I am currently studying panel data. I am using fixed effects estimators with cluster robust standard errors to account for the possibility of heteroskedasticity/serial correlation in the error terms. Since these errors differ quite a bit from "normal" fixed effects SEs, I assume that its reasonable to use them.
However, I wonder when it is appropriate to use cluster robust errors in a fixed effects model. Obviously, if serial correlation is a problem in my model. What I do not understand is: Is it problematic if the serial correlation occurs in my demeaned errors or in my original (not demeaned) errors? Or does it not matter? And which test can I use to decide whether it is appropriate to use cluster robust standard errors in my fixed effects model or not?
I came across a test proposed by Wooldridge (2002/2010 pp. 319 f.) that tests whether the original errors of a panel model are uncorrelated based on the residuals from a first differences model. Is it appropriate to use this test to decide whether or not to use cluster robust errors?
Update: After again reading the Section (Wooldridge, 2010) I am quite sure that the proposed test is sensible in this situation! However, does anybody know other tests for serial correlation in panel data with fixed effects?
Thank you very much for your help and thoughts!
Source: Wooldridge, Jeffrey M. Econometric analysis of cross section and panel data. MIT press, 2002/2010.