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

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).