Estimating Treatment Effects With Limited Exogeneity: A Machine Learning Approach to Selection Bias

Abstract

This paper presents a novel method for estimating treatment effects in cases where prior knowledge of the exogeneity of the treatment variable is limited. We employ a machine learning technique, double selection via Lasso, to identify a robust set of control variables without requiring prior assumptions about their specific identities or functional forms. Our approach then leverages the principle that, under certain conditions, the selection on observables can provide bounds on the selection bias from unobservables. To illustrate the effectiveness of this method, we apply it to an empirical analysis examining the impact of legalized abortion on crime rates.