arXiv 1 Jul 2026 · Econometrics
arXiv:2607.01429 · PDF · DOI · OpenAlex · Extracted main text
This article introduces an empirical condition for the nonparametric point-identification of multivariate instrumental variable models with continuous endogenous variables using binary instruments. Verifying this condition can confirm point-identification in settings in which traditional approaches are not applicable. In particular, it shows that nonlinear instrumental variable models with general heterogeneity can be point-identified with only a binary instrument. This generalizes existing identification results which either restrict the unobserved heterogeneity substantially or require the instrument to have a large support. The main assumption on the instrumental variable model is cyclic monotonicity of its first stage, a multivariate generalization of the classical rank-invariance assumption for univariate models. Asymptotic convergence results for the empirical observable distributions are derived that allow to check the condition in practice. The identification rests on a fixed-set convergence result of cyclically monotone maps between quasi-concave functions. The corrigendum corrects the proof of Lemma 1. The proof given there incorrectly identifies preservation of distributional level sets with preservation of the underlying probability measure via Brenier maps. We replace that argument by one based on inverse Brenier maps, which play the role of multivariate ranks. The corrected argument applies to a different but significantly more flexible class of distributions than the quasi-concave class considered in the original paper. In particular, it allows for smooth non-quasi-concave and multimodal densities on compact supports, provided the associated rank fixed set satisfies a nondegeneracy condition. Moreover, it is generically satisfied for smooth parmetric classes of distributions.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | d'Haultfœuille, Xavier and Février, Philippe (2015) Identification of nonseparable triangular models with discrete instruments | 1.000 | 6 | 4 | 100% |
| 2 | Imbens, Guido W and Newey, Whitney K (2009) Identification and estimation of triangular simultaneous equations models without additivity | 1.000 | 6 | 4 | 100% |
| 3 | Matzkin, Rosa L (2003) Nonparametric estimation of nonadditive random functions | 0.950 | 7 | 3 | 86% |
| 4 | Hoderlein, Stefan and Holzmann, Hajo and Kasy, Maximilian and Meiste… (2017) Corrigendum: Instrumental variables with unrestricted heterogeneity and continuous treatment | 0.928 | 4 | 3 | 100% |
| 5 | Villani, Cédric (2003) Topics in Optimal Transportation | 0.874 | 9 | 4 | 67% |
| 6 | Torgovitsky, Alexander (2015) Identification of nonseparable models using instruments with small support | 0.855 | 24 | 9 | 62% |
| 7 | Shi, Xiaoxia and Shum, Matthew and Song, Wei (2018) Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity | 0.811 | 4 | 2 | 100% |
| 8 | Rockafellar, R Tyrrell (1997) Convex Analysis. Princeton landmarks in mathematics | 0.737 | 4 | 2 | 75% |
| 9 | Duclos, Jean-Yves and Sahn, David E and Younger, Stephen D (2006) Robust multidimensional poverty comparisons | 0.737 | 3 | 2 | 100% |
| 10 | Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R (1995) Microeconomic theory | 0.737 | 3 | 2 | 100% |
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