(d) Assume that X = 1 if Z z* and X = 0 if Z...

 

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(d) Assume that Xį = 1 if Zį ≥ z* and Xį = 0 if Zį < z*. Then the regression discontinuity estimate of the effect of X on Y is equal to lim E(Y | Z = z) – lim E(Y | Z = z). 27z* Which potential outcome is Y equal to for observations i with Z; ≥ z*? (That is, is their Y equal to Y;(1) or to Y;(0)?) How about for observations with Z z*? Use this to write the regression discontinuity estimate above as a difference in the limits of conditional expectations of potential outcomes, rather than a difference in the limits of conditional expectations of Y. (d) Assume that Xį = 1 if Zį ≥ z* and Xį = 0 if Zį < z*. Then the regression discontinuity estimate of the effect of X on Y is equal to lim E(Y | Z = z) – lim E(Y | Z = z). 27z* Which potential outcome is Y equal to for observations i with Z; ≥ z*? (That is, is their Y equal to Y;(1) or to Y;(0)?) How about for observations with Z z*? Use this to write the regression discontinuity estimate above as a difference in the limits of conditional expectations of potential outcomes, rather than a difference in the limits of conditional expectations of Y.

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