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Question 1 Consider a dummy treatment D, where D = 1 denotes that the individual receives the treatment. Let Y (0) and Y(1) be the

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Question 1 Consider a dummy treatment D, where D = 1 denotes that the individual receives the treatment. Let Y (0) and Y(1) be the potential outcomes corre- sponding to the treatment status 0 and 1 respectively. Let X be a dummy variable whose value is determined before the treatment. Assume that the Con- ditional Independence Assumption (CIA) holds, such that conditional on X, {Y(0), Y(1)} are independent of the treatment D. Define the treatment effect conditional on X: 8x = E(Y(1) - Y(0)|D =1, X). Consider regressing Y on D and X: Y = Bo+6D+

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