Develop Double/Debiased Machine Learning for Instrumental Variable Quantile Regression (IVQR)

Develop a double/debiased machine learning procedure for instrumental variable quantile regression (IVQR) models that enables valid estimation and inference on structural quantile functions in the presence of endogeneity and high-dimensional nuisance components. Specifically, construct Neyman-orthogonal scores and a DML algorithm that can accommodate flexible machine learning learners for the conditional quantile and propensity functions without compromising asymptotic normality or confidence interval validity for the structural quantile parameters.

Background

The book introduces the IV quantile model, which specifies the outcome as Y = f(D, X, E) with the structural function f(D, X, ·) strictly increasing and the latent shock E uniformly distributed, thus capturing structural quantiles in endogenous settings. Identification relies on testable restrictions such as P[Y ≤ f(D, X, u) | Z, X] = u, but existing methods typically do not integrate modern machine learning in a way that preserves valid inference.

Double/debiased machine learning (DML) has been developed throughout the book for a range of partially linear and interactive models, leveraging Neyman-orthogonal scores and cross-fitting to allow high-dimensional nuisance estimation. Extending DML to IVQR would permit flexible learners to estimate the conditional quantile and instrument-related functions while maintaining valid inference on structural quantile parameters under endogeneity—an important and currently unresolved challenge.