A Positive Semi-definite Covariance Matrix for Hausman Specification Tests of Conditional and Marginal Densities.

When the joint density of data can be factorized into conditional and marginal densities, the Hausman (1978) test can be used for diagnosing misspecifications of these densities. However, since common covariance estimates of the difference of the two estimators used in the Hausman test need not be positive semidefinite in finite samples, the test statistic may be negative. This paper presents a simple and consistent covariance matrix that is positive semidefinite in any finite sample. Copyright 1995 by Blackwell Publishing Ltd