promote studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. Econometrica has no tightly controlled policy towards subject matter. No paper is rejected because it is or too quantitative, but because our membership includes economists with a variety of research interests, it is necessary that full-length contributions be prepared so that the nonspecialist is informed of what they are about and why the results are important. At the same time, no paper is rejected because it is not mathematical enough or applied, nor need papers make a methodological contribution. What is important is that the papers we publish should be interesting, original, and well crafted, and that they use whatever mathematical and/or statistical tools are appropriate for the problem at hand
The author considers the problem of estimation in a panel data sample selection model, where both the selection and the regression equation of interest contain unobservable individual-specific effects. He proposes a two-step estimation procedure, which 'differences out' the sample selection effect and the unobservable individual effect from the equation of interest. In the first step, the unknown coefficients of the 'selection' equation are consistently estimated. The estimates are then used to estimate the regression equation of interest. The estimator proposed in this paper is shown to be consistent and asymptotically normal. The proposed estimator is shown to be consistent and asymptotically normal. Its finite sample properties are investigated in a small Monte Carlo simulation
This paper provides an empirical analysis of how the U.S. Social Security and Medicare insurance system affect the labor supply of older males in the presence of incomplete markets for loans, annuities, and insurance. We estimate a detailed dynamic programming (DP) model of the joint labor supply and Social Security acceptance decision, focusing on a sample of males in the low to middle income brackets whose only pension is Social Security. The DP model delivers a rich set of predictions about the dynamics of retirement behavior, and comparisons of actual vs. predicted behavior show that the DP model is able to account for wide variety of phenomena observed in the data, including the pronounced peaks in the distribution of retirement ages at 62 and 65 (the ages of early and normal eligibility for Social Security benefits, respectively). We identify a significant fraction of health insurance constrained individuals who have no form of retiree insurance other than Medicare, and who can only obtain fairly priced private insurance via their employer's group plan. The combination of significant individual risk aversion and a long tailed (Pareto) distribution of care expenditures implies that there is a significant security value for these individuals to remain employed until they are eligible for Medicare coverage at age 65. Overall, our model suggests that a number of heretofore puzzling aspects of retirement behavior can be viewed as artifacts of particular details of the Social Security rules, whose incentive effects are especially strong for lower income individuals and those who do not have access to fairly priced loans, annuities, and insurance
To obtain consistency and asymptotic normality, a generalized method of moments (GMM) estimator typically is defined to be an approximate global minimizer of a GMM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. In consequence, practitioners usually ignore the problem and take the GMM estimator to be the result of a local optimization algorithm. This yields an estimator that is not necessarily consistent and asymptotically normal. The use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function, which makes it difficult to know when to stop the algorithm. To alleviate these problems of global and local optimization, we propose a stopping-rule (SR) procedure for computing GMM estimators. The SR procedure eliminates the need for global search with high probability. And, it provides an explicit SR for problems of stability that may arise with local optimization problems.
This paper considers the problem of determining the number of factors in a multivariate nonparametric relationship. The definition of factors given is broad enough to encompass a number of potential applications in econometrics, including inferring the rank of demand, consistent tests for lack of identification in linear instrumental variable models, and testing arbitrage pricing theory. The paper gives both series and kernel methods for testing hypotheses concerning, and consistent estimation of, the number of factors. The methods are compared in a small simulation study and in an application to determining the rank of demand systems