Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect

In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), each of which can be motivated by Abadie's (2003) kappa theorem. Our framework presumes a binary treatment and a binary instrument, which may only be valid after conditioning on additional covariates. 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 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. The importance of normalization is particularly apparent in applications to real data. The simulations also suggest that covariate balancing estimation of instrument propensity scores may be more robust to misspecification. Software for implementing these methods is available in Stata.