arXiv 18 Aug 2026 · Econometrics
arXiv:2608.18057 · PDF · Extracted main text
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.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bai, Yuehao and Romano, Joseph P. and Shaikh, Azeem M (2022) Inference in Experiments with Matched Pairs | 1.000 | 8 | 4 | 100% |
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| 5 | Hahn, Jinyong (1998) On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects | 0.928 | 4 | 3 | 100% |
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| 9 | Li, Xinran and Ding, Peng and Rubin, Donald B (2018) Asymptotic Theory of Rerandomization in Treatment–Control Experiments | 0.737 | 3 | 2 | 100% |
| 10 | Abadie, Alberto and Imbens, Guido W (2006) Large Sample Properties of Matching Estimators for Average Treatment Effects | 0.644 | 2 | 2 | 100% |
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