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I have monthly panel data and I want to estimate the effects of two different treatments that occur in different time periods. The treatment groups are not the same. An individual can belong one, both or neither of the treatment groups. If one belongs to the first treatment group it is likely that one also belongs to the second group. Both treatments are permanent. What kind of difference in differences specification should I use?

I have been thinking the following kind of equation, but I don't know if it makes sense.

$Y_{it}=B0*\text{Treated1}_i + B0'*\text{Treated2}_i + B1*\text{Treated1}_i*Post1_t + B2*\text{Treated2}_i*\text{Post2}_t + \text{VectorOfTimeDummys}_t + B3'*\text{VectorOfControlVariables}_{it} + \text{ErrorTerm}_{it}$

Arne Jonas Warnke
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Laine
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1 Answers1

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Yes it make sense. You should include also an intercept term (unless you have good reason to not do so) which is excluded from your formula.

Individuals who do not belong to treatment group 1 or 2 will form the reference (or control) group.

If a large group of individuals belong to both groups, it might be difficult to separate $B1$ and $B2$ (imperfect multicollinearity issue) and you might have no choice but to stick with only one treatment indicator for both of them.

Arne Jonas Warnke
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