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I see most of the applied econometrics papers using the two-way fixed effects model, controlling for time and units fixed effects, so: $$y_{it}=\alpha_{i}+ \gamma_{t} +\beta x_{it} +\epsilon_{it}$$ I understand the reasoning behind it.

I would like to know if there are situations when we should not control for unit-fixed effects for some reason. For instance, suppose I have a panel with 500 units across 10 time periods. By controlling for unit-fixes effects I loose 500 degrees of freedom, right? Is it still better than not controlling? As an example I found this paper with similar setup (they include a spatial covariate, but it doesn't matter for this point). Their main model is a panel regression (640 units across 12 time periods) controlling for time-fixed effects only.

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It is always a good default to include individual fixed effects.

If you believe that omitting the individual fixed effect would not induce bias, then you can perform random effects estimation and attain small standard errors.

If treatment (or any covariate) is time-invariant, then by including individual fixed effects, we can't estimate the coefficients for those variables. If you really care about those coefficients, then you must exclude individual fixed effects and hope that doing so doesn't induce bias. (There are some creative methods to attempt to estimate coefficients for time-invariant regressors while including individual fixed effects, Chapter 11 of the 7th edition of Green's Econometric Analysis is a reference).

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  • $\begingroup$ Are there any concerns of including unit-fixed effects related to the total number of units? $\endgroup$
    – Oalvinegro
    Mar 1, 2023 at 15:38
  • $\begingroup$ Yes - you mentioned it above. But these concerns are overridden by the extremely familiar and salient concern of bias. $\endgroup$ Mar 1, 2023 at 16:36
  • $\begingroup$ If you have 500 units with 10 time periods each, you have 5,000 observations. Including 500 regressors and losing 500 degrees of freedom should be okay. $\endgroup$ Mar 1, 2023 at 16:48

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