Statistical treatment rules for heterogeneous populations

Charles F. Manski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

101 Scopus citations

Abstract

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 statistical treatment rules, 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 conditional empirical success 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 sufficient sample sizes 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.

Original languageEnglish (US)
Pages (from-to)1221-1246
Number of pages26
JournalEconometrica
Volume72
Issue number4
DOIs
StatePublished - Jul 2004

Keywords

  • Finite sample theory
  • Large-deviations theory
  • Minimax regret
  • Randomized experiments
  • Risk
  • Social planner
  • Statistical decision theory
  • Treatment response

ASJC Scopus subject areas

  • Economics and Econometrics

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