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Can one “estimate” the distribution of unit fixed effects in a population? What I mean is, consider a standard TWFE model with unit and time FE:

$Y_{i,t} = X_{i,t}+\lambda_i + \theta_t + \epsilon_{i,t}$

I would like to know how much variation in $Y$ is due to unit fixed effects as opposed to $X$. My basic intuition is that one would need large $t$ to retrieve meaningful unit fixed effects for individual $i$, is that the correct way to think about it? If not, what is? Could one estimate the value of FEs for some subgroups of the population even with small $t$?

user368567
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  • could expand TWFE? Also, consider explaining what are $\lambda_i,\theta_t,\epsilon_{it}$.. – utobi Oct 08 '22 at 16:13
  • Two way fixed effects model (TWFE) with unit and time fixed effects (as indexed by i and t) – user368567 Oct 08 '22 at 16:26
  • please, consider adding any extra information that may be useful to the reader directly in the post. – utobi Oct 08 '22 at 16:28
  • Related? https://stats.stackexchange.com/questions/435821/need-intercept-for-plm-fixed-effects-in-r/435865#435865 https://stats.stackexchange.com/questions/446705/how-to-obtain-a-distribution-of-the-unobserved-time-invariant-fixed-effects-in-a/446721#446721 – Christoph Hanck Oct 10 '22 at 09:22

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