A Machine-Learning-Compatible Omnibus Test for Treatment Effect Heterogeneity

Abstract

This study proposes a formal, computationally efficient nonparametric omnibus test for treatment-effect heterogeneity that is compatible with a broad class of estimators, including modern machine-learning methods. The test is designed for settings in which identification can rely on high-dimensional controls while heterogeneity is assessed with respect to a low-dimensional subset of covariates. We derive the test statistic's asymptotic null distribution and develop a bootstrap procedure that is efficient because it avoids re-estimating nuisance parameters in each iteration. The testing approach applies to multiple empirical designs, including randomized experiments, selection-on-observables, difference-in-differences, and instrumental-variables settings. Monte Carlo simulations show that the test attains near-nominal size under the null and exhibits good power against heterogeneous alternatives. We further illustrate the procedure using two empirical applications on retirement savings and trade liberalization.