Knowledge that Transforms

A new form of the information matrix test is developed for a wide variety of statistical models. The test is constructed against an explicit alternative with random parameter variation. It is computed using a double-length artificial regression instead of the more conventional outer-product-of-the-gradient regression, which is known to have very poor finite-sample properties. In Monte Carlo experiments for the case of univariate linear regression models, the new form performs remarkably well. Some approximate finite-sample distributions are also calculated for this case and lend support to the use of the new form. Copyright 1992 by The Econometric Society.

Title from cover.

This paper considers a class of statistics that can be written as the ratio of the sample variance of a filtered time series to the sample variance of the original series. Any such statistic is shown to be optimal under normality for testing a null of white noise against some class of serially dependent alternatives. A simple characterization of the alternative class is provided. The results are used to show that a variance ratio test for mean reversion is an optimal test and to illustrate the forms of mean reversion it is best at detecting. Copyright 1992 by The Econometric Society.

This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vector autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t-statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is found to inflate variance and MSE of the kernel estimators. Since confidence interval coverage probabilities and over-rejection of t-statistics are usually of primary concern, prewhitened kernel estimators provide a significant improvement over the standard non-prewhitened kernel estimators.

In this paper, it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term. This identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term. The estimator is shown to be strongly consistent, and a two step procedure for its calculation is developed. The paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results.

In models of asymmetric information, possession of private information leads to rents for the possessors. This induces mechanism designers to distort away from efficiency. The authors show that this is an artifact of the presumption that information is independently distributed. Rent extraction in a large class of mechanism design games is analyzed, and a necessary and sufficient condition for arbitrarily small rents to private information is provided. Additionally, the two-person bargaining game is shown to have an efficient solution under first-order stochastic dominance and a hazard rate condition. Similar conditions allow full rent extraction in Milgrom-Weber auctions.

In this paper, a new estimator is proposed for discrete choice models with choice-based sampling. The estimator is efficient and can incorporate information on the marginal choice probabilities in a straightforward manner and for that case leads to a procedure that is computationally and intuitively more appealing than the estimators that have been proposed before. The idea is to start with a flexible parametrization of the distribution of the explanatory variables and then rewrite the estimator to remove dependence on these parametric assumptions. Copyright 1992 by The Econometric Society.

A stochastic differential formulation of recursive utility is given sufficient conditions for existence, uniqueness, time consistency, monotonicity, continuity, risk aversion, concavity, and other properties. In the setting of Brownian information, recursive and intertemporal expected utility functions are observationally distinguishable. However, one cannot distinguish between a number of non-expected-utility theories of one-shot choice under uncertainty after they are suitably integrated into an intertemporal framework. In a "smooth" Markov setting, the stochastic differential utility model produces a generalization of the Hamilton-Bellman-Jacobi characterization of optimality. A companion paper explores the implications for asset prices. Copyright 1992 by The Econometric Society.

Most of the available results on the existence of marginal cost pricing equilibrium are unsatisfactory in that they make a survival assumption that is stated as a condition on the production equilibria of the economy. The primary objective of this paper is to provide a relatively elementary existence result that replaces such an assumption with one on the primitive data of the economy. The author's main assumption is that no firm faces unbounded increasing returns in the sense that if it uses some input then the rate at which this input can be substituted into an output is finite. Copyright 1992 by The Econometric Society.