Minimum number of observations required to estimate Panel data?

[Sameen Ho]

Dear all, I have a panel data with both N and T small, 25 cities and 10 years respectively. Is the panel fixed effect regression a good methodology? And what is the minimum number of observations required to estimate panel data ?

Thank you for your help in advance.

[Maxence Morlet]

For a fixed effects or first difference estimation, all you need is at least two observations per unit (here, cities).

In your case, I woud go for two way fixed effects with bootstrapped standard errors.

[George Ford]

or clustered errors, and maybe bootstrap those as Max suggests (boottest makes quick work of it).

[Maxence Morlet]

Thing is with 25 clusters, not sure whether that is enough for custer-robust standard errors to be unbiased...

Cameron & Miller recommend at least 42 clusters I think

[George Ford]

There's some analysis that says about 10 xsections is adequate. My own MC analysis confirms that. And boottest helps.

[Sameen Ho]

Dear all,
I really appreciate your suggestions. They are very helpful!

[Jeff Wooldridge]

I believe “42” was suggested by Angrist and Pischke, somewhat facetiously. It comes from the Hitchhiker’s Guide to the Galaxy. N = 25 is perhaps pushing it but clustering can work well, even with T = 10. Theoretically, the bootstrap requires large N, too.

[Carlo Lazzaro]

A funny (at the outset) but technical demanding explanation about the bias of clustered standard error when we have less than 42 clusters, is reported in https://press.princeton.edu/books/pa...s-econometrics, paragraph 8.2.3.

[Rich Goldstein]

to help clarify, or maybe add to the confusion, I note that Rabe-Hesketh, S and Skrondal, A (2022), Multilevel and Longitudinal Modeling using Stata, fourth edition, uses the following: number of clusters minus number of cluster-level covariates should be at least 42 (they call this a "rule of thumb") and they provide at least one example showing problems with smaller numbers