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A New Form of the Information Matrix Test

Russell Davidson
James G. MacKinnon

Abstract

We develop a new form of the information matrix test for a wide variety of statistical models. Chesher (1984) showed that the implicit alternative of this test is a model with random parameter variation, a fact which we exploit by constructing the test against an explicit alternative of this type. The new test is computed using a double-length artificial regression, instead of the more conventional outer-product-of-the-gradient regression, which, although easy to use, is known to give test statistics with distributions very far from the asymptotic nominal distribution even in rather large samples. The new form on the other hand performs remarkably well, at least for the case of univariate regression models. Some approximate finite-sample distributions are calculated for this case, and lend support to the use of the new form of the test.