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\begin_layout Standard
The two-period difference-in-differences regression model with fixed effects
is:
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
Y_{t}=\beta_{0}+\beta_{1}I_{t=t^{0}}+\beta_{2}D+\delta D\times I_{t=t^{0}}+\varepsilon_{t}
\]
\end_inset
and the difference-in-differences estimator is
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
\hat{\Delta}^{DID}=(\bar{Y}_{1,D=1,t^{0}}-\bar{Y}_{0,D=1,t^{0}-1})-(\bar{Y}_{0,D=1,t^{0}}-\bar{Y}_{0,D=0,t^{0}-1})=\hat{\delta}
\]
\end_inset
Two-period DID assumes the treatment effect is the same across all units,
such that
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
\Delta^{ATE}=\Delta^{ATET}=\Delta^{ATEN}=\delta
\]
\end_inset
\end_layout
\begin_layout Standard
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