This paper presents an overview of the Cowles Commission effort in the area of econometric theory and a critical review of the Brookings Project, but flaws are noted in both efforts. The Brookings part reflects a view of the project as seen by one of the younger members of the coordinating team; it is a view shared to some extent by other members. The paper deals with the research work stimulated by both projects and contains a brief but frank discussion of the emergence of a commercial econometric services industry. Finally, promising areas for future research are noted.

When estimating the seemingly unrelated regression (SUR) model in small samples, the bootstrap feasible generalized least-squares (FGLS) covariance estimator has been widely advocated as less biased than the conventional FGLS covariance estimator obtained by evaluating the asymptotic covariance matrix. Assuming multivariate normal errors and an unbiased estimator of the error covariance, Eaton proves that the conventional estimator is biased downward for a general SUR model. Ignoring terms O(T–2) for this model, we prove that the bootstrap estimator is also biased downward. However, from these results, the relative magnitude of these two biases is indeterminant in general. By ignoring terms O(T–2) for Zellner's two-equation, orthogonal regressor model with bivariate normal errors, we show that the bias of both estimators is downward and that the bootstrap estimator exhibits a smaller bias than the conventional estimator. Monte Carlo simulation results indicate that, in general, neither estimator uniformly dominates the other.

A simple formula for computing the best linear unbiased estimate of the mean of an autoregressive process as well as its variance is given. Numerical results show that the estimate can have much lower variance than that of the usual sample mean.

This article considers methods of simulated moments for estimation of discrete response models. It is possible to use the same set of random numbers to simulate the choice probabilities for each individual in the sample. In addition to the method of simulated moments of McFadden, we have considered also maximum simulated likelihood estimation methods. An asymptotic theory for such procedures is provided. The estimators are shown to be consistent and asymptotically normal by the theory of generalized U-statistics. Asymptotic efficiency is discussed. Monte Carlo experiments on the finite sample performance of the estimators are reported.

A well-known result in the method of moments literature is that the efficient instruments for the estimation of a model are functions of the conditional expectation of its gradient. Some recent studies have suggested the nonparametric estimation of these instruments when they are of unknown functional form. When these instruments in turn depend on the unknown parameters it has been suggested that these be replaced by preliminary consistent estimates. It is shown here that solving the sample moment equations simultaneously over the instruments and the residuals of the model will generally produce the same asymptotic efficiency and avoid the disadvantages inherent with the use of preliminary estimates.

Positive definiteness of income effect matrices provides a sufficient condition for the law of demand to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the bootstrap method to simulate the distribution of the smallest eigenvalue of random matrices and to test their positive definiteness. Here, theoretical aspects of this bootstrap test of positive definiteness are considered. The asymptotic distribution of the smallest eigenvalue , of the matrix estimate is obtained. This theory applies generally to symmetric, asymptotically normal random matrices. A bootstrap approximation to the distribution of is shown to converge in probability to the asymptotic distribution of . The bootstrap test is illustrated using British family expenditure survey data.

It is shown that the Cox modified likelihood-ratio statistic for testing partially non-nested hypotheses H0 and H1 is asymptotically equivalent to a bilinear form in nondegenerate asymptotically normal random vectors for sequences of data-generating processes converging to the intersection of H0 and H1 but not necessarily belonging to either H0 or H1. One of the asymptotically normal vectors is the complete parametric encompassing vector of Mizon and Richard, while the other is a close relative. The results are valid regardless of whether or not the data-generating process is exponential and imply that the Cox statistic is not generally asymptotically locally normal. This corrects an assumption made in recent literature.

The use of probit and logit models has become quite common whenever the dependent variable in a regression is qualitative. These models have been used to explain either/or choices and decisions involving multiple alternatives. A two-dimensional graphical interpretation of these different models has been provided by Johnson [3]. The purpose of this paper is to provide a three-dimensional graphical exposition of the ordered probit model, which was first estimated by McKelvey and Zavoina [4] and is now built into computer packages, such as LIMDEP [1].

Bruce E. Hamsem? Strong Laws for Dependent Heterogeneous Processes Econometric Theory 7(1992): 213–221.