IN A STIMULATING RECENT PAPER, Abreu and Matsushima (1992) (hereafter A-M) show how a class of social choice functions can be virtually implemented in iteratively undominated strategies. This work has several important features: the mechanisms used are finite and not too difficult to understand, and so less objectionable in this regard than many in the literature; the class of social choice functions implemented is large; and the solution concept-Nash equilibrium determined uniquely by iterative elimination of strongly dominated strategies-is relatively uncontroversial. The point of this note is to argue that the mechanisms used by A-M unfortunately tend to generate games in which the iterative removal of strongly dominated strategies sometimes is indeed (or ought to be) controversial.2 We proceed by first examining an example of a related but simpler implementation problem in which the argument is easily exposed, then indicating how the argument applies generally in the A-M setup. Consider the following much-discussed two-player coordination game:
One elicitation diagnostic identifies a family of prior distributions that are so diffuse that they are practically equivalent to the completely diffuse prior. Another elicitation diagnostic identifies a family of prior distributions that concentrate enough mass in the neighborhood of zero that they are practically equivalent to the dogmatic prior that sets a parameter exactly equal to zero. If either question thus posed can be answered in the affirmative then there is no need to go to the expense of a more accurate elicitation of the prior distribution. Copyright 1992 by The Econometric Society.
The feasibility of Bertrand undercutting with nonuniform prices is established and properties are derived for Bertrand equilibrium in nonuniform price strategies. With free entry, equilibrium entails zero-profit minimum average cost production. If there is more than one producing firm, all prices collapse to a minimum average cost uniform price. An existence condition is compared to conditions from uniform price theory. Without free entry equilibrium, prices may not collapse to a uniform price. Positive profit may occur but all firms earn equal profit and incur equal marginal cost, while consumers pay average outlay no greater than marginal cost. Copyright 1992 by The Econometric Society.
This paper supposes an individual cares about his/her own wealth not only directly but also via the relative standing that this wealth induces. The implications for risk-taking are investigated in particular. Such a model provides a natural explanation of the "concave-convex-concave" utility described by M. Friedman and L. Savage (1948). However, there are a number of key differences between the present model and any model based on own wealth alone. For example, an equilibrium wealth distribution here may have a middle class. Further, the status interaction involves an externality and an equilibrium wealth distribution may be Pareto inefficient. Copyright 1992 by The Econometric Society.
The purpose of this note is to point out that the bimodality is a consequence of the special case considered by N-S. The exact finite sample distribution of the IV estimator has been derived in the economic literature earlier, but its tabulation or plotting involves some assumptions about the nuisance parameters. In this note we plot the densities of the exact finite sample distribution of the IV estimator for several parameter values and show that the bimodality feature noted by N-S is a consequence of a singular covariance matrix and not of a poor instrument.
This paper is concerned with a problem of implementation of a given social choice correspondence. The authors introduces an essential monotonicity condition and show that any implementable social choice correspondence satisfies this condition. Conversely, in a case of three or more participants, any essentially monotone social choice correspondence is implementable. In a case of two participants, the essential monotonicity condition must be completed by a requirement that the social choice correspondence is close to an individually rational correspondence. Copyright 1992 by The Econometric Society.
This paper analyzes a class of alternating-offer bargaining games with one-sided incomplete information for the case of gap. If sequential equilibria are required to satisfy the additional restrictions of stationarity, monotonicity, pure strategies, and no free screening, we establish the Silence Theorem: When the time interval between successive periods is made sufficiently short, the informed party never makes any serious offers in the play of alternating-offer bargaining games. A class of parametric examples suggests that the time interval required to assure silence is not especially brief. As a byproduct of the analysis, we also prove (under the same set of assumptions) a uniform version of the Coase Conjecture: When the time interval between successive periods is made sufficiently short, the initial serious offer by either party in an alternating-offer bargaining game must be less than E times the highest possible buyer valuation, for an entire family of distribution functions.
A new procedure for statistical inference in cointegrating regressions is developed. The author introduces canonical cointegrating regressions (regressions formulated with the transformed data). The required transformations involve simple adjustments of the integrated processes using stationary components in cointegrating models. Canonical cointegrating regressions, therefore, represent the same cointegrating relationships as the original models. They are, however, constructed in such a way that the usual least squares procedure yields asymptotically efficient estimators and chi-square tests. The methodology presented here is applicable to a very wide class of cointegrating models, including models with deterministic and singular, as well as stochastic and regular, cointegrations. Copyright 1992 by The Econometric Society.
Non-nested tests are proposed for competing models estimated by generalized method of moments. Results are presented for non-nested linear regression models with het- eroskedasticity and serial correlation of unknown form and differing instrument validity assumptions. Regression forms of the statistics are also presented. THIS PAPER IS CONCERNED with providing a procedure whereby non-nested models estimated by generalized method of moments (GMM) (Hansen (1982)) may be com- pared. In particular, Cox-type (Cox (1961, 1962)) and encompassing tests (Mizon and Richard (1986)) are proposed. Implicit in such tests is a degree of arbitrariness in the way the statistics are constructed as, typically, the assumptions underlying GMM estima- tion techniques are minimal and do not fully specify the data generation process (DGP) underlying the observable random variables, in contradistinction to the method of maximum likelihood. Our procedures allow the population moment conditions on which GMM estimation of the competing models is based to differ in the conditioning sets under which conditional expectation is taken; such differences may reflect different a priori assumptions concerning the exogeneity status of random variables in the models. These tests may be regarded as generalizations of Singleton (1985). More recent work includes Ghysels and Hall (1990) which requires the specification of the DGP under the null hypothesis and Wooldridge (1990b) which proposes heteroskedasticity-robust tests for non-nested non-linear regression models. Our results are specialized to provide non-nested tests for competing regression models estimated by instrumental variables, where we allow a degree of heteroskedastic- ity and serial correlation in the process generating the disturbance terms, by assuming appropriate mixing conditions (White (1984)), and the instrument validity assumptions to differ across the models; cf. Godfrey (1983, 1984) which assume a scalar covariance matrix for the disturbances and that the set of instruments is valid in both models. Thus, our framework includes models which may be both simultaneous and dynamic. Section 2 describes procedures for obtaining Cox-type and encompassing tests for competing models estimated by GMM. Section 3 specializes these results to competing linear regression models estimated by instrumental variables; regression forms for the statistics are presented. The paper is concluded by Section 4. In our presentation, we eschew detailed regularity assumptions.
The authors provide conditions on an exchange economy with asymmetric information that guarantee that when the economy is replicated sufficiently often, there will be an allocation that is incentive compatible, individually rational, and nearly efficient. The main theorem covers both the case in which aggregate uncertainty remains when the economy is replicated and the case in which replication eliminates aggregate uncertainty. In addition, the authors demonstrate how their theorem does or does not apply to standard asymmetric information problems such as the buyer's bid double auction problem, Akerlof's lemons problem, and insurance with asymmetric information. Copyright 1992 by The Econometric Society.