Susan Athey, and Guido W. Imbens, “Recursive Partitioning for Heterogeneous Causal Effects”, December 2015.
In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies, and for conducting hypothesis tests about the magnitude of the differences in treatment effects across subsets of the population. We provide a datadriven approach to partition the data into subpopulations which differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even in samples with many covariates relative to the sample size, and without “sparsity” assumptions. To accomplish this, we propose an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criteria focus on improving the prediction of treatment effects conditional on covariates, anticipating that bias will be eliminated by honest estimation, but also accounting for the change in the variance of treatment effect estimates within each subpopulation as a result of the split. We also address the challenge that the “ground truth” for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that honest estimation can result in substantial improvements in coverage of confidence intervals, where our method attains nominal coverage rates, without much sacrifice in terms of fitting treatment effects.
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