published in: Econometric Reviews, 2004, 23 (2), 167-174
Propensity score matching is widely used in treatment evaluation to estimate average
treatment effects. Nevertheless, the role of the propensity score is still controversial. Since
the propensity score is usually unknown and has to be estimated, the efficiency loss arising
from not knowing the true propensity score is examined. Hahn (1998) derived the asymptotic
variance bounds for known and unknown propensity scores. Whereas the variance of the
average treatment effect is unaffected by knowledge of the propensity score, the bound for
the treatment effect on the treated changes if the propensity score is known. However, the
reasons for this remain unclear. In this paper it is shown that knowledge of the propensity
score does not lead to a “dimension reduction”. Instead it enables a more efficient estimation
of the distribution of the confounding variables.
c efficiency bound
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