Econometrica: Jul 2004, Volume 72, Issue 4

Statistical Treatment Rules for Heterogeneous Populations

https://doi.org/10.1111/j.1468-0262.2004.00530.x
p. 1221-1246

Charles F. Manski

An important objective of empirical research on treatment response is to provide decision makers with information useful in choosing treatments. This paper studies minimax‐regret treatment choice using the sample data generated by a classical randomized experiment. Consider a utilitarian social planner who must choose among the feasible , these being functions that map the sample data and observed covariates of population members into a treatment allocation. If the planner knew the population distribution of treatment response, the optimal treatment rule would maximize mean welfare conditional on all observed covariates. The appropriate use of covariate information is a more subtle matter when only sample data on treatment response are available. I consider the class of rules; that is, rules assigning persons to treatments that yield the best experimental outcomes conditional on alternative subsets of the observed covariates. I derive a closed‐form bound on the maximum regret of any such rule. Comparison of the bounds for rules that condition on smaller and larger subsets of the covariates yields for productive use of covariate information. When the available sample size exceeds the sufficiency boundary, a planner can be certain that conditioning treatment choice on more covariates is preferable (in terms of minimax regret) to conditioning on fewer covariates.

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