Title: Identification and Estimation of Joint Treatment Effects with Instrumental Variables
Abstract- Over the last twenty years, a literature spanning several fields of applied statistics has analyzed how to identify and estimate causal effects of a nonrandomized treatment when a instrumental variable (IV) is available. But researchers often have multiple treatments and want to estimate either the direct or joint effect of these treatments. This paper introduces a set of novel estimands for instrumental variables with multiple treatments and multiple instruments. These estimands are similar to previous IV estimands as they are ``local’’ to strata defined by the joint compliance status across the treatments. Furthermore, I show that these estimands are nonparametrically identified under standard instrumental variable assumptions. The paper further develops nonparametric estimators for these quantities and assess their performance relative to classic parametric approaches like two-stage least squares. Finally, I demonstrate the method through an empirical application to a voter mobilization field experiment with both a telephone and in-person treatments.