Using Nonparametric Regression Trees to Estimate Different Forms of Heterogeneous Treatment Effects

Graham Buhrman, Xiangyi Liao, Jee-Seon Kim

DOI: 10.64028/pulr698375

Keywords: nonparametric regression, causal inference, heterogeneous treatment effects, Bayesian additive regression trees

TL;DR: This chapter explores how different nonparametric regression tree methods recover heterogeneous treatment effects following a variety of functional forms.

Abstract:

Interest in heterogeneous treatment effects has substantially increased in recent years. Treatment het-
erogeneity describes the case when individuals are differentially affected by an intervention or exposure
according to their characteristics, and accurate estimation of these differential effects can support cost-
effectiveness evaluations of interventions and inform policy decisions about which individuals or groups
will benefit most from an intervention. However, the functional form of heterogeneous treatment effects
can vary and is typically unknown to researchers. For instance, the effect of math tutoring on students’
test scores might vary across students’ prior math scores as a negative quadratic function, meaning that
students who benefit most do not have particularly high or low prior scores. Such “Goldilocks” effects and
other complex treatment functions have motivated the use of nonparametric regression techniques which
make few or no assumptions about the true data generating model. While previous studies have proposed
and compared the performance of different nonparametric methods across different datasets, few studies
have explicitly explored how the complexity of the functional form of the heterogeneous treatment effects
impacts the performance of nonparametric regression tree methods. We initially sought out to explore
how the monotonicity of the treatment effect function impacted performance, but present findings that
pertain to the overall complexity of the treatment effect function. In these proceedings, we 1) explain why
complexity of the treatment effect function is a relevant and important consideration and 2) provide results
from a preliminary simulation study which examines how variation in the functional form of treatment
effects impacts the accuracy of popular nonparametric regression tree approaches in the context of clustered
data with a non-random treatment assignment. We conclude with a discussion of the limitations of the
study and possible avenues for future research. Our results suggest that functional complexity, rather than
monotonicity, plays a more critical role in the accuracy of nonparametric treatment effect estimators.

Submission Number: 15