normality assumption

[hend elgamiel]

hi every body , 1) which more relevant to check normality in xtreg with fixed effect with robust standard errors cluster

• Residual plus fixed effects (total residual):

predict [new variable name], ue

• Fixed effects (individual specific residual component):

predict [new variable name], u

• Non-specific residual:

predict [new variable name], e.

2) i have Skewness less than zero and excess Kurtosis more than zero 6 . in this case normal distribution is violated or not

[hend elgamiel]

norm.gph this is normal distribution

[Clyde Schechter]

For a fixed effects regression, there are no distributional assumptions about the fixed effects (u). So the only thing that might be relevant is the bottom residual (e). That said, if you have a large sample size, the normality assumption is not necessary for correct inference because the central limit theorem comes to the rescue. Also, even with modest sample sizes where central limit theorem effects do not kick in, if the distribution is reasonably close to normal, and particularly if it is symmetric, you are probably still OK. Finally, the robust standard error provides protection. It is very unlikely that you have anything to worry about here.

[hend elgamiel]

hi , Clyde Schechter thank you for reply me
when i use residual (e) the Skewness less than zero and excess Kurtosis 10 but the histogram display close to normal . my sample is 685 observation , i use fixed effect with robust standard errors with cluster . the normality assumption is necessary for correct inference in my case ? did you mean symmetric is the Skewness

[Clyde Schechter]

A symmetric distribution is one with skewness = 0. You say yours is < 0, but from the appearance of your histogram, I would imagine it is not a lot less. In any case, with 685 observations I think you are in safe territory due to the central limit theorem anyway. I don't think I would worry about normality in this data set.

[hend elgamiel]

thank you Clyde Schechter
i want know about robust standard errors with cluster is relaxed the violation of normality assumption in general? and the normality assumption is not necessary when the sample more than 30 observation?

[Clyde Schechter]

While the main purpose of robust variance estimation is to overcome heteroscedasticity and non-independence of observations, it is also robust to departures from normality, at least if the non-normality is not terribly severe.

Concerning the sample size, I would not endorse 30, or any other particular number, as a general lower bound for relying on the central limit theorem. It depends on the distributions of the predictors and the outcome variables. The solution to the normal equations is b = (X'X)^-1Xy. So each coefficient is a sum of products of x's, other numbers derived from the x's, and y--all of them identically distributed. The central limit theorem says that as the number of terms in the sum goes to infinity, the distribution approaches normality. In extreme cases, 30 would not be enough. In most cases, it probably would. In any event, you have 685 observations, and it would take a very bizarre distribution of the X's and y to have (X'X)^-1Xy's components to fail to be normal. Possible, but very, unusual.

[hend elgamiel]

hi Clyde Schechter , plz give me short answer . in my case the normality assumption is necessary or not ? because i confuse from final paragraph and my language not english?

[Clyde Schechter]

Normality assumption is not necessary in your case.

[hend elgamiel]

thank you very much Clyde Schechter