From LATE to ATE
A Bayesian Approach
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We develop a Bayesian model that produces a posterior distribution of the marginal treatment effect (MTE) function. The method can be used even when the MTEs are not identified—as is the case in RCTs with imperfect compliance—thereby producing posterior distributions of unidentified estimands such at the overall average treatment effect (ATE) or the average effect on the always takers. While we focus on the case of RCTs with imperfect compliance, the model is general and allows for non-binary instruments and/or additional exogenous variables. Using the model, we show for the Oregon Health Insurance Experiment that the main source of the uncertainty in the ATE is not uncertainty due to the non-identifiability of the full MTE function and instead traditional statistical uncertainty, i.e., uncertainty in the true values of the observed moments due to the finite sample-size.
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