On the Asymptotic Properties of Debiased Machine Learning Estimators

TL;DR

This paper analyzes the asymptotic behavior of debiased machine learning estimators, revealing that DML2 outperforms DML1 in bias and mean squared error under a new framework, and offers practical guidance for enhancement.

Contribution

It introduces a novel asymptotic framework that distinguishes DML2 from DML1, demonstrating DML2's superior asymptotic properties and providing strategies for improving DML2 in practice.

Findings

DML2 asymptotically dominates DML1 in bias and MSE.

Weaker conditions than previous methods are sufficient for standard asymptotic properties.

Guidance is provided for optimizing DML2 performance.

Abstract

This paper studies the properties of debiased machine learning (DML) estimators under a novel asymptotic framework, offering insights for improving the performance of these estimators in applications. DML is an estimation method suited to economic models where the parameter of interest depends on unknown nuisance functions that must be estimated. It requires weaker conditions than previous methods while still ensuring standard asymptotic properties. Existing theoretical results do not distinguish between two alternative versions of DML estimators, DML1 and DML2. Under a new asymptotic framework, this paper demonstrates that DML2 asymptotically dominates DML1 in terms of bias and mean squared error, formalizing a previous conjecture based on simulation results regarding their relative performance. Additionally, this paper provides guidance for improving the performance of DML2 in applications.