Proxy Controls and Panel Data

Abstract

We present a flexible approach to the identification and estimation of causal objects in nonparametric, non-separable models with confounding. Key to our analysis is the use of `proxy controls': covariates that do not satisfy a standard `unconfoundedness' assumption but are informative proxies for variables that do. Our analysis applies to both cross-sectional and panel models. Our identification results motivate a simple and `well-posed' nonparametric estimator and we analyze its asymptotic properties. In panel settings, our methods provide a novel approach to the difficult problem of identification with non-separable general heterogeneity and fixed $T$. In panels, observations from different periods serve as proxies for unobserved heterogeneity and our key identifying assumptions follow from restrictions on the serial dependence structure. We apply our methodology to two empirical settings. We estimate causal effects of grade retention on cognitive performance using cross-sectional variation and we estimate a structural Engel curve for food using panel data.Comment: 76 pages, 1 table, 1 figur