EconBase
← All papers

The Limits of Experimental Design: Covariate Balance Beyond Low Dimension

Max Cytrynbaum

arXiv 18 Aug 2026 · Econometrics

arXiv:2608.18057 · PDF · Extracted main text

Abstract

We study how fast experimental designs can approach the semiparametric efficiency bound in finite samples, as measured by the excess variance of unadjusted treatment effect estimation. We prove an impossibility theorem: under weak conditions, no design can approach the variance bound uniformly over smooth outcome models unless covariate dimension $d \ll \log n$. Even in experiments with thousands of units, this permits only a handful of covariates. Motivated by this, we propose new designs based on discrepancy minimization that instead attempt to control imbalances over restricted-complexity nonparametric function classes. Such designs achieve fast rates to their corresponding restricted efficiency targets, permitting $d \ll n$ covariates in an additive nonparametric specification. They can also be combined with matching to protect against unmodeled outcome variation. In simulations calibrated to 12 published experiments, our designs reduce variance relative to matched pairs randomization in every empirical setting.

Citation extraction

64
references
122
in-text mentions
64
distinct cited
2
self-citations
12,093
main-text words

appendix boundary found by appendix_command · 34% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Bai, Yuehao and Romano, Joseph P. and Shaikh, Azeem M (2022) Inference in Experiments with Matched Pairs1.00084100%
2Kallus, Nathan (2018) Optimal A Priori Balance in the Design of Controlled Experiments1.00054100%
3Bai, Yuehao and Liu, Jizhou and Shaikh, Azeem M. and Tabord-Meehan,… (2026) On the Efficiency of Highly Stratified Experiments1.00053100%
4Bansal, Nikhil and Dadush, Daniel and Garg, Shashwat and Lovett, Sha… (2019) The Gram–Schmidt Walk: A Cure for the Banaszczyk Blues0.9416383%
5Hahn, Jinyong (1998) On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects0.92843100%
6Cytrynbaum, Max (2026) Fine Stratification of Survey Experiments self0.8558662%
7Harshaw, Christopher and Sävje, Fredrik and Spielman, Daniel A. and… (2024) Balancing Covariates in Randomized Experiments with the Gram–Schmidt Walk Design0.85113562%
8Harshaw, Christopher Robert (2021) Algorithmic Advances for the Design and Analysis of Randomized Experiments0.8434375%
9Li, Xinran and Ding, Peng and Rubin, Donald B (2018) Asymptotic Theory of Rerandomization in Treatment–Control Experiments0.73732100%
10Abadie, Alberto and Imbens, Guido W (2006) Large Sample Properties of Matching Estimators for Average Treatment Effects0.64422100%

Showing the top 10 of 64 scored citations.