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I'm doing a difference-in-differences analysis with one pre-treatment time point (0), and two post-treatment time points (1, 2).

What would the regression model be?

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Consider first the most basic form of a DID model, where $T$ is a dummy variable that equals one past the treatment time and 0 otherwise, and $S$ is a dummy variable that equals one if in the treatment group and 0 otherwise, and $\varepsilon$ is iid error:

\begin{equation} y = \beta_0 + \beta_1T +\beta_2S + \beta_3(S*T) + \varepsilon \end{equation}

The DID effect is equal to $\beta_3$

We could just extend this basic format to accommodate more treatment times in the following way. Let $T_1$ equal one when time is after the first treatment time but before the second treatment time and 0 otherwise and $T_2$ equal one when time is after the second treatment time and 0 otherwise. S and $\varepsilon$ are still defined as they were above.

\begin{equation} y = \beta_0 + \beta_1T_1 +\beta_2T_2 + \beta_3S + \beta_4(S*T_1) + \beta_5(S*T_2) + \varepsilon \end{equation}

The DID effects for treatment times $T_1$ and $T_2$ are $\beta_4$ and $\beta_5$ respectively.

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  • $\begingroup$ Very clear and helpful, thanks. $\endgroup$ – hassapikos Jun 5 '19 at 14:33

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