On the falsification of instrumental variable models for heterogeneous treatment effects

TL;DR

The paper develops a comprehensive framework for falsifying IV models with heterogeneous treatment effects when instruments are discrete. It derives testable implications by transforming an (potentially infinite) collection of exclusion restrictions into finite linear constraints on a distribution over instrument-response types, using an optimal-transport/flow perspective. The binary-instrument case yields sharp inequalities, framed as generalized FOSD conditions linked to nonparametric random utility, and the approach extends naturally to multiple instruments. By coupling A_Z p ≤ r_Z and A_X p = r_X with A_Y p ≤ Ψ (and their multi-instrument analogs), the author provides practical, finite tests for instrument validity that distinguish violations of exclusion from violations of instrument-response restrictions. The methodology unifies transport-theoretic and graph-theoretic ideas to study IV identifiability under heterogeneous effects and offers a concrete path for empirical falsification and sensitivity analysis.

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.

Figures (12)

• Figure 1: Upper bounds on always takers.
• Figure 2:
• Figure 3:
• Figure 4: Sufficiency of the necessary conditions
• Figure 5: General case

Theorems & Definitions (27)

• Definition 2.1
• Definition 2.2
• Remark 2.1
• Definition 2.3: Consistency
• Proposition 2.1: Sharp observable implications of assumption \ref{['Assumption:SelectionModel']}
• Theorem 3.1
• Definition 4.1: Binary relation associated to $R\subset\mathcal{T}_Z$
• Definition 4.2: Common lower contour of $\geq^R$
• Theorem 4.1
• Corollary 4.1: Sharp observable implications of binary monotone instruments