The Generalized Falsification Adaptive Set for Violations of the Exclusion Restriction and Exogeneity

Abstract

The falsification adaptive set (FAS) as proposed by Masten and Poirier (2021) provides an identified set for a treatment effect when the baseline model is falsified, assuming invalid instruments violate exclusion only. We show that whether an invalid instrument is a confounder or collider has important consequences: incorrect treatment can cause the FAS to exclude the true parameter. We derive pattern-specific falsification adaptive sets for each combination of violations and propose a generalized FAS as their union, containing the true parameter value if any instrument is valid. We illustrate our results with the roads and trade application of Duranton et al. (2014).