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I have different treatments, on different groups, that occur at different times (e.g., 2000 on treat 1, 2009 on treat 2, etc.). I want to fit a DiD model, and I want to standardize the treatment years to year "0" as the the treatment time. To control for treatment year heterogeneity, I included the true year fixed effects.

\begin{align} y_{it} = &β_0 + β_1{\rm Treat} + β_2{\rm After} + β_3({\rm Treat} \times {\rm After}) + \\ &({\rm pre}_3 + {\rm pre}_2 + {\rm pre}_1 + {\rm now} + {\rm post}_1 + {\rm post}_2 + {\rm post}_3) + γC_{it} + ϵ_{it} \end{align}

Questions:

  1. Is there anything wrong with this model? What should the time for the controlled group?

  2. Can I still include the time fixed effect as {pre1,2,3, now, post1,2,3}?

I know there is another way of writing the multiple treatment as to just include the interaction term (which do not require time standardization): variable("Treat") equals to 1 is the treated groups in the time when treated already, and variable("Treat") equals to 0 for controlled groups and for treated groups in the time when not yet treated. But I need the standardized method as well.

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