#StackBounty: #statistical-significance #stata #fixed-effects-model #clustered-standard-errors Variance-covariance matrix of individual…

Bounty: 50

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 ).

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