Question: 13.12 Consider the potential outcomes framework from Appendix 13.3. Suppose that Xi is a binary treatment that is independent of the potential outcomes Yi(1) and

13.12 Consider the potential outcomes framework from Appendix 13.3. Suppose that Xi is a binary treatment that is independent of the potential outcomes Yi(1) and Yi(0). Let TEi = Yi (1) – Yi (0) denote the treatment effect for individual i.

a. Can you consistently estimate E [Yi(1)] and E[Yi(0)]? If yes, explain how; if not, explain why not.

b. Can you consistently estimate E (TEi)? If yes, explain how; if not, explain why not.

c. Can you consistently estimate var[Yi(1)] and var[Yi (0)]? If yes, explain how; if not, explain why not.

d. Can you consistently estimate var(TEi)? If yes, explain how; if not, explain why not.

e. Do you think you can consistently estimate the median treatment effect in the population? Explain.

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