Doubly robust estimation of the local average treatment effect curve

We consider estimation of the causal effect of a binary treatment on an outcome, conditionally on covariates, from observational studies or natural experiments in which there is a binary instrument for treatment. We describe a doubly robust, locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates V when randomization of the instrument is only true conditionally on a high dimensional vector of covariates X, possibly bigger than V. We discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on V that assumes no treatment-instrument interaction. We illustrate our methods with the estimation of the local average effect of participating in 401(k) retirement programmes on savings by using data from the US Census Bureau's 1991 Survey of Income and Program Participation.