  This paper studies the estimation of causal parameters in the generalized
local average treatment effect (GLATE) model, a generalization of the classical
LATE model encompassing multi-valued treatment and instrument. We derive the
efficient influence function (EIF) and the semiparametric efficiency bound
(SPEB) for two types of parameters: local average structural function (LASF)
and local average structural function for the treated (LASF-T). The moment
condition generated by the EIF satisfies two robustness properties: double
robustness and Neyman orthogonality. Based on the robust moment condition, we
propose the double/debiased machine learning (DML) estimators for LASF and
LASF-T. The DML estimator is semiparametric efficient and suitable for high
dimensional settings. We also propose null-restricted inference methods that
are robust against weak identification issues. As an empirical application, we
study the effects across different sources of health insurance by applying the
developed methods to the Oregon Health Insurance Experiment.
