Alternative ways of obtaining Hausman's test using artificial regressions

Hausman [1978. Specification tests in econometrics. Econometrica 46, 1251–1271] showed that his specification test in panel data, which is based on the contrast between fixed effects (FE) and the random effects (RE) estimators, can also be obtained as a Wald test from an artificial OLS regression. This paper generalizes this result to the 2SLS counterpart. Instead of a contrast based on FE 2SLS and RE 2SLS as proposed more recently by Baltagi [2004. A Hausman test based on the difference between fixed effects two-stage least squares and error components two-stage least squares, problem 04.1.1. Econometric Theory 20, 223–224] artificial regressions are proposed that would generate this Hausman test using 2SLS regressions.