On the Asymptotic Properties of Debiased Machine Learning Estimators

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Abstract: This paper studies the properties of debiased machine learning (DML) estimators under a novel asymptotic framework, offering insights for improving estimator performance in applications. DML is an estimation method suited to economic models in which 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 the two alternative versions of DML estimators, namely, 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 the simulation results of their relative performance. Additionally, this paper provides guidance for improving DML2 performance in applications.