Coupling Designs for Randomized Experiments with Complex Treatments

TL;DR

This paper introduces a new family of coupling designs for randomized experiments with complex treatments, improving estimation efficiency by matching units and dispersing treatments.

Contribution

It extends stratified randomization to irregular treatment spaces using Monte Carlo coupling, with spectral analysis linking efficiency to influence function and coupling shape.

Findings

Coupling designs improve estimation efficiency proportional to dispersion and match quality.

Spectral analysis reveals how efficiency depends on the match between influence function and coupling directions.

Practical applications include a cash transfer experiment and a discrete-choice experiment.

Abstract

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.