Asymptotic Efficiency Bounds for a Class of Experimental Designs

TL;DR

This paper establishes fundamental asymptotic efficiency bounds for a broad class of experimental designs involving sequential treatment assignment, including adaptive and stratified methods, focusing on estimating average treatment effects.

Contribution

It derives universal efficiency bounds applicable to various experimental designs and shows no further asymptotic improvement is possible beyond a known optimal estimator.

Findings

No first order asymptotic efficiency improvement beyond the Hahn (1998) bound.

Bounds apply to adaptive, stratified, and covariate-based sampling designs.

Results extend to multiple treatments and constrained treatment settings.

Abstract

We consider an experimental design setting in which units are assigned to treatment after being sampled sequentially from an infinite population. We derive asymptotic efficiency bounds that apply to data from any experiment that assigns treatment as a (possibly randomized) function of covariates and past outcome data, including stratification on covariates and adaptive designs. For estimating the average treatment effect of a binary treatment, our results show that no further first order asymptotic efficiency improvement is possible relative to an estimator that achieves the Hahn (1998) bound in an experimental design where the propensity score is chosen to minimize this bound. Our results also apply to settings with multiple treatments with possible constraints on treatment, as well as covariate based sampling of a single outcome.