Non- normal residuals

[Bernt Evensen]

I ran the following regression based on 998 observations:

reg hce BNP o65 BD i.land i.year

To investigate the residuals I typed:

Predict res, residuals

To investigate these residuals I typed:

kdensity res, normal

This command gave me the attached figure. To my inexperinced eye the residuals looks kind of normally distriubuted. At least good enough.

But when I run a more formal test:

sktest res

I get:

Skewness/Kurtosis tests for Normality
------ joint ------
Variable | Obs Pr(Skewness) Pr(Kurtosis) adj chi2(2) Prob>chi2
-------------+---------------------------------------------------------------
res | 998 0.0000 0.0000 . 0.0000


Which means my residuals are not normally distributed.

My question is this: Is it ok to say that I assume normal distribution of the residuals in the analysis, or is this something I must pursue further?

[Maarten Buis]

It looks like your errors are quite non-normal in the sense that they are too peaked, and as a consequence (though this is less visible in the type of graph you use) the tails are too fat. You can see the latter more clearly if you used qnorm res. So I don't see a big discrepancy between the graph and the test. However, with almost a 1000 observations I would not be too worried about it. If you want you can use robust standard errors by adding the vce(robust) option to regress.

[Bernt Evensen]

Thanks a lot. I thought clustered and robust standard errors were for heteroscedasticity and autocorrelation? Do they also correct for non- normal distributed residuals?

[Carlo Lazzaro]

Bernt:
-robust- and -cluster()- options for standard errors are intechangeable only under -xt- commands, such as -xtreg-, where they do the same job;
- under -regress- you should use -robust- if you suspect/have evidence of heteroskedasticity in your residual distribution and -cluster()- if you suspect residuals autocorrelation in mutiple waves of data for the same id (that is, if you're dealing with a panel data in that rare instance when, say -regress- outperforms -xtreg, fe-. It happens whenever the F-test appearing as a footnote of -xtreg- outcome table fails to reach statistical significance. Please note that the test allows default standard errors only).

[Bernt Evensen]

I am sorry but I don`t think I follow. I thought that using reg with i.land was identical to using xtreg fe? So when I use reg, I can not use vce(robust) to account for heteroscedasticity and autocorrelation?

[Carlo Lazzaro]

Bernt:
if you're dealing with a panel dataset and you want to go -regress-, it's manadatory to impose the -cluster()- option for standard errors, as your observations are not independent.
In that way, heteroskedasticity, if present, remains an issue that you cannot deal with.

[Bernt Evensen]

Hmm. But if I go xtreg Y X1 X2 i.year, fe vce(robust) I deal with both autocorrelation and heteroskedasticity?

[Carlo Lazzaro]

Bernt:
yes, you're right.

[Bernt Evensen]

Maarten Buis or Carlo Lazarro. Could you provide a reference that says non- normal resisiduals is not so much of a problem in panel data when N is large?

[Carlo Lazzaro]

Bernt:
see this thread: https://stats.stackexchange.com/ques...ly-distributed