Angrist (1998) shows that the analogous saturated-in-X; regression model (with dummies for the same cells as the matching estimator) produces the estimand: Eo.[ P(D, = 1IX, = x)(1 - P(D, = 1IX, = x)) ]P(X, =x) OR = E[P(D, = 1IX, = x)(1 - P(D, = 1IX, = x))]P(X, = x) x where 8x = E[Y; I X;, Di = 1] - E[Y; I Xi, Di = 0], P(X/ = x | Di = 1) is the probability that X; takes on the value x, given Di = 1, and Xi takes on all possible combination of covariates. Note: these weights are based on the variance of the probability of treatment (P X (1 - P)). . Compare the regression-based estimand with the matching-based estimand of the Average Treatment Effect on the Treated (ATT) and state the implications for empirical analyses based on these [7]