Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models

TL;DR

This paper introduces a regularized orthogonal machine learning method for high-dimensional nonlinear semiparametric models, effectively handling nuisance functions with modern machine learning tools and achieving oracle convergence rates.

Contribution

It develops a Neyman-orthogonal Lasso estimator for single index models that accounts for nuisance functions estimated by machine learning, ensuring robust and efficient inference.

Findings

Estimator converges at the oracle rate

Method successfully applied to welfare reform impact analysis

Handles high-dimensional nuisance functions with modern ML tools

Abstract

This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias, preserving the single index property. We then take the loss function to be an indefinite integral of the adjusted moment function with respect to the single index. The proposed Lasso estimator converges at the oracle rate, where the oracle knows the nuisance function and solves only the parametric problem. We demonstrate our method by estimating the short-term heterogeneous impact of Connecticut's Jobs First welfare reform experiment on women's welfare participation decision.