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Identification of Nonseparable Triangular Models With Discrete Instruments

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  • Xavier D'Haultfœuille
  • Philippe Février

Abstract

We study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable. Using group and dynamical systems theories, we show that full identification can be achieved under strong exogeneity of the instrument and a dual monotonicity condition, even if the instrument is discrete. When identified, the model is also testable. Our results therefore highlight the identifying power of strong exogeneity when combined with monotonicity restrictions.

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  • Xavier D'Haultfœuille & Philippe Février, 2015. "Identification of Nonseparable Triangular Models With Discrete Instruments," Econometrica, Econometric Society, vol. 83(3), pages 1199-1210, May.
    • Handle: RePEc:wly:emetrp:v:83:y:2015:i:3:p:1199-1210
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    Cited by:

    1. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    2. Huang, Liquan & Khalil, Umair & Yıldız, Neşe, 2019. "Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables," Journal of Econometrics, Elsevier, vol. 208(2), pages 346-366.
    3. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    4. Wüthrich, Kaspar, 2019. "A closed-form estimator for quantile treatment effects with endogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 219-235.
    5. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    6. Chen, Songnian & Khan, Shakeeb & Tang, Xun, 2024. "Endogeneity in weakly separable models without monotonicity," Journal of Econometrics, Elsevier, vol. 238(1).

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