Panel Regression, Fixed Effects, problems with normality and skewness (part 2)

[Oyvind Snilsberg]

Hi everyone,
a few days ago I posted this topic:

http://www.statalist.org/forums/foru...rust-the-tests

Basically asking if I could trust the results of the regression analyzis.

Mr. Lazzaro was kind enough to answer, and I was very pleased with the fact that his answer was exactly what I wanted, however, I can't for the life of me justifiy how I'm suppose to disregard the results of, especially, the skewness/kurtiosis tests of both the variables as well as the residuals. Is it something else I should provide in order to make things more clear?

Thank you for your attention.

Screenshot of previous post:

[Clyde Schechter]

You are asking the same question you posed a few days ago, and Carlo's answer remains correct.

Normality of residuals is really entirely irrelevant here. First of all, it is never relevant to the question of unbiasedness of the regression coefficient estimates. In small samples, the assumption of normality underpins the use of t-distributions for inferences (hypothesis testing) about those coefficients. But in large samples, you don't need the normality of the residuals for this because, if your observations are independent, the central limit theorem tells you that the coefficient estimates will have, asymptotically, a normal sampling distribution centered at the "true" (population) values. Yes, there are some distributions so highly skewed that the asymptotic normality would not be reached until sample size is much larger than yours: but based on your kdensity plot, this isn't one of those situations: you have plenty of room to spare here. So skewness and kurtosis have no bearing on this issue. My advice to you is to just discard these results and proceed as if you had never generated them. Don't give them another thought. They are a distraction.

The only issue raised here that is of some concern is the heteroscedasticity. But, again, as Carlo points out, the use of the robust variance estimator will deal with that. So, nothing to see here. Move on.

[federica rossi]

Hi everyone,
I have the same problem. Where ca I check about the non- normality of residuals ? Is there any reference (textbook or paper) where this issue is discussed? I need to justify it.

[Carlo Lazzaro]

Federica:
welcome to this forum.
FWIW, normality of residual distribution is an issue that can be relaxed using asymptotic theory (see https://www.wiley.com/en-us/Introduc...-9780470032701, page 67). I read this statement as nomality not being really an issue (see also Clyde Schechter's excellent replies to the OP in this thread).
That said, you can graphically check the normality of your residual distribution via -qnorm- and/or -kdensity-.
Analytical checks include -swilk-.

[federica rossi]

Thank you very much Carlo!

Best Regards