**Due:** At the start of class on Thursday, Feb. 9.
Please turn in a hard copy.

**Textbook Questions** 3.2, 3.3, 3.5, 3.7, 3.22, 3.24,
3.25

**Extra Question**

Consider the case with a binary treatment and suppose that unconfoundedness holds. Show that \(ATE\) is identified in this case (and provide an expression for it that indicates that it is identified).

How does this expression compare to the one that we derived for \(ATT\) in class?

Now, additionally suppose a linear model for untreated potential outcomes: \(Y_i(0) = X_i'\beta + e_i\) with \(\E[e|X]=0\) and treatment effect homogeneity: \(Y_i(1) - Y_i(0) = \alpha\) for all units. Explain how to use a linear regression to estimate the causal effect of participating in the treatment in this case (and explain where you use each condition above to provide this result).

How does this regression compare to the one that we derived in class after we had identified the ATT? Is it the same or different? Any comments/explanations?