Using Forests in Multivariate Regression Discontinuity Designs

Abstract: We discuss estimation and inference of conditional treatment effects in regression discontinuity (RD) designs with multiple scores. In addition to local linear regressions and the minimax-optimal estimator more recently proposed by Imbens and Wager (2019), we argue that two variants of random forests, honest regression forests and local linear forests, should be added to the toolkit of applied researchers working with multivariate RD designs; their validity follows from results in Wager and Athey (2018) and Friedberg et al. (2020). We design a systematic Monte Carlo study with data generating processes built both from functional forms that we specify and from Wasserstein Generative Adversarial Networks that closely mimic the observed data. We find no single estimator dominates across all specifications: (i) local linear regressions perform well in univariate settings, but the common practice of reducing multivariate scores to a univariate one can incur under-coverage, possibly due to vanishing density at the transformed cutoff; (ii) good performance of the minimax-optimal estimator depends on accurate estimation of a nuisance parameter and its current implementation only accepts up to two scores; (iii) forest-based estimators are not designed for estimation at boundary points and are susceptible to finite-sample bias, but their flexibility in modeling multivariate scores opens the door to a wide range of empirical applications, as illustrated by an empirical study of COVID-19 hospital funding with three eligibility criteria.