Normality of OLS-residuals and sample size

[Mike Smet]

Dear Statalist members,

I have a practical question regarding normality of the residuals in OLS: what is the minimum sample size (or the number of degrees of freedom) for which normality of the residuals becomes a non-issue to perform inference (i.e. that we obtain 'reliable' t-statistics,etc.)?
I know that normality is not required for OLS to be BLUE and that (thanks to the central limit theorem) there is no problem for large samples, but what can be considered as a smal/large sample regarding this isssue? I also assume that non-normality is not caused by heteroscedasticity, outliers or any misspecification of the functional form.

Thanks for sharing your opinion, rule of thumb, references on this, ...
Kind regards,
Mike

[Joao Santos Silva]

Dear Mike,

With independent data, what we need is that the square of the number of parameters divided by the sample size is "small"; see Portnoy (1988).

Best wishes,

Joao

[Mike Smet]

Dear Joao,

Thank you for the reference. But now the question is: "When is p²/N close enough to zero?"

Kind regards,
Mike

[Marcos Almeida]

P stems from parameter. N indicates sample size. But this was fully underlined by Joao in #2.

[Mike Smet]

Sorry for the confusion I may have caused in post #3: What I meant to ask was what acual number (i.e. number of parameters squared divided by number of observations) can be considered as "small"? E.g. suppose I have 10 parameters and 100 observations: would the result (=1) be small enough in order not to bother about normality of the residuals?

Kind regards,
Mike

[Joao Santos Silva]

How long is a piece of string? I would say that for independent data p²/N = 1 should be just acceptable, but it depends also on how non-normal the errors are. Why don't you compute bootstrap confidence intervals (not CI based on bootstrap standard errors)? For that you do not need normality.

Best wishes,

Joao