Post Data Model Evaluation

Abstract

JHE PURPOSE of this article is to bring to the attention of the readers of this journal a number of related and important estimators that are currently being discussed in the statistical literature which have implications for applied work since rules are employed which seek to improve the performance of conventional estimators. In spite of the rapid advances, over the last three decades, of economic theory, econometric procedures, and data relating to economic processes and institutions, the search for quantitative economic knowledge still remains to some extent an essay in persuasion. In the process of nonexperimental model building there are typically many admissible economic and statistical models which do not contradict our perceived knowledge of human behavior. Thus, in model specification there is usually uncertainty, for example, relative to the algebraic form, classification, number and timing of variables to be included in the behavioral and technical relations, and the corresponding stochastic assumptions. When econometric models are correctly specified, statistical theory provides procedures for obtaining point and interval estimates and evaluating the performance of various linear and usually unbiased (at least asymptotically) estimators. But, the applied worker must inevitably work with false models, where the true specification of the sampling model is unknown. Furthermore, the statistical model employed is usually determined by some preliminary testing of hypotheses using the data at hand. This search procedure, involving two-stage or repeated significance test procedures applied to the same set of data and yielding an estimate after the preliminary test(s) if significance, is often used in applied work in economics with little or no information on the sampling properties of the resulting estimator and with little or no consideration to the possible distortion of subsequent inferences. Within this context, we, seek to generalize and extend the results of Wallace and Ashar (1972) relative to preliminary test or two-stage estimating procedures and call attention to another important class of estimators and estimator comparisons. In particular, we review the possible statistical consequences of using preliminary test or sequential estimators in the search process and suggest old and new estimators, that are superior, under a squared error loss measure for gauging estimator performance, to the conventional estimators usually employed. We also note that conventional estimating procedures currently used in applied work may not be appropriate for the problem at hand and, perhaps more importantly for the researcher, we show that better alternative estimators exist. Perhaps it is appropriate at this point to note that, when making a choice between estimators, the traditional solution is to restrict consideration to the class of linear unbiased estimators and hope that among the estimators in the restricted class, one has uniformly smallest risk. Fortunately for many problems a best linear unbiased estimate exists. In this paper, in discussing the estimators that are alternatives to the conventional least squares estimator, we will leave the class of linear unbiased estimators. The notion of unbiasedness which has been accepted by or perhaps forced on applied workers, although intuitively plausible, is an arbitrary restriction or property and has no direct connection with the loss due to incorrect decisions. The economist who is interested in parameter estimates or predictions appropriate for choice purposes, may not care if he is right on the average, and thus the unbiasedness property may be unsatisfactory from a decision point of view. In any event our purpose, which is to some extent expository in nature, is to focus on point estimation under a squared error loss measure of goodness and bring the statistical consequences of making use of conventional and Received for publication October 2, 1972. Revision accepted for publication April 3, 1973. *Arnold Zellner read an early draft of this paper and made many helpful comments.