Optimal Experimental Design and Estimation when Potential Outcomes are Bounded

Peter Hull

No 35629, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized by independent random assignment and an unconventional regression of the support-midpoint-centered outcome on the recentered treatment, with no intercept. This contrasts with the usual prescription of balanced complete randomization and difference-in-means estimation: when outcomes are bounded, randomness in the realized treatment share is informative. The worst-case gain over full-sample complete randomization is asymptotically small, but gains can be first-order relative to other designs: complete within-pair randomization and pair-fixed-effect regression have twice the worst-case MSE. I then consider the general problem, allowing for any measurable estimator. Independent random assignment remains optimal, and the generally-nonlinear optimal estimator can meaningfully reduce worst-case MSE.

JEL-codes: C21 C9 (search for similar items in EconPapers)
Date: 2026-08
Note: TWP
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