Testing Monotonicity of Mean Potential Outcomes in a Continuous Treatment with High-Dimensional Data
Review of Economics and Statistics · 2026 · Yu‐Chin Hsu、Martin Huber、Ying‐Ying Lee、Chu-An Liu
Abstract
Abstract We propose a Cramér–von Mises–type test for testing whether the mean potential outcome given a specific treatment level has a weakly monotonic relationship with the continuous treatment under unconfoundedness. To flexibly control for a possibly high-dimensional set of covariates, our test is based on a double debiased machine learning method. We show that our test controls asymptotic size and is consistent against any fixed alternative. We apply our test to evaluate the Job Corps program and reject a weakly negative relationship between the treatment (hours in academic and vocational training) and labor market performance among relatively low treatment values.