Consider the potential outcomes framework from Section 2.7a, where y i (0) and y i (1) are

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Consider the potential outcomes framework from Section 2.7a, where yi(0) and yi(1) are the potential outcomes in each treatment state.

(i) Show that if we could observe yi(0) and yi(1) for all i then an unbiased estimator of τate would be

nELy(1) – y.(0)] = y(1) – y(0). i=1

This is sometimes called the sample average treatment effect.

(ii) Explain why the observed sample averages, y̅0 and y̅1, are not the same as y̅(0) and y̅(1), respectively, by writing y̅0 and y̅1 in terms of yi(0) and yi(1), respectively.

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