Econometric Inference with Machine-Learned Proxies: Partial Identification via Data Combination

TL;DR

This paper introduces a new econometric framework for inference with machine-learned proxies, leveraging data combination and optimal transport to address biases without requiring strict ML assumptions.

Contribution

It develops a partial identification approach that uses two datasets and optimal transport, avoiding the need for ML consistency or validation samples.

Findings

Reliable size control demonstrated in Monte Carlo simulations

Provides informative confidence sets across various predictive scenarios

Does not require restrictive assumptions on ML procedures

Abstract

Empirical researchers increasingly use upstream machine-learning (ML) methods to construct proxies for latent target variables from complex, unstructured data. A naive plug-in use of such proxies in downstream econometric models, however, can lead to biased estimation and invalid inference. This paper develops a framework for partial identification and inference in general moment models with ML-generated proxies. Our approach does not require restrictive assumptions on the upstream ML procedure, such as consistency or known convergence rates, nor does it require a complete validation sample containing all variables used in the downstream analysis. Instead, we assume access to two datasets: a downstream sample containing observed covariates and the proxy, and an auxiliary validation sample containing joint observations on the proxy and its target variable. We treat the proxy as a linking variable between these two samples, rather than as a literal noisy substitute for the latent target variable. Building on this idea, we develop a sharp identification strategy based on an unconditional optimal transport characterization and an inference procedure that controls asymptotic size using analytical critical values without resampling. Monte Carlo simulations show reliable size control and informative confidence sets across a range of predictive-accuracy scenarios.