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Toggling the Defiers to Relax Monotonicity: The Difference-in-Instrumental-Variables Estimand

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  • Johann Caro-Burnett

Abstract

Standard instrumental variables (IV) methods identify a Local Average Treatment Effect under monotonicity, which rules out defiers. In many empirical environments, however, distinct instruments may induce heterogeneous and even opposing behavioral responses. This paper introduces the Difference-in-Instrumental-Variables (DIIV) estimand, which exploits two instruments with opposing compliance patterns to recover a point-identified and behaviorally interpretable causal effect without imposing monotonicity. The estimand yields a convex combination of the marginal treatment effects on compliers and defiers, with weights reflecting differential shifts in treatment take-up across instruments. When monotonicity holds, DIIV coincides with the standard IV estimand. The approach can be implemented using simple linear transformations and standard two-stage least squares procedures. Applications using replication data illustrate its applicability in practice.

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  • Johann Caro-Burnett, 2026. "Toggling the Defiers to Relax Monotonicity: The Difference-in-Instrumental-Variables Estimand," Papers 2602.12504, arXiv.org.
    • Handle: RePEc:arx:papers:2602.12504
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