SMU SOE Seminar Series (February 3, 2026): Treatment Effect Estimation with Noisy Conditioning Variables

TOPIC:

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. I show that, under appropriate conditions, there exists a one-to-one mapping between the distribution of unobserved confounding factors and the distribution of proxies, which in turn implies that holding constant the proxy distribution controls for the unobserved confounding factors. 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 grade retention on academic performance.

Keywords: Treatment Effects, L2-completeness, Control Functions, Non-Classical Measurement Errors.

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