Minimally capturing heterogeneous complier effect of endogenous treatment for any outcome variable

Goeun Lee (), Choi Jin-young () and Myoung-jae Lee
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Choi Jin-young: Division of Economics, Hankuk University of Foreign Studies, 107, Imun-ro, Dongdaemun-gu, Seoul 02450, Republic of Korea

Journal of Causal Inference, 2023, vol. 11, issue 1, 25

Abstract: When a binary treatment D D is possibly endogenous, a binary instrument δ \delta is often used to identify the “effect on compliers.” If covariates X X affect both D D and an outcome Y Y , X X should be controlled to identify the “ X X -conditional complier effect.” However, its nonparametric estimation leads to the well-known dimension problem. To avoid this problem while capturing the effect heterogeneity, we identify the complier effect heterogeneous with respect to only the one-dimensional “instrument score” E ( δ ∣ X ) E\left(\delta | X) for non-randomized δ \delta . This effect heterogeneity is minimal, in the sense that any other “balancing score” is finer than the instrument score. We establish two critical “reduced-form models” that are linear in D D or δ \delta , even though no parametric assumption is imposed. The models hold for any form of Y Y (continuous, binary, count, …). The desired effect is then estimated using either single index model estimators or an instrumental variable estimator after applying a power approximation to the effect. Simulation and empirical studies are performed to illustrate the proposed approaches.

Keywords: endogenous treatment; complier effect; instrument score; propensity score; single index model; instrumental variable estimator (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:11:y:2023:i:1:p:25:n:1015

DOI: 10.1515/jci-2022-0036

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