Identification with possibly invalid IVs

This paper proposes a novel identification strategy relying on quasi-instrumental variables (quasi-IVs). A quasi-IV is a relevant but possibly invalid IV because it is not completely exogenous and/or excluded. We show that a variety of models with discrete or continuous endogenous treatment, which are usually identified with an IV - quantile models with rank invariance additive models with homogenous treatment effects, and local average treatment effect models - can be identified under the joint relevance of two complementary quasi-IVs instead. To achieve identification we complement one excluded but possibly endogenous quasi-IV (e.g., ``relevant proxies'' such as previous treatment choice) with one exogenous (conditional on the excluded quasi-IV) but possibly included quasi-IV (e.g., random assignment or exogenous market shocks). In practice, our identification strategy should be attractive since complementary quasi-IVs should be easier to find than standard IVs. Our approach also holds if any of the two quasi-IVs turns out to be a valid IV.