Treatment Effect Estimation with Noisy Conditioning Variables

Understand

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.