Knowledge that Transforms

IN AN INTERESTING RECENT PAPER, Sarin and Wakker (1992) (henceforth S-W) have provided a new axiomatization of expected utility maximization with (CEU). Its simplicity is attractive in that it provides a constructive interpretation of the role of capacities and Choquet integration in the main representation theorem. An important issue raised by the paper is the interpretation of the key Axiom P4 (Cumulative Dominance). S-W suggest an appreciation of the axiom as an adaptation of principles to nonadditive-probability contexts, most eloquently on page 1260. If viable, such an interpretation would supply the CEU model with a powerful intuitive foundation that has been lacking so far. This note argues that a interpretation can be maintained only at the price of either an arbitrary choice of specification which undermines its intuitive force or, alternatively, of an unintended restriction of the class of characterized preferences. Two logically independent arguments are presented. The first points out an arbitrariness in the of the more-likely-than relation in terms of preferences (Proposition 1). The second shows a similar arbitrariness in the of a stochastic dominance relation in terms of a more-likely-than relation (Proposition 2). In each case, the invoked symmetry conditions yield a characterization of CEU preferences with symmetric capacities, a nontrivial generalization of the SEU model that has received little attention in the literature. For notation and definitions, the reader is referred to S-W's paper. S-W's concern is to develop an intuitively convincing axiomatization of CEU-representable preference relations. Their key Axiom P4 is formulated in terms of a more-likelythan relation > on the algebra v of events that is defined in terms of the preference relation a on the set of acts Y To facilitate the subsequent discussion, their definition is introduced here formally as a condition on the pair of relations (a, >):

The paper analyzes a first price, sealed bid auction with a random reservation price where the object has an unknown common value, but one buyer has better information than the others. We permit the reservation price to be correlated with the information of the informed buyer, which reflects both his assessment of the value of the object and probability of rejection at any bid. Assuming all random variables are affiliated, we establish the following results. (1) The rate of increase in the distribution of the uninformed bidder is never greater than the rate of increase in the distribution of the informed bid. (2) The distributions are identical at bids above the support of the reservation price. (3) The informed buyer is more likely to submit low bids. We demonstrate that these restrictions are satisfied by bid data from the federal sales of offshore drainage leases.

We establish conditions which (in various settings) guarantee the existence of equilib-ria described by ergodic Markov processes with a Borel state space S. Let 9(S) denote the probability measures on S, and let s- G(s) c 4?(S) be a (possibly empty-valued) correspondence with closed graph characterizing intertemporal consistency, as prescribed by some particular model. A nonempty measurable set J c S is self-justified if G(s) n 9?(J) is not empty for all s E J. A time-homogeneous Markov equilibrium (THME) for G is a self-justified set J and a measurable selection TI: J-9 _(J) from the restriction of G to J. The paper gives sufficient conditions for existence of compact self-justified sets, and applies the theorem: If G is convex-valued and has a compact self-justified set, then G has an THME with an ergodic measure. The applications are (i) stochastic overlapping generations equilibria, (ii) an extension of the Lucas (1978) asset market equilibrium mnodel to the case of heterogeneous agents, and (iii) equilibria for discounted stochastic games with uncountable state spaces.

The new economics of regulation is an application of the principal-agent methodology to the contractual relationship between regulators and regulated firms. After a critique of the traditional paradigms of regulation from the point of view of information economics a canonical model of regulation under asymmetric information is developed. A survey of the main results obtained in the new economics of regulation is then provided, in particular concerning the implementation of optimal contracts by a menu of linear contracts, the dichotomy between pricing and cost reimbursement rules, the auctioning of incentive contracts, the dynamics of contracting under limited commitment, and the hierarchical problems in regulation. Empirical implications are then discussed and avenues of further research are described in the conclusion.

Jean Mercenier, Philippe Michel, Discrete-Time Finite Horizon Approximation of Infinite Horizon Optimization Problems with Steady-State Invariance, Econometrica, Vol. 62, No. 3 (May, 1994), pp. 635-656

The paper considers the OLS, the IV, and two method-of-moments estimators, MM and MMK, of the coefficients of a single equation, where the explanatory variables are correlated with the disturbance term. The MM and MMK estimators are generalizations of the LIML and LIMLK estimators, respectively. Multivariate first-order approximations to the distributions are derived under normality, using a parameter sequence where the number of instruments increases as the number of observations increases. Numerical results show these approximations are more accurate, compared to large-sample approximations, even if the number of instruments is small. The moments of the multivariate limit distributions of the MM and MMK estimators can be consistently estimated under a variety of parameter sequences, including the large-sample sequence. The new approximate confidence regions perform well in terms of exact levels, compared to traditional ones. The IV estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator, which is dominated, in practical cases, by the MM and MMK estimators in terms of nearness to the true value in the sense of Pitman.

Knowledge of the asymptotic variance of an estimator is important for large sample inference, efficiency, and as a guide to the specification of regularity conditions.The purpose of this paper is the presentation of a general formula for the asymptotic variance of a semiparametric estimator.A particularly important feature of this formula is a way of accounting for the presence of nonparametric estimates of nuisance functions.The general form of an adjustment factor for nonparametric estimates is derived and analyzed.The usefulness of the formula is illustrated by deriving propositions on asymptotic equivalence for different nonparametric estimators of the same function, conditions for estimation of the nuisance functions to have no effect on the asymptotic variance, and the form of a correction term for the presence of linear function of a conditional expectation estimator, or other projection estimator (e.g.partially linear and/or additive nonparametric projections), and for a function of a density.Specific results cover a semiparametric random effects model for binary panel data, nonparametric consumer surplus, nonparametric prediction, and average derivatives.Regularity conditions are given for many of the propositions.These include primitive conditions for v'n-consistency, asymptotic normality, and consistency of an asymptotic variance estimator with series estimators of conditional expectations (or projections), in each of the examples.

The authors provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Their results extend the framework of L. Ljung previously utilized by A. Marcet-T. J. Sargent and M. Woodford by permitting nonlinear laws of motion driven by stochastic processes that may exhibit moderate dependence, such as mixing and mixingale processes. The authors draw on previous work by H. J. Kushner and D. S. Clark to provide readily verifiable and/or interpretable conditions ensuring algorithm convergence, chosen for their suitability in the context of adaptive learning. Copyright 1994 by The Econometric Society.

This paper provides a general framework for proving the "square root of" T-consistency and asymptotic normality of a wide variety of semiparametric estimators. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The method of proof exploits results concerning the stochastic equicontinuity of stochastic processes. The results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models. Primitive conditions are given for "square root of" T-consistency and asymptotic normality of this estimator. Copyright 1994 by The Econometric Society.