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Abstract:
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Although the conventional instrumental variable (IV) estimator has been widely studied for the estimation of compliers averaged causal effect and can be used to identify complier distribution function, it is typically nonmonotone and not bounded in [0, 1]. We propose a novel monotone estimator of distribution functions for compliers in a randomized trial where some subjects fail to follow their assigned treatments. Our estimator is based on quantile IV regression and postestimation rearrangement, which is guaranteed to be monotone and bounded in [0, 1], and is more stable and more efficient particularly under weak instruments. We derive the asymptotic properties of the proposed estimator and we also propose a modification to reach the semiparametric efficiency bound locally and is robust under misspecification of unknown density functions. A Wilcoxon-type test is proposed to test the equivalence of distribution functions for compliers under treatment arm and control arm. Simulation results are presented to compare the proposed estimator to the conventional IV estimator and semiparametric efficient estimator. A real data example illustrates the application of the proposed estimator.
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