🤖 AI Summary
This study addresses the testability of the exclusion restriction and monotonicity assumptions in instrumental variable models under heterogeneous treatment effects by proposing a unified identification and testing framework. By linking latent response-type restrictions to first-order stochastic dominance and generalized random utility models, the approach uniquely distinguishes between two key forms of assumption violations. Leveraging measure-theoretic arguments and integral aggregation of inequality constraints, the paper derives sharp testable implications for both single and multiple discrete instruments. The method achieves sharp identification in the binary instrument case and offers empirical researchers a novel, implementable pathway for assessing instrumental variable validity.
📝 Abstract
In this paper I derive a set of testable implications for econometric models defined by three assumptions: (i) the existence of strictly exogenous discrete instruments, (ii) restrictions on how the instruments affect adoption of a finite number of treatment types (such as monotonicity), and (iii) the assumption that the instruments only affect outcomes through their effect on treatment adoption (i.e. an exclusion restriction). The testable implications aggregate (via integration) an otherwise potentially infinite set of inequalities that must hold for every measurable subset of the outcome's support. For binary instruments the testable implications are sharp. Furthermore, I propose an implementation that links restrictions on latent response types to a generalization of first-order stochastic dominance and random utility models, allowing to distinguish violations of the exclusion restriction from violations of monotonicity-type assumptions. The testable implications extend naturally to the many instruments case.