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For some reasons, I am interested in the variance-covariance matrix of the individual fixed-effects when regressing wages on personal characteristics: $Y_{i,t} = X_{i,t} \times \beta + c_i + \epsilon_{i,t} $ where $c_i$ stand for the individual fixed effects and $\epsilon_{i,t}$ stand for the perturbations

1/ Quite surprisingly (to me), when clustering the standard errors (SE) by individuals, the variance associated to the coefficients of the individuals fixed effects is drastically reduced. For instance, in the simple case without covariates, it goes from $0.19...$ to $2.07 \times 10^{-14}$.

2/ Moreover, when I make a Monte Carlo simulation (with i.i.d. draws for the perturbations $\epsilon_{i,t}$), this still holds. Hence, the clustering is obviously a bad idea for my purpose. But why ?

Note 1 : The data and codes (in Stata) are available here: https://sites.google.com/view/acazenave-lacroutz/stackexchange_question1

Note 2 : I am aware that the standard errors are adjusted by stata for small-size sample. It explains why the results I get with $reg$ for the SE of the $\beta$ are not the same than the results I get with $xtreg$ ; but cannot explain such difference for the SE of the $c_i$.

Note 3 : Assertion 2 seems to prevent the usual explanation that cluster standard errors can be smaller than the unclustered ones due to intraclass correlations (e.g. cluster-robust standard errors are smaller than unclustered ones in fgls with cluster fixed effects ).

Alexandre C-L
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  • This might help with [#1](https://stats.stackexchange.com/q/394055/7071). – dimitriy Jun 25 '19 at 20:27
  • Thanks for the link. However, the answers to the referred link still talk about intraclass correlations of the perturbations $\epsilon_{i,t}$. Which is not the case in #2 (that I did only to check whether this kind of things could explain #1). So I do not think this applies to #1 as well. – Alexandre C-L Jun 26 '19 at 08:00
  • I had Section III.B of the linked paper in mind, particularly p.15. – dimitriy Jun 26 '19 at 16:17
  • Thanks for the comment. I also though to that (see Note 2). But: note_a/ save a mistake from me, Cameron & Miller made a small typo and the multiplier should be the inverse of what is written in page 15 (see an example on the link in Note 1 ). note_b/ once you know that, the (incorrect) standard errors associated with reg should be above those of xtreg (this is indeed the case for those associated with the beta coefficients) note_c/ whatever, this small-size sample coefficient is not a factor of 10 or much more. Hence, something else is happening here. – Alexandre C-L Jun 27 '19 at 19:33

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