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Testing Generalized Regression Monotonicity

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Abstract

We propose a test for a generalized regression monotonicity (GRM) hypothesis. The GRM hypothesis is the sharp testable implication of the monotonicity of certain latent structures, as we show in this paper. Examples include the monotone instrumental variable assumption of Manski and Pepper (2000) and the monotonicity of the conditional mean function when only interval data are available for the dependent variable. These instances of latent monotonicity can be tested using our test. Moreover, the GRM hypothesis includes regression monotonicity and stochastic monotonicity as special cases. Thus, our test also serves as an alternative to existing tests for those hypotheses. We show that our test controls the size uniformly over a broad set of data generating processes asymptotically, is consistent against fixed alternatives, and has nontrivial power against some n−1/2 local alternatives. JEL Classification: C01, C12, C21

Suggested Citation

  • Yu-Chin Hsu & Chu-An Liu & Xiaoxia Shi, 2016. "Testing Generalized Regression Monotonicity," IEAS Working Paper : academic research 16-A009, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:16-a009
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    Cited by:

    1. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    2. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    3. Yoichi Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under Monotone Heteroskedasticity," Papers 2210.13843, arXiv.org, revised Jan 2024.
    4. Lixiong Li & Désiré Kédagni & Ismaël Mourifié, 2024. "Discordant relaxations of misspecified models," Quantitative Economics, Econometric Society, vol. 15(2), pages 331-379, May.
    5. Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    6. Henry, Marc & Méango, Romuald & Mourifié, Ismaël, 2024. "Role models and revealed gender-specific costs of STEM in an extended Roy model of major choice," Journal of Econometrics, Elsevier, vol. 238(2).
    7. Yu-Chin Hsu & Martin Huber & Ying-Ying Lee & Chu-An Liu, 2021. "Testing Monotonicity of Mean Potential Outcomes in a Continuous Treatment with High-Dimensional Data," Papers 2106.04237, arXiv.org, revised Aug 2022.
    8. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.
    9. Sun, Zhenting, 2023. "Instrument validity for heterogeneous causal effects," Journal of Econometrics, Elsevier, vol. 237(2).
    10. Yu‐Chin Hsu & Shu Shen, 2021. "Testing monotonicity of conditional treatment effects under regression discontinuity designs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 346-366, April.

    More about this item

    Keywords

    Generalized regression monotonicity; hypothesis testing; monotone instrumental variable; interval outcome; uniform size control;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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