st: Residuals and fixed effects analysis

[<redacted> <redacted>]

Dear members of Statalist.

I'm running a fixed-effects (within) regression with clustered robust standard errors on panel data consisting of 50 countries, and around 4 time periods.

One of the FE assumptions is that the idiosyncratic errors (the unobserved time-varying factors that affect the dependent variable) must be normally distributed (''conditional on the explanatory variables and the unobserved time-constant effect''), unless I have a large number of countries and few time periods (Wooldridge 2013, p. 690).

Thus, I did the following:

- I ran a FE regression using xtreg on my panel data and then ''saved'' the residuals by typing ''predict residuals , e'' in Stata 12. 

- I analyzed a simple histogram of the distrubution of these residuals. These residuals seem approximately normally distributed.

- I concluded that as long as the residuals are ''sufficiently'' normally distributed, I can make use of t-tests for inference (since I have 50 countries and 2-4 time periods, i.e. a quite large N and a small T). 

Again, I understand that the normality assumption is not particularly important when working with large samples, but I would still like to know if the abovementioned procedure is correct?

I haven't found any info on this when it comes to panel data and fixed-effects, but only for cross-sections and OLS. I would really, really appreciate any kind of (short) answer.

Best,
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