st: Fixed effects and residuals

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Dear Statalist.

I'm doing a fixed-effects (within) analysis on panel data, with about 50 countries, and around 4 time periods.

One of the FE assumptions is that the idiosyncratic errors (the factors that change over time and that we do not observe) must be normally distributed (''conditional on Xi and ai''), unless I have a big 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 good info on this when it comes to panel data and fixed-effects, but only for cross-sections and OLS.

Best,
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