Double/Debiased CoCoLASSO of Treatment Effects with Mismeasured High-Dimensional Control Variables

TL;DR

This paper introduces a novel estimator for treatment effects in high-dimensional models with measurement error, extending the double/debiased machine learning framework to correct for errors without prior covariance knowledge.

Contribution

We develop the Double/Debiased CoCoLASSO estimator that corrects for measurement error in high-dimensional settings, providing theoretical guarantees and practical implementation methods.

Findings

Estimator achieves $\,\sqrt{N}$-consistency and asymptotic normality.

Method performs robustly across various measurement error levels.

Covariance-oblivious approach nearly matches known-error efficiency.

Abstract

We develop an estimator for treatment effects in high-dimensional settings with additive measurement error, a prevalent challenge in modern econometrics. We introduce the Double/Debiased Convex Conditioned LASSO (Double/Debiased CoCoLASSO), which extends the double/debiased machine learning framework to accommodate mismeasured covariates. Our principal contributions are threefold. (1) We construct a Neyman-orthogonal score function that remains valid under measurement error, incorporating a bias correction term to account for error-induced correlations. (2) We propose a method of moments estimator for the measurement error variance, enabling implementation without prior knowledge of the error covariance structure. (3) We establish the $\sqrt{N}$-consistency and asymptotic normality of our estimator under general conditions, allowing for both the number of covariates and the magnitude of measurement error to increase with the sample size. Our theoretical results demonstrate the estimator's efficiency within the class of regularized high-dimensional estimators accounting for measurement error. Monte Carlo simulations corroborate our asymptotic theory and illustrate the estimator's robust performance across various levels of measurement error. Notably, our covariance-oblivious approach nearly matches the efficiency of methods that assume known error variance.