non-normality of residuals in a large sample

[Loic DUBOIS]

Hello everyone,

I hope you're all well?

I'm wondering about fixed-effect regressions.

I have large samples (7,000 to 14,000 observations) and it turns out that when I run my fixed-effect regression, I estimate my residuals and they don't follow a normal distribution.

But I've seen that the tests are valid for samples of less than 2,000 observations. So I'm wondering, should I be concerned about the non-normality of the residuals for large samples?

Thank you in advance,

[George Ford]

No.

[Carlo Lazzaro]

Loic:
I do echo's George's "No". With such a large sample, departures from normality (by the way, a weak requirement for systematic residuals) are pretty frequent and with no consequences.
In addition, visual inspection is much more reliable than tests.

[Nick Cox]

If restricted to one word, I would align myself firmly behind or indeed alongside george Ford.

I am not restricted to one word. I am quite optimistic about plotting and more generally examining residuals and think that in total that should be done more.

Yet again, residual plotting can indicate clearly that something is not perfect about a model fit, but contrary to the examples in some textbooks it's not always clear (a) whether a better model exists or (b) what it is.

[Loic DUBOIS]

Thanks a lot for your comments,

[Loic DUBOIS]

Just one more question: the sample size is around 1600 observations or even less than 1000 observations. Do we need to take account of the normality of the residuals?

[Carlo Lazzaro]

Loic:
no again for me.

[George Ford]

With a sample that large, a normality test will reject even when there are tiny departures from normality.

As Carlo and Nick say, it's always worth looking the residuals, in part to see if something weird is going on. In the same way, it's good to look at all the data for peculiarities.

In any case, the regression coefficients and hypothesis tests will not be much affected (if at all), even with very non-normal disturbances (except, perhaps, in cases of impulse dummies).

There are lots of posts on Statalist discussing this topic you can review.

[Loic DUBOIS]

ok thank you very much for your confirmations