Minimax-regret treatment rules with many treatments

Statistical treatment rules map data into treatment choices. Optimal treatment rules maximize social welfare. Although some finite sample results exist, it is generally difficult to prove that a particular treatment rule is optimal. This paper develops asymptotic and numerical results on minimax-regret treatment rules when there are many treatments. I first extend a result of Hirano and Porter (Econometrica 77:1683–1701, 2009) to show that an empirical success rule is asymptotically optimal under the minimax-regret criterion. The key difference is that I use a permutation invariance argument from Lehmann (Ann Math Stat 37:1–6, 1966) to solve the limit experiment instead of applying results from hypothesis testing. I then compare the finite sample performance of several treatment rules. I find that the empirical success rule performs poorly in unbalanced designs, and that when prior information about treatments is symmetric, balanced designs are preferred to unbalanced designs. Finally, I discuss how to compute optimal finite sample rules by applying methods from computational game theory.

Duke Scholars

Author Matthew A Masten Economics