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Generalized instrumental inequalities: testing the instrumental variable independence assumption

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  • Désiré Kédagni
  • Ismael Mourifié

Abstract

SummaryThis paper proposes a new set of testable implications for the instrumental variable independence assumption for discrete treatment, but unrestricted outcome and instruments: generalized instrumental inequalities. When outcome and treatment are both binary, but instruments are unrestricted, we show that the generalized instrumental inequalities are necessary and sufficient to detect all observable violations of the instrumental variable independence assumption. To test the generalized instrumental inequalities, we propose an approach combining a sample splitting procedure and an inference method for intersection bounds. This idea allows one to easily implement the test using existing Stata packages. We apply our proposed strategy to assess the validity of the instrumental variable independence assumption for various instruments used in the returns to college literature.

Suggested Citation

  • Désiré Kédagni & Ismael Mourifié, 2020. "Generalized instrumental inequalities: testing the instrumental variable independence assumption," Biometrika, Biometrika Trust, vol. 107(3), pages 661-675.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:3:p:661-675.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa003
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    Cited by:

    1. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
    2. Shengjie Hong & Yu-Chin Hsu & Yuanyuan Wan, 2023. "Subvector inference for Varying Coefficient Models with Partial Identification," Working Papers tecipa-756, University of Toronto, Department of Economics.
    3. Ban, Kyunghoon & Kedagni, Desire, 2020. "Nonparametric Bounds on Treatment Effects with Imperfect Instruments," ISU General Staff Papers 202010120700001113, Iowa State University, Department of Economics.
    4. Lixiong Li & D'esir'e K'edagni & Ismael Mourifi'e, 2020. "Discordant Relaxations of Misspecified Models," Papers 2012.11679, arXiv.org, revised Dec 2022.
    5. Chaoran Chen & Zhigang Feng & Jiaying Gu, 2022. "Health, Health Insurance, and Inequality," Working Papers tecipa-730, University of Toronto, Department of Economics.
    6. Zhewen Pan & Zhengxin Wang & Junsen Zhang & Yahong Zhou, 2024. "Marginal treatment effects in the absence of instrumental variables," Papers 2401.17595, arXiv.org.
    7. Zhenting Sun & Kaspar Wuthrich, 2022. "Pairwise Valid Instruments," Papers 2203.08050, arXiv.org, revised Jan 2024.

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