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

Abstract

Recent research has demonstrated the importance of flexibly controlling for covariates in instrumental variables estimation. In this article we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), motivated by Abadie’s 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.

Keywords:

• Instrumental variables
• Local average treatment effect
• Weighting estimation

Acknowledgments

For helpful comments, we thank the Editor, an Associate Editor, two anonymous referees, Alberto Abadie, Josh Angrist, Bryan Graham, Phillip Heiler, Toru Kitagawa, Chris Muris, Tomasz Olma, Pedro Sant’Anna, Yuya Sasaki, Liyang Sun, seminar participants at Brandeis University, Goethe University Frankfurt, University of Bonn, and University of Tübingen, and conference participants at CFE, CRC Retreat, EEA, ESEM, Frankfurt Econometrics Workshop, IAAE, MEG, NY Camp Econometrics, SEA, Statistical Week, VfS, and the World Congress of the Econometric Society. We also thank Frances Hoffen and Qihui Lei for excellent research assistance.

Disclosure Statement

The authors report there are no competing interests to declare.

Data Availability Statement

Our companion Stata package, kappalate, is available on the SSC. To download this package, type ssc install kappalate in Stata.

Additional information

Funding

Słoczyński acknowledges financial support from the Theodore and Jane Norman Fund. Uysal acknowledges financial support from the German Research Foundation through CRC TRR 190 (project no. 280092119).