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Treatment Effect Estimation with Noisy Conditioning Variables

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  • Kenichi Nagasawa

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.

Suggested Citation

  • Kenichi Nagasawa, 2018. "Treatment Effect Estimation with Noisy Conditioning Variables," Papers 1811.00667, arXiv.org, revised Sep 2022.
  • Handle: RePEc:arx:papers:1811.00667
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