Computational pitfalls of the Hausman test

Hausman-type tests for the correct specification of econometric models are now available in various statistical software packages and widely used in empirical research. However, an examination of the literature reveals that the test often is not employed in a proper way, either through a failure to recognize that the quadratic form in the test statistic is singular, or through ascribing the wrong degrees of freedom to the test statistic. It is shown how these problems can be overcome when testing for the independence of regressors and disturbances in the linear regression model, with the help of a Hausman test that is available in, for example, the IAS-SYSTEM econometric software package (Sonnberger, 1985). The only error that is commonly made in practice concerns the Hausman test's rejection region, which is often derived from an incorrect assumption about the test statistic's degrees of freedom. The induced decrease in the size of the test can be dramatic.