Testing Monotonicity of Mean Potential Outcomes in a Continuous Treatment with High-Dimensional Data

TL;DR

This paper introduces a novel statistical test for assessing the monotonic relationship between a continuous treatment and mean potential outcomes, using high-dimensional covariates and machine learning techniques, with theoretical guarantees and empirical validation.

Contribution

It develops a Cramér-von Mises-type test combined with a double debiased machine learning estimator to handle high-dimensional covariates in continuous treatment settings.

Findings

Test controls asymptotic size effectively.

Test is consistent against fixed alternatives.

Empirical application rejects weak negative relationship.

Abstract

While most treatment evaluations focus on binary interventions, a growing literature also considers continuously distributed treatments. We propose a Cram\'{e}r-von Mises-type test for testing whether the mean potential outcome given a specific treatment has a weakly monotonic relationship with the treatment dose under a weak unconfoundedness assumption. In a nonseparable structural model, applying our method amounts to testing monotonicity of the average structural function in the continuous treatment of interest. To flexibly control for a possibly high-dimensional set of covariates in our testing approach, we propose a double debiased machine learning estimator that accounts for covariates in a data-driven way. We show that the proposed test controls asymptotic size and is consistent against any fixed alternative. These theoretical findings are supported by the Monte-Carlo simulations. As an empirical illustration, we apply our test to the Job Corps study and reject a weakly negative relationship between the treatment (hours in academic and vocational training) and labor market performance among relatively low treatment values.