Asymptotic Expansions of the Information Matrix Test Statistic.

Conventional chi(superscript "2") approximations to the distribution of the information matrix test are shown to be inaccurate in models and with sample sizes commonly encountered. Interpreting a version of the information matrix test as an efficient score test leads to an alternative Edgeworth type approximation. This is calculated for the normal regression model and shown to be an improvement. Generally, the quality of the approximations is sensitive to the covariate design. However, the authors are able to provide design-independent, second-order size corrections for the widely used information matrix tests which detect nonnormal skewness and kurtosis in regression models. Copyright 1991 by The Econometric Society.