The Information Matrix Test for the Linear Model

Abstract

We derive the information matrix test, suggested by White, for the normal fixed regressor linear model, and show that the statistic decomposes asymptotically into the sum of three independent quadratic forms. One of these is White's general test for heteroscedasticity and the remaining two components are quadratic forms in the third and fourth powers of the residuals respectively. Our results show that the test will fail to detect serial correlation and never be asymptotically optimal against heteroscedasticity, skewness and non-normal kurtosis.