Working Paper: NBER ID: w22976
Authors: Sam Asher; Denis Nekipelov; Paul Novosad; Stephen P. Ryan
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.
Keywords: Classification Trees; Heterogeneous Models; Moment-Based Models; Empirical Research
JEL Codes: C14; C18; C51; C52; O12; O18
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| bootstrap procedure (Y20) | valid confidence sets for estimated parameters (C51) |
| classification trees (C38) | control for unobserved heterogeneity (C21) |
| complexity of unobserved heterogeneity grows sublinearly (C21) | ensures classification trees do not affect uniform convergence (C38) |
| method of using moment trees (C69) | estimation of heterogeneous treatment effects (C21) |
| method partitions the covariate space (C21) | captures varying relationships between outcome variable and covariates (C34) |
| method captures varying relationships (C30) | leads to more accurate estimates of treatment effects (C51) |
| method can uncover significant treatment effects (C90) | improves estimation of heterogeneous treatment effects (C21) |