Knowledge that Transforms

A maximum likelihood estimator for models containing nuisance parameters is proposed. The estimator is shown to be asymptotically normal and attain the semiparametric efficiency bounds for a number of important econometric models. The idea is to find a parametric model that passes through the true model. The score for the parametric model is then estimated nonparametrically and the estimator is obtained by setting the estimated score to zero.

Allowing for incomplete information, this paper characterizes the social choice functions that can be approximated by the equilibrium outcomes of a mechanism: incentive compatibility is necessary and almost sufficient for virtual Bayesian implementability. In conjunction with a second condition, Bayesian incentive consistency, incentive compatibility is also sufficient. This new condition is weak--under standard topological and informational assumptions it is satisfied by every social choice function. The type sets of the agents are taken to be arbitrary (possibly infinite) measurable spaces. An example shows that there are virtually (in fact, exactly) Bayesian implementable social choice functions that are not virtually implementable in iteratively undominated strategies.

This paper introduces a conditional Kolmogorov test of model specification for parametric models with covariates (regressors). The test is an extension of the Kolmogorov test of goodness-of-fit for distribution functions. The test is shown to have power against 1/√n local alternatives and all fixed alternatives to the null hypothesis. A parametric bootstrap procedure is used to obtain critical values for the test.

This paper provides a fairly systematic study of general economic conditions under which rational asset pricing bubbles may arise in an intertemporal competitive equilibrium framework.Our main results are concerned with non-existence of asset pricing bubbles in those economies.These results imply that the conditions under which bubbles are possible inc1uding sorne well-known examples of monetary equilibria-are relatively fragile.

This paper establishes a set of conditions for the uniqueness and stability of the equilibrium price in exchange and production economies. Building on the earlier work of J. M. Grandmont and W. Hildenbrand, it shows that increasing heterogeneity in preferences (in some well-defined sense) causes aggregate Engel curves to become increasingly linear. So sufficient dispersion, together with the assumption that preferences and endowments are independently distributed, leads to the aggregate excess demand function satisfying the law of demand. Uniqueness and stability of the equilibrium price follows.

We establish the asymptotic sampling distribution of general functions of quantile-based estimators computed from samples that are not necessarily independent. The results provide the statistical framework within which to assess the progressivity of taxes and benefits, their horizontal inequity, and the change in the inequality of income which they cause. By the same token, these findings characterise the sampling distribution of a number of popular indices of progressivity, horizontal inequity, and redistribution. They can also be used to assess welfare and inequality changes using panel data, and to assess poverty when it depends on estimated population quantiles. We illustrate these results using micro data on the incidence of taxes and benefits in Canada.

This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the curse of dimensionality for a subclass of MDPs known as discrete decision processes (DDPs).

Game theory, Duopoly supergame, Asymmetric Cournot duopoly

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.