Fisher–Schultz Lecture: Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments, With an Application to Immunization in India

Abstract

We propose strategies to estimate and make inference on key features of heteroge-neous effects in randomized experiments. These key features include best linear predic-tors of the effects using machine learning proxies, average effects sorted by impact groups,and average characteristics of most and least impacted units. The approach is valid inhigh-dimensional settings, where the effects are proxied (but not necessarily consis-tently estimated) by predictive and causal machine learning methods. We post-processthese proxies into estimates of the key features. Our approach is generic; it can beused in conjunction with penalized methods, neural networks, random forests, boostedtrees, and ensemble methods, both predictive and causal. Estimation and inference arebased on repeated data splitting to avoid overfitting and achieve validity. We use quan-tile aggregation of the results across many potential splits, in particular taking mediansof p-values and medians and other quantiles of confidence intervals. We show thatquantile aggregation lowers estimation risks over a single split procedure, and establishits principal inferential properties. Finally, our analysis reveals ways to build provablybetter machine learning proxies through causal learning: we can use the objective func-tions that we develop to construct the best linear predictors of the effects, to obtainbetter machine learning proxies in the initial step. We illustrate the use of both infer-ential tools and causal learners with a randomized field experiment that evaluates acombination of nudges to stimulate demand for immunization in India.