I have a large panel dataset. Examination of a pooled OLS regression with Breusch Pagan showed heteroskedasticity with all model specifications. I consequently chose to use panel-corrected standard error parameter estimates (PCSE, after Beck and Katz, 1996).
Nonetheless, I decided to test the robustness of my model against one with (country) fixed effects. Now, at least in Stata, the Hausman test doesn't work with robust standard errors. Since it looks at the coefficients, not the standard deviation, though, I can use the FE with uncorrected standard errors without problems for the Hausman test.
My question is, though, whether there is any reason to assume that the FE model's error term might not be heteroskedastic. That is, is it necessary to perform another Breusch Pagan test on the FE model, even though I know from the Pooled OLS that there is heteroskedasticity? I'd rather just run the Hausman test on the uncorrected FE and the PCSE model, then report the corrected FE together with the PCSE model in my appendix. The reason being that Stata is a little sturdy when it comes to postestimation tests after
xtreg, i.e. the FE estimations.