Efficient and Robust Estimation of the Generalized LATE Model

Abstract–This paper studies the estimation of causal parameters in the generalized local average treatment effect (GLATE) model, which expands upon the traditional LATE model to include multivalued treatments. We derive the efficient influence function (EIF) and the semiparametric efficiency bound (SPEB) for two types of causal parameters: the local average structural function (LASF) and the local average structural function for the treated (LASFT). The moment conditions generated by the EIF satisfy two robustness properties: double robustness and Neyman orthogonality. Based on the robust moment conditions, we propose the double/debiased machine learning (DML) estimator for estimating the LASF. The DML estimator is well-suited for high dimensional settings. We also propose null-restricted inference methods that are robust against weak identification issues. As an empirical application of these methods, we examine the potential health outcome across different types of health insurance plans using data from the Oregon Health Insurance Experiment.Keywords: Double RobustnessEfficient Influence FunctionMultivalued TreatmentNeyman OrthogonalityUnordered MonotonicityWeak Identification.DisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.