Endogenous treatment effect for any response conditional on control propensity score
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Cited by 2 publications
References 9 publications
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.
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.
Direct, indirect, and interaction effects based on principal stratification with a binary mediator
Given a binary treatment and a binary mediator, mediation analysis decomposes the total effect of the treatment on an outcome variable into various sub-effects, and there appeared two-, three-, and four-way decompositions in the literature. Using “principal stratification” based on the potential mediator types, we consider sub-treatment effects for “mediative never-takers, compliers, defiers, and always takers.” In this approach, although it is difficult to pick any one decomposition over the others in general, a particular three-way decomposition becomes well suited, which is thus advocated to use. We present identification conditions for the effects using conditional means, which is then followed by simple estimators that are applicable to any outcome variable (binary, count, continuous, etc.). We also provide simulation and empirical studies.
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