Evaluating treatment protocols using data combination

In real-life, individuals are often assigned to binary treatments according to existing treatment protocols. Such protocols, when designed with "taste-based" motives, would be productively inefficient in that the expected returns to treatment for the marginal treatment recipient would vary across covariates and be larger for discriminated groups. This cannot be directly tested if assignment is based on more covariates than the researcher observes, because then the marginal treatment recipient is not identified. We present (i) a partial identification approach to detecting such inefficiency which is robust to selection on unobservables and (ii) a novel way of point-identifying the necessary counterfactual distributions by combining observational datasets with experimental estimates. These methods can also be used to (partially) infer risk-preferences which may rationalize the observed treatment allocations. Specifically, existing healthcare datasets can be analzyed with the proposed tools to test the allocational efficiency of medical treatments. Using our methodology on data from the Coronary Artery Surgery Study in the US, which combined experimental and observational components, we find that after controlling for age, smokers in the observational dataset had to overcome a higher threshold of expected survival relative to non-smokers in order to qualify for surgery. Our methods are applicable when individuals cannot alter their potential treatment outcomes in response to the treatment regime, unlike in the case of law enforcement