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.

The local power of test statistics is analyzed by considering sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative. The three classical test statistics-LR, Wald, and LM-are shown to tend asymptot ically to the same random variable under all such sequences. The powe r of these statistics depends on the null, the alternative, and the sequence of DGPs in a geometrically intuitive way. This implies that, for any statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power.

Several procedures are proposed for testing the specification of an econometric model in the presence of one or more other models which purport to explain the same phenomenon.These procedures are shown to be closely related, but not identical, to the non-nested hypothesis tests recently proposed by Pesaran and Deaton [7], and to have similar asymptotic properties..They are remarkably simple both conceptually and computationally, and, unlike earlier techniques, they may be used to test against several alternative models simultaneously.Some empirical results are presented which suggest that the ability of the tests to reject false hypotheses is likely to be rather good in practice.

The widely used Cochrane-Orcutt and Hildreth-Lu procedures for estimating the parameters of a linear regression model with first-order autocorrelation typically ignore the first observation. An alternative maximum likelihood procedure which incorporates the first observation and the stationarity condition of the error process is proposed in this paper. It is similar to the Cochrane-Orcutt procedure, and appears to be at least as computationally efficient. This estimator is superior to the conventional ones on theoretical grounds, and sampling experiments suggest that it may yield substantially better estimates in some circumstances.