I have estimated a random effects model (N=84 and T=4) and I am now inspecting the assumptions of the model. Using the FAQ guidelines, I tested my model for heteroscedasticity (and the other assumptions). This test confirmed that my models suffered from heteroscedasticity. I was advised to re-estimate the model with robust standard errors. I understand that these standard errors are robust against a heteroscedasticity bias, but I am unsure whether the reported statictics (p-value, R_square) are valid (since this is not the case with heteroscedasticity and the default standard errors in xtreg re).
Another problem is that the tests for cross sectional correlation do not work for my dataset because either my panel is to unbalanced or I have to few observations to complete these tests according to the errors I receive when performing these tests (xtcsd). Is this a problem for my model? And are there other possible tests?
exploring the manual learned me that I can use the xtgls ,panels (heteroscedastic) option to estimate a FGLS model for panel data in which the assumption of heteroscedasticity is relaxed, but I am unsure how this model relates to the random effects model (in essence my question is whether it is also assumed that corr(u_i, X) = 0) ). Can I thus use the xtgls function instead of the xtreg re model?