Efficient Estimation of Distributional Treatment Effects with Endogenous Treatments: A Machine Learning Approach

We introduce a novel, robust estimator for the Distributional Instrumental Variable Local Average Treatment Effect (D-IV-LATE) when the treatment is endogenous and an instrumental variable is available. Understanding the full distributional impact of policies or interventions, rather than just average effects, is crucial for informed decision-making. Yet existing methods often assume exogeneity or are not designed for distributional parameters in an IV context. We bridge this gap by extending the double/debiased machine learning (DML) framework to estimate the D-IV-LATE. Our proposed estimator leverages flexible machine learning models to control for high-dimensional covariates whilst achieving Neyman orthogonality. This ensures robustness to regularisation bias in the nuisance function estimates. We establish the asymptotic normality of our D-IV-LATE estimator. A Monte Carlo simulation study demonstrates its excellent finite-sample performance, showing low bias and root mean squared error. We illustrate the practical utility of our method with an empirical application, analysing the distributional effects of 401(k) participation on net financial assets using data from the Survey of Income and Program Participation. The results reveal heterogeneous impacts across the wealth distribution that would be masked by a simple average effect estimate.