Locally Robust Semiparametric Estimation

TL;DR

This paper develops a general framework for constructing orthogonal moment functions in GMM that are robust to model selection and regularization bias, especially useful for machine learning first steps in high-dimensional settings.

Contribution

It introduces a method to create orthogonal moments using nonparametric influence functions, enabling debiased estimation of complex high-dimensional parameters.

Findings

Provides a general construction of orthogonal moments for GMM.

Develops debiased machine learning estimators for high-dimensional functionals.

Characterizes double robustness and regularity conditions for inference.

Abstract

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where moment conditions have zero derivative with respect to first steps. We show that orthogonal moment functions can be constructed by adding to identifying moments the nonparametric influence function for the effect of the first step on identifying moments. Orthogonal moments reduce model selection and regularization bias, as is very important in many applications, especially for machine learning first steps. We give debiased machine learning estimators of functionals of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that adding to identifying moments the nonparametric influence function provides a general construction of orthogonal moments, including regularity conditions, and show that the nonparametric influence function is robust to additional unknown functions on which it depends. We give a general approach to estimating the unknown functions in the nonparametric influence function and use it to automatically debias estimators of functionals of high dimensional conditional location learners. We give a variety of new doubly robust moment equations and characterize double robustness. We give general and simple regularity conditions and apply these for asymptotic inference on functionals of high dimensional regression quantiles and dynamic discrete choice parameters with high dimensional state variables.