I have a twin panel data and want to estimate simple wage equation (interest in return to education). I use fixed effects(first differencing) to account for family background.(Based on: Ashenfelter and Kreuger 1994)
I have a strong economic argument that unobserved family invariant effect is correlated with the explanatory variables, implying that random effects are not a good idea. But I need to test it.
I want to perform the ordinary Hausman test. However, I know my education variable is measured with an error and thus is endogenous, causing FE estimator to be inconsistent.
Is the test valid in case FE is not consistent? Can I modify the test to work?
I have IVs (to correct the measurement error) at hand so my idea is to test FE_IV against RE_IV, but I am not sure if I can do it.