Debiased Machine Learning: Identification, Estimation, and Shape Constraints

We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest θ0 is identified by a moment condition involving a nuisance γ0 that may be high dimensional. We establish conditions under which the Riesz representer α0, which is at the core of DML, is identified, and show that the identification occurs precisely when α0 uniquely optimizes a quadratic functional. This characterization enables us to develop a general estimation procedure for α0 that allows for generic γ0 including those defined by models with endogeneity and encompasses both classical sieves and modern architectures such as deep neural networks. To improve estimation precision and mitigate the curse of dimensionality, we incorporate shape constraints on γ0 by embedding them into a possibly nonlinear parameter space. We illustrate our estimation procedure through simulations and empirical applications.