Doubly Robust Inference in Causal Latent Factor Models

TL;DR

This paper proposes a new doubly robust estimator for average treatment effects in high-dimensional settings with unobserved confounding, combining outcome imputation, inverse probability weighting, and cross-fitting, with proven theoretical guarantees.

Contribution

It introduces a novel estimator that integrates multiple techniques for causal inference under unobserved confounding, with finite-sample and asymptotic guarantees.

Findings

Estimator converges to a mean-zero Gaussian distribution.

Simulation results validate the theoretical properties.

Method performs well in large, data-rich environments.

Abstract

This article introduces a new estimator of average treatment effects under unobserved confounding in modern data-rich environments featuring large numbers of units and outcomes. The proposed estimator is doubly robust, combining outcome imputation, inverse probability weighting, and a novel cross-fitting procedure for matrix completion. We derive finite-sample and asymptotic guarantees, and show that the error of the new estimator converges to a mean-zero Gaussian distribution at a parametric rate. Simulation results demonstrate the relevance of the formal properties of the estimators analyzed in this article.