Suppose you have the same data as in Exercise 13.7 (panel data with two periods, (n) observations),
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Suppose you have the same data as in Exercise 13.7
(panel data with two periods, \(n\) observations), but ignore the \(W\) regressor. Consider the alternative regression model
\[ Y_{i t}=\beta_{0}+\beta_{1} X_{i t}+\beta_{2} G_{i}+\beta_{3} D_{t}+u_{i t} \]
where \(G_{i}=1\) if the individual is in the treatment group and \(G_{i}=0\) if the individual is in the control group. Show that the OLS estimator of \(\beta_{1}\) is the differences-in-differences estimator in Equation (13.4).
Equation (13.4)
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