st: Errors in panel data analysis

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Dear Statalist, I'm a swedish undergraduate economics student at Lund University.

So basically I have a question about econometrics in general and Stata in particular. 

The background is the following: I'm doing a fixed-effects analysis (FE) on panel data, with about 50 countries, and around 4 time periods.

My question concerns the assumption 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 (according to Wooldridge's standard textbook), in order to perform inference with t-statistic and so on.

In order to analyze whether the assumption of normally distributed idiosyncratic errors is true, I did the following:

- I ran a FE regression 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). 

Is this correct?

I really have not been able to find any good info on this when it comes to panel data and fixed-effects, but only for cross-sections and OLS.

To clarify what I was asking for when in comes to Stata: 

I do not quite get the difference between e and u in Stata after running the xtreg command. If I write ''predict residuals , e'' do I then get estimates of the idiosyncratic errors (the time-changing factors that are not observed)? The assumption in Wooldridge is that only the nonobserved factors that change over time (the idiosyncratic errors ) should be normally distributed when using fixed-effects panel data . What exactly do I predict when I instead write ''predict residuals , u''? From the generated data I get, I can see that u only change between countries and not over time, while e change both across countries and time periods. Thus, this should mean that u are estimates of the timeconstant unobserved factors, while e are the estimates of the time-changing nonobserved factors (the idiosyncratic errors), right? If so, it is the e that should be normal (if the sample isn't big enough), correct?

I have read everything in the Stata manual but I still do not understand fully. I know a lot of people say that normality is not very important, but if I still want to check the residuals, is the abovementioned procedure correct?

Best,
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