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

TL;DR

This paper evaluates various weighting estimators for the local average treatment effect, highlighting the advantages of normalized estimators and demonstrating their properties through simulations and empirical applications.

Contribution

It introduces and compares normalized and unnormalized weighting estimators for LATE, recommending normalized estimators for their scale and translation invariance.

Findings

Normalized estimators are generally preferable.

Unnormalized estimators are sensitive to measurement units.

Normalized estimator performs well in one-sided noncompliance cases.

Abstract

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.