Where to Experiment? Site Selection Under Distribution Shift via Optimal Transport and Wasserstein DRO

How should researchers select experimental sites when the deployment population differs from observed data? I formulate the problem of experimental site selection as an optimal transport problem, developing methods to minimize downstream estimation error by choosing sites that minimize the Wasserstein distance between population and sample covariate distributions. I develop new theoretical upper bounds on PATE and CATE estimation errors, and show that these different objectives lead to different site selection strategies. I extend this approach by using Wasserstein Distributionally Robust Optimization to develop a site selection procedure robust to adversarial perturbations of covariate information: a specific model of distribution shift. I also propose a novel data-driven procedure for selecting the uncertainty radius the Wasserstein DRO problem, which allows the user to benchmark robustness levels against observed variation in their data. Simulation evidence, and a reanalysis of a randomized microcredit experiment in Morocco (Cr\'epon et al.), show that these methods outperform random and stratified sampling of sites when covariates have prognostic R-squared > .5, and alternative optimization methods i) for moderate-to-large size problem instances ii) when covariates are moderately informative about treatment effects, and iii) under induced distribution shift.