In other words, where within-group correlations are high, we can expect
tests of statistical significance to be biased toward unjustifiably
rejecting the null hypothesis of no statistically significant
relationship. Clustering is easily extended to other kinds of analyses,
and it is perfectly compatible with the simultaneous conclusion of group
fixed effects or group dummy variables, and there is nothing
inappropriate about including in a given model country fixed effects
while at the same time controlling for within-country variance
correlation by clustering by country. Fixed effects are usually
employed solely to control for potential omitted-variable bias affecting
the estimated coefficients. Clustering addresses the entirely different
problem of within-group correlation of variance, and it "works", in most
cases, by adjusting standard errors upward. Clustering will not affect
coefficient estimates; including fixed effects nearly always will.
I am not a statistician, however, so maybe I am missing something here.
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