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.
Bio: Kenichi Nagasawa is an Assistant Professor of Economics at the University of Warwick. His main research interest lies in theoretical econometrics. He has worked on bootstrap-based inference procedures for estimators with non-standard asymptotics and identification of causal effects using proxy variables. He obtained a Ph.D. in Economics from the University of Michigan in 2019.