Instrumented Common Confounding

Abstract: Causal inference is difficult in the presence of unobserved confounders. We introduce the instrumented common confounding (ICC) approach to (nonparametrically) identify causal effects with instruments, which are exogenous only conditional on some unobserved common confounders. The ICC approach is most useful in rich observational data with multiple sources of unobserved confounding, where instruments are at most exogenous conditional on some unobserved common confounders. Suitable examples of this setting are various identification problems in the social sciences, nonlinear dynamic panels, and problems with multiple endogenous confounders. The ICC identifying assumptions are closely related to those in mixture models, negative control and IV. Compared to mixture models [Bonhomme et al., 2016], we require less conditionally independent variables and do not need to model the unobserved confounder. Compared to negative control [Cui et al., 2020], we allow for non-common confounders, with respect to which the instruments are exogenous. Compared to IV [Newey and Powell, 2003], we allow instruments to be exogenous conditional on some unobserved common confounders, for which a set of relevant observed variables exists. We prove point identification with outcome model and alternatively first stage restrictions. We provide a practical step-by-step guide to the ICC model assumptions and present the causal effect of education on income as a motivating example.