Max Cytrynbaum (Yale)

Title

Coupling Designs for Randomized Experiments with Complex Treatments

Abstract

In this paper we introduce a new family of coupling designs, which extend the basic principle of stratified randomization to experiments with continuous, constrained multivariate, text/image and otherwise irregular treatment spaces. Our basic 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 coupling design randomization are proportional to dispersion times match quality, where dispersion measures how spread out the samples are under a given coupling relative to iid randomization. We develop a novel spectral analysis, which shows that estimation efficiency depends on a suitable match between the smoothness and shape of the estimator's influence function and the "principal directions'' of a given coupling. We apply this analysis to compare couplings such as Latin hypercube sampling, randomly shifted lattice designs, and the Gaussian copula. We show how​ coupling designs can be applied to randomize efficiently in cash transfer experiments in development economics, as well as discrete-choice experiments in two-sided marketplaces.