On Asymptotic Theory and Finite Sample Experiments

Abstract

theme of the volume is doggedly operational. In effect, one is encouraged to formulate each Econometric problem precisely as dictated by the requisite Economic Theory, and solve the resultant estimation problem directly, by numerically maximizing the relevant likelihood function, thus eschewing approximations of unknown magnitude and importance. finite sample behaviour of the adopted estimator can then be simulated to provide evidence on the reliability of the empirical results. In this rather novel methodology, the large body of established theory on the asymptotic of estimators is assigned a limited role and merits discussion in but one chapter. The small sample problem stems from the fact that asymptotic results provide no clear guide to finite sample distributions (p. 219), although . . one would like to know how large is 'large' (p. 76). Agreed, and specifically investigating this should surely be an important objective of experimental work on small-sample properties. However, comparisons with asymptotic results materialize only for situations in which the Maximum Likelihood Estimator is believed consistent and asymptotically efficient, even though Goldfeld and Quandt (G-Q below) consider a most commendable number of examples of mis-specified models or incorrect estimator choices. One of the main purposes of this review article is to indicate how valuable asymptotic theory can be in clarifying simulation work by applying it to their findings on the magnitudes and directions of the biases observed in Ordinary Least Squares estimates for their system