In this paper we study the problems of estimating heterogeneity in causal effects in experimental or observational studies and conducting inference about the magnitude of the differences in treatment effects across subsets of the population. In applications, our method provides a data-driven approach to determine which subpopulations have large or small treatment effects and to test hypotheses about the differences in these effects. For experiments, our method allows researchers to identify heterogeneity in treatment effects that was not specified in a pre-analysis plan, without concern about invalidating inference due to multiple testing. In most of the literature on supervised machine learning (e.g. regression trees, random forests, LASSO, etc.), the goal is to build a model of the relationship between a unit's attributes and an observed outcome. A prominent role in these methods is played by cross-validation which compares predictions to actual outcomes in test samples, in order to select the level of complexity of the model that provides the best predictive power. Our method is closely related, but it differs in that it is tailored for predicting causal effects of a treatment rather than a unit's outcome. The challenge is that the "ground truth" for a causal effect is not observed for any individual unit: we observe the unit with the treatment, or without the treatment, but not both at the same time. Thus, it is not obvious how to use cross-validation to determine whether a causal effect has been accurately predicted. We propose several novel cross-validation criteria for this problem and demonstrate through simulations the conditions under which they perform better than standard methods for the problem of causal effects. We then apply the method to a large-scale field experiment re-ranking results on a search engine.
