Hausman (1978) developed a widely-used model specification test that has passed the test of time. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Three illustrative examples are used, namely an exogeneity test for the linear regression model, a test for the Box-Cox transformation, and a test for sample selection bias.

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doi.org/10.1016/j.econlet.2014.03.005, hdl.handle.net/1765/76717
Economics Letters
Erasmus School of Economics

Nawata, K., & McAleer, M. (2014). The maximum number of parameters for the Hausman test when the estimators are from different sets of equations. Economics Letters, 123(3), 291–294. doi:10.1016/j.econlet.2014.03.005