Cross-Fitting-Free Debiased Machine Learning with Multiway Dependence

TL;DR

This paper introduces a new asymptotic theory for debiased machine learning estimators in GMM models with multiway dependence, eliminating the need for cross-fitting and enabling valid inference with complex clustering.

Contribution

It develops a cross-fitting-free approach combining Neyman-orthogonal moments with local empirical process techniques for multiway clustered data.

Findings

Valid asymptotic normality achieved without sample splitting.

New maximal inequalities for exchangeable arrays underpin the theory.

Method applicable to complex multiway clustered dependence structures.

Abstract

This paper develops an asymptotic theory for two-step debiased machine learning (DML) estimators in generalised method of moments (GMM) models with general multiway clustered dependence, without relying on cross-fitting. While cross-fitting is commonly employed, it can be statistically inefficient and computationally burdensome when first-stage learners are complex and the effective sample size is governed by the number of independent clusters. We show that valid inference can be achieved without sample splitting by combining Neyman-orthogonal moment conditions with a localisation-based empirical process approach, allowing for an arbitrary number of clustering dimensions. The resulting debiased GMM estimators are shown to be asymptotically linear and asymptotically normal under multiway clustered dependence. A central technical contribution of the paper is the derivation of novel global and local maximal inequalities for general classes of functions of sums of separately exchangeable arrays, which underpin our theoretical arguments and are of independent interest.