On the falsification of instrumental variable models for heterogeneous treatment effects

TL;DR

This paper derives testable implications for instrumental variable models with heterogeneous treatment effects, focusing on assumptions like exogeneity, monotonicity, and exclusion, and provides methods to detect violations.

Contribution

It introduces a set of testable inequalities for IV models with multiple assumptions and links them to stochastic dominance and utility models for better violation detection.

Findings

Sharp implications for binary instruments.

Method to distinguish violations of exclusion from monotonicity.

Extensions to models with many instruments.

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.