arXiv 10 Apr 2026 · Econometrics
arXiv:2604.09858 · PDF · DOI · OpenAlex · Extracted main text
We describe a new family of coupling designs, extending the basic principle of stratified randomization to experiments with continuous, constrained multivariate, text/image and other irregular treatment spaces. Our approach is to first match units into homogeneous groups, then use Monte Carlo coupling techniques to assign within-group treatments that are highly dispersed over the treatment space. We show that ensuring similar experimental units receive highly dissimilar treatments generically improves estimation efficiency. In particular, the efficiency gains from a coupling design are proportional to the product of dispersion and match quality, where dispersion measures how spread out the treatment assignments are under a given coupling relative to independent randomization. We develop a new spectral analysis, revealing how efficiency depends on a match between the smoothness and shape of the estimator's influence function and the principal directions of a given coupling. We illustrate how coupling designs work in practice using a cash transfer experiment in development economics and a discrete-choice experiment in two-sided marketplaces.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Brenier, Yann (1991) Polar Factorization and Monotone Rearrangement of Vector-Valued Functions | 0.737 | 3 | 3 | 67% |
| 2 | Mérigot, Quentin (2011) A Multiscale Approach to Optimal Transport | 0.737 | 3 | 3 | 67% |
| 3 | Greevy, Robert and Lu, Bo and Silber, Jeffrey H. and Rosenbaum, Paul (2004) Optimal multivariate matching before randomization | 0.644 | 2 | 2 | 100% |
| 4 | Bai, Yuehao and Romano, Joseph P. and Shaikh, Azeem M (2021) Inference in Experiments with Matched Pairs | 0.644 | 2 | 2 | 100% |
| 5 | Cytrynbaum, Max (2023) Optimal Stratification of Survey Experiments self | 0.644 | 2 | 2 | 100% |
| 6 | Harshaw, Christopher and Sävje, Fredrik and Spielman, Daniel A. and… (2024) Balancing covariates in randomized experiments with the Gram–Schmidt Walk design | 0.644 | 2 | 2 | 100% |
| 7 | Harshaw, Christopher and Sävje, Fredrik and Wang, Yitan (2025) A General Design-Based Framework and Estimator for Randomized Experiments | 0.644 | 2 | 2 | 100% |
| 8 | Carlier, Guillaume and Galichon, Alfred and Santambrogio, Filippo (2010) From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport | 0.511 | 2 | 2 | 50% |
| 9 | Thangavelu, Sundaram (1993) Lectures on Hermite and Laguerre Expansions | 0.511 | 2 | 2 | 50% |
| 10 | Bai, Yuehao and Liu, Jizhou and Shaikh, Azeem M. and Tabord-Meehan,… (2023) On the Efficiency of Finely Stratified Experiments | 0.511 | 2 | 1 | 100% |
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