Automatic debiased machine learning and sensitivity analysis for sample selection models

TL;DR

This paper introduces a robust method for causal inference in sample selection models using debiased machine learning and sensitivity analysis, improving stability and interpretability over traditional approaches.

Contribution

It extends the Riesz representation framework to sample selection, providing a stable estimator and a transparent bias decomposition, with practical advantages over existing methods.

Findings

ForestRiesz estimator outperforms traditional methods in simulations.

Application reveals larger gender wage gap estimates when accounting for sample selection.

Sensitivity analysis shows results are robust to unobserved confounding.

Abstract

In this paper, we extend the Riesz representation framework to causal inference under sample selection, where both treatment assignment and outcome observability are non-random. Formulating the problem in terms of a Riesz representer enables stable estimation and a transparent decomposition of omitted variable bias into three interpretable components: a data-identified scale factor, outcome confounding strength, and selection confounding strength. For estimation, we employ the ForestRiesz estimator, which accounts for selective outcome observability while avoiding the instability associated with direct propensity score inversion. We assess finite-sample performance through a simulation study and show that conventional double machine learning approaches can be highly sensitive to tuning parameters due to their reliance on inverse probability weighting, whereas the ForestRiesz estimator delivers more stable performance by leveraging automatic debiased machine learning. In an empirical application to the gender wage gap in the U.S., we find that our ForestRiesz approach yields larger treatment effect estimates than a standard double machine learning approach, suggesting that ignoring sample selection leads to an underestimation of the gender wage gap. Sensitivity analysis indicates that implausibly strong unobserved confounding would be required to overturn our results. Overall, our approach provides a unified, robust, and computationally attractive framework for causal inference under sample selection.