Asymptotics for statistical treatment rules

This paper develops asymptotic optimality theory for statistical treatment rules in smooth parametric and semiparametric models. Manski (2000, 2002, 2004) and Dehejia (2005) have argued that the problem of choosing treatments to maximize social welfare is distinct from the point estimation and hypothesis testing problems usually considered in the treatment effects literature, and advocate formal analysis of decision procedures that map empirical data into treatment choices. We develop large-sample approximations to statistical treatment assignment problems in both randomized experiments and observational data settings in which treatment effects are identified. We derive a local asymptotic minmax regret bound on social welfare, and a local asymptotic risk bound for a two-point loss function. We show that certain natural treatment assignment rules attain these bounds.