  Recent research has demonstrated the importance of flexibly controlling for
covariates in instrumental variables estimation. In this paper we study the
finite sample and asymptotic properties of various weighting estimators of the
local average treatment effect (LATE), motivated by Abadie's (2003) kappa
theorem and offering the requisite flexibility relative to standard practice.
We argue that two of the estimators under consideration, which are weight
normalized, are generally preferable. Several other estimators, which are
unnormalized, do not satisfy the properties of scale invariance with respect to
the natural logarithm and translation invariance, thereby exhibiting
sensitivity to the units of measurement when estimating the LATE in logs and
the centering of the outcome variable more generally. We also demonstrate that,
when noncompliance is one sided, certain weighting estimators have the
advantage of being based on a denominator that is strictly greater than zero by
construction. This is the case for only one of the two normalized estimators,
and we recommend this estimator for wider use. We illustrate our findings with
a simulation study and three empirical applications, which clearly document the
sensitivity of unnormalized estimators to how the outcome variable is coded. We
implement the proposed estimators in the Stata package kappalate.
