Automatic Debiased Estimation with Machine Learning-Generated Regressors

Abstract

Many parameters of interest in economics and other social sciences depend on generated regressors. Examples in economics include structural parameters in models with endogenous variables estimated by control functions and in models with sample selection, treatment effect estimation with propensity score matching, and marginal treatment effects. More recently, Machine Learning (ML) generated regressors are becoming ubiquitous for these and other applications such as imputation with missing regressors, dimension reduction, including autoencoders, learned proxies, confounders and treatments, and for feature engineering with unstructured data, among others. We provide the first general method for valid inference with regressors generated from ML. Inference with generated regressors is complicated by the very complex expression for influence functions and asymptotic variances. Additionally, ML-generated regressors may lead to large biases in downstream inferences. To address these problems, we propose Automatic Locally Robust/debiased GMM estimators in a general three-step setting with ML-generated regressors. We illustrate our results with treatment effects and counterfactual parameters in the partially linear and nonparametric models with ML-generated regressors. We provide sufficient conditions for the asymptotic normality of our debiased GMM estimators and investigate their finite-sample performance through Monte Carlo simulations.

Tasks

Reproductions