Estimation of Causal Effects Using Instrumental Variables
Recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables (IV) for causal inference. A basic idea is that instrumental variables serve as an "experimental handle", turning 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 identifies the average treatment effect for those whose treatment status is changed in this hypothetical experiment. We build on the modern IV framework including assumptions and identification results, 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 in order to balance different instrument groups with respect to covariates. For both methods, modelling assumptions are made directly on observed data and separated from the IV assumptions that impose weak restrictions on observed data, while causal effects are inferred by combing observed-data models with the IV assumptions through identification results. This approach is flexible enough to host various semiparametric and nonparametric techniques (including model building and checking) that attempt to learn associational relationships from observed data. We illustrate the methods by an application to estimating return to education.