This work was supported, in part, by a grantfrom the Social Sciences and Humanities Research Council of Canada. The paper was written mostly while the author was on sabbatical at the University of California, San Diego. I am grateful to everyone there for providing such a hospitable environment, and to Anil Bera, Russell Davidson, David Hendry, Timo Teriisvirta, Pravin Trivedi, three referees, and seminar participants at the University of -Indiana for helpful comments on earlier versions.

A new form of the information matrix test is developed for a wide variety of statistical models. The test is constructed against an explicit alternative with random parameter variation. It is computed using a double-length artificial regression instead of the more conventional outer-product-of-the-gradient regression, which is known to have very poor finite-sample properties. In Monte Carlo experiments for the case of univariate linear regression models, the new form performs remarkably well. Some approximate finite-sample distributions are also calculated for this case and lend support to the use of the new form.