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Expected value of potential outcome under Conditional Independence assumption watch

    • Thread Starter

    Yi=DiYi1+(I-Di)Yi0 with Di treatment indicator, Di=1 if treated and 0 otherwise
    Xi is a variable such that Yi0 and Yi1 are independent from Di after conditioning on Xi. Can someone show how to get to the following results:
    a) E[Yi1]=E[DiYi/P(Xi)]
    b) E[Yi0]=E[(1-Di)Yi/(I-P(Xi)]
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