PRACTITIONERS CORNER - A POSITIVE SEMIDEFINITE COVARIANCE-MATRIX FOR HAUSMAN SPECIFICATION TESTS OF CONDITIONAL AND MARGINAL DENSITIES

When the joint density of data can be factorized into a conditional an d marginal densities, Hausman test can be used for diagnosing misspeci fications of these densities. However, since common covariance estimat es of the difference of the two estimators used in Hausman test need n ot be positive semi-definite in finite samples, the test statistic may be negative. This paper presents a simple and consistent covariance m atrix which is positive semi-definite in any finite sample.