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I wish to estimate a pooled difference-in-differences specification in the following form:

$y_{i,t}=\alpha_i+\theta_t + \beta \times \mathbf{1}\left(t > \bar{t}\right) \times Treatment_i + \epsilon_{i,t}$

The issue is that each unit $i$ only appears in two times $t$. The question is whether it makes sense to consider unit fixed effects when each unit only appears twice.

Any thoughts? Any references with a similar specification?

Thanks

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Yes, it does. The individual effects will be imprecisely estimated, but those coefficients are not of primary interest.

The assumption you need is strict exogeneity, $E[\epsilon_{i,t}|X_i]=0$, where $X_i$ denotes all regressors for individual $i$ at all time periods.

I can provide more technical details regarding this if you care, but from an applied perspective, there's nothing wrong with using individual FE with only two time periods.

You asked for a reference. It is well-known that, with 2 time periods, the fixed effects and first difference estimators are equivalent. This is a question about that. One of the first really famous papers on the labour market effects of the minimum wage had data on only two time periods and used the first difference estimator. Here is a link to that paper.

Good luck with your analysis.

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