A New Form of the Information Matrix Test

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Abstract
We develop a new form of the information matrix test for a wide variety of statistical models, and present full details for the special case of univariate nonlinear regression models. Chesher (1984) showed that the implicit alternative of the information matrix test is a model with random parameter variation. We exploit this fact 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 in the context of regression models. Some approximate finite-sample distributions are calculated and lend support to the use of the new form of the test.
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