arXiv 13 Feb 2026 · Econometrics
arXiv:2602.12504 · PDF · DOI · OpenAlex · Extracted main text
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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| 5 | Angrist, Joshua D. and Imbens, Guido W. and Rubin, Donald B (1996) Identification of causal effects using instrumental variables | 0.511 | 2 | 1 | 100% |
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| 7 | Balke, Alexander and Pearl, Judea (1997) Bounds on treatment effects from studies with imperfect compliance | 0.405 | 1 | 1 | 100% |
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