  We discuss estimating conditional treatment effects in regression
discontinuity designs with multiple scores. While local linear regressions have
been popular in settings where the treatment status is completely described by
one running variable, they do not easily generalize to empirical applications
involving multiple treatment assignment rules. In practice, the multivariate
problem is usually reduced to a univariate one where using local linear
regressions is suitable. Instead, we propose a forest-based estimator that can
flexibly model multivariate scores, where we build two honest forests in the
sense of Wager and Athey (2018) on both sides of the treatment boundary. This
estimator is asymptotically normal and sidesteps the pitfalls of running local
linear regressions in higher dimensions. In simulations, we find our proposed
estimator outperforms local linear regressions in multivariate designs and is
competitive against the minimax-optimal estimator of Imbens and Wager (2019).
The implementation of this estimator is simple, can readily accommodate any
(fixed) number of running variables, and does not require estimating any
nuisance parameters of the data generating process.

Econometrics