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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.12504 |
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| _version_ | 1866918335525945344 |
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| author | Caro-Burnett, Johann |
| author_facet | Caro-Burnett, Johann |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12504 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toggling the Defiers to Relax Monotonicity: The Difference-in-Instrumental-Variables Estimand Caro-Burnett, Johann Econometrics 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. |
| title | Toggling the Defiers to Relax Monotonicity: The Difference-in-Instrumental-Variables Estimand |
| topic | Econometrics |
| url | https://arxiv.org/abs/2602.12504 |