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We revisit the problem of estimating the local average treatment effect(LATE) and the local average treatment effect on the treated (LATT) whencontrol variables are available, either to render the instrumental variable(IV) suitably exogenous or to improve precision. Unlike previous approaches,our doubly robust (DR) estimation procedures use quasi-likelihood methodsweighted by the inverse of the IV propensity score - so-called inverseprobability weighted regression adjustment (IPWRA) estimators. By properlychoosing models for the propensity score and outcome models, fitted values areensured to be in the logical range determined by the response variable,producing DR estimators of LATE and LATT with appealing small sampleproperties. Inference is relatively straightforward both analytically and usingthe nonparametric bootstrap. Our DR LATE and DR LATT estimators work well insimulations. We also propose a DR version of the Hausman test that can be usedto assess the unconfoundedness assumption through a comparison of differentestimates of the average treatment effect on the treated (ATT) under one-sidednoncompliance. Unlike the usual test that compares OLS and IV estimates, thisprocedure is robust to treatment effect heterogeneity.

Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment