Classification Trees for Heterogeneous Moment-Based Models

Abstract

A basic problem in applied settings is that different parameters may apply to the same model in different populations. We address this problem by proposing a method using moment trees; leveraging the basic intuition of a classification tree, our method partitions the covariate space into disjoint subsets and fits a set of moments within each subspace. We prove the consistency of this estimator and show standard rates of convergence apply post-model selection. Monte Carlo evidence demonstrates the excellent small sample performance and faster-than-parametric convergence rates of the model selection step in two common empirical contexts. Finally, we showcase the usefulness of our approach by estimating heterogeneous treatment effects in a regression discontinuity design in a development setting.