I am trying to estimate a difference in difference model with 10 time periods (t=10) and many different plots of land, which are the unit of observation. Each plot of land which becomes treated at some period t (but never at t=1, so there is a pre-treatment time period) corresponds to a 'control' plot of land, which never becomes treated. Let's call the treated and untreated plots of land that correspond to each other 'pairs'. Let's assume that the parallel trends assumption does hold between all of the pairs.

Would it be correct to include pair fixed effects in the difference in difference set up? So, should the regression would look like:

$$ Y_{ist} = \alpha + \gamma_s*Treatment + \lambda*d_t+\delta*(Treatment*d_t)+\phi_t+\psi_p+\epsilon_{ist} \,. $$

Where $\psi_p$ is the pair fixed effect and $\phi_t$ is the year fixed effect

Or should the pair fixed effect be omitted, and simply including the control plots is sufficient?


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