Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect
Tymon Słoczyński, S. Derya Uysal, Jeffrey M. Wooldridge
In this paper we study the finite sample and asymptotic properties of various
weighting estimators of the local average treatment effect (LATE), several of
which are based on Abadie (2003)'s kappa theorem. Our framework presumes a
binary endogenous explanatory variable ("treatment") and a binary instrumental
variable, which may only be valid after conditioning on additional covariates.
We argue that one of the Abadie estimators, which we show is weight normalized,
is likely to dominate the others in many contexts. A notable exception is in
settings with one-sided noncompliance, where certain unnormalized estimators
have the advantage of being based on a denominator that is bounded away from
zero. We use a simulation study and three empirical applications to illustrate
our findings. In applications to causal effects of college education using the
college proximity instrument (Card, 1995) and causal effects of childbearing
using the sibling sex composition instrument (Angrist and Evans, 1998), the
unnormalized estimates are clearly unreasonable, with "incorrect" signs,
magnitudes, or both. Overall, our results suggest that (i) the relative
performance of different kappa weighting estimators varies with features of the
data-generating process; and that (ii) the normalized version of Tan (2006)'s
estimator may be an attractive alternative in many contexts. Applied
researchers with access to a binary instrumental variable should also consider
covariate balancing or doubly robust estimators of the LATE.