Treatment Effect Estimation with Noisy Conditioning Variables

TL;DR

This paper introduces a novel method for estimating treatment effects using noisy proxy variables for unobserved confounders, enabling causal inference even with imperfect measurements.

Contribution

It proposes a new identification strategy leveraging proxy variables and exclusion restrictions to recover causal effects with noisy confounders.

Findings

Established asymptotic distributional results for estimators.

Demonstrated empirical application estimating college attendance effects.

Showed the method's effectiveness with noisy confounding data.

Abstract

I develop a new identification strategy for treatment effects when noisy measurements of unobserved confounding factors are available. I use proxy variables to construct a random variable conditional on which treatment variables become exogenous. The key idea is that, under appropriate conditions, there exists a one-to-one mapping between the distribution of unobserved confounding factors and the distribution of proxies. To ensure sufficient variation in the constructed control variable, I use an additional variable, termed excluded variable, which satisfies certain exclusion restrictions and relevance conditions. I establish asymptotic distributional results for semiparametric and flexible parametric estimators of causal parameters. I illustrate empirical relevance and usefulness of my results by estimating causal effects of attending selective college on earnings.