Regression and Weighting Methods for Causal Inference Using Instrumental Variables

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Please see the supplementary material for a correction and a new result.Recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables (IVs) for causal inference. A basic idea is that IVs serve as an experimental handle, the turning of which may change each individual's treatment status and, through and only through this effect, also change observed outcome. The average difference in observed outcome relative to that in treatment status gives the average treatment effect for those whose treatment status is changed in this hypothetical experiment. We build on the modern IV framework and develop two estimation methods in parallel to regression adjustment and propensity score weighting in the case of treatment selection based on covariates. The IV assumptions are made explicitly conditional on covariates to allow for the fact that instruments can be related to these background variables. The regression method focuses on the relationship between responses (observed outcome and treatment status jointly) and instruments adjusted for covariates. The weighting method focuses on the relationship between instruments and covariates to balance different instrument groups with respect to covariates. For both methods, modeling assumptions are made directly on observed data and separated from the IV assumptions, whereas causal effects are inferred by combining observed data models with the IV assumptions through identification results. This approach is straightforward and flexible enough to host various parametric and semiparametric techniques that attempt to learn associational relationships from observed data. We illustrate the methods by an application to estimating returns to education.