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

Tymon Słoczyński, Selver Uysal and Jeffrey Wooldridge
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Jeffrey Wooldridge: Michigan State University

No 424, Rationality and Competition Discussion Paper Series from CRC TRR 190 Rationality and Competition

Abstract: 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'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 one of the Abadie estimators, which is weight normalized, is preferable in many contexts. Several other estimators, which are unnormalized, do not generally 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. On the other hand, when noncompliance is one-sided, certain unnormalized estimators have the advantage of being based on a denominator that is bounded away from zero. To reconcile these findings, we demonstrate that when the instrument propensity score is estimated using an appropriate covariate balancing approach, the resulting normalized estimator also shares this advantage. We use a simulation study and three empirical applications to illustrate our findings. In two cases, the unnormalized estimates are clearly unreasonable, with ``incorrect'' signs, magnitudes, or both.

Date: 2023-09-07
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Related works:
Journal Article: Abadie’s Kappa and Weighting Estimators of the Local Average Treatment Effect (2025)
Working Paper: Abadie's kappa and weighting estimators of the local average treatment effect (2023)
Working Paper: Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect (2022)
Working Paper: Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect (2022)
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