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Testing For A General Class Of Functional Inequalities

Author

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  • Sokbae Lee

    (Department of Economics, Seoul National University)

  • Kyungchul Song

    (Vancouver School of Economics, University of British Columbia)

  • Yoon-Jae Whang

    (Department of Economics, Seoul National University and Institute of Economic Research at Kyoto University)

Abstract

In this paper, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a uni ed framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version of Lp functionals of kernel-type estimators (1 ≤ p

Suggested Citation

  • Sokbae Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing For A General Class Of Functional Inequalities," KIER Working Papers 889, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:889
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    Cited by:

    1. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    2. Chen, Le-Yu & Lee, Sokbae, 2019. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," Journal of Econometrics, Elsevier, vol. 210(2), pages 482-497.
    3. Jun, Sung Jae & Zincenko, Federico, 2022. "Testing for risk aversion in first-price sealed-bid auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 295-320.
    4. Horowitz, Joel L. & Lee, Sokbae, 2017. "Nonparametric estimation and inference under shape restrictions," Journal of Econometrics, Elsevier, vol. 201(1), pages 108-126.
    5. Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions," Papers 2004.08318, arXiv.org, revised Oct 2023.
    6. Lee, K. & Linton, O. & Whang, Y-J., 2020. "Testing for Time Stochastic Dominance," Cambridge Working Papers in Economics 20121, Faculty of Economics, University of Cambridge.
    7. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    8. Denis Chetverikov & Daniel Wilhelm, 2016. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 48/16, Institute for Fiscal Studies.
    9. Joel L. Horowitz & Sokbae (Simon) Lee, 2016. "Nonparametric estimation and inference under shape restrictions," CeMMAP working papers 29/16, Institute for Fiscal Studies.
    10. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    11. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Sung Jae Jun & Sokbae (Simon) Lee, 2020. "Causal inference in case-control studies," CeMMAP working papers CWP19/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Aradillas-López, Andrés & Gandhi, Amit & Quint, Daniel, 2016. "A simple test for moment inequality models with an application to English auctions," Journal of Econometrics, Elsevier, vol. 194(1), pages 96-115.
    14. Jin, Sainan & Corradi, Valentina & Swanson, Norman R., 2017. "Robust Forecast Comparison," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1306-1351, December.
    15. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    16. Krasnokutskaya, Elena & Song, Kyungchul & Tang, Xun, 2022. "Estimating unobserved individual heterogeneity using pairwise comparisons," Journal of Econometrics, Elsevier, vol. 226(2), pages 477-497.
    17. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    18. Aradillas-López, Andrés, 2019. "Nonparametric tests for strategic interaction effects with rationalizability," Economics Letters, Elsevier, vol. 181(C), pages 149-153.
    19. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2021. "A Nonparametric Test for Testing Heterogeneity in Conditional Quantile Treatment Effects," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202117, University of Kansas, Department of Economics, revised Aug 2021.
    20. Lee, Kyungho & Linton, Oliver & Whang, Yoon-Jae, 2023. "Testing for time stochastic dominance," Journal of Econometrics, Elsevier, vol. 235(2), pages 352-371.
    21. Elena Krasnokutskaya & Kyungchul Song & Xun Tang, 2019. "Estimating Unobserved Individual Heterogeneity Using Pairwise Comparisons," Papers 1908.01272, arXiv.org, revised Nov 2020.
    22. Kawaguchi, Kohei, 2017. "Testing rationality without restricting heterogeneity," Journal of Econometrics, Elsevier, vol. 197(1), pages 153-171.
    23. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 39/15, Institute for Fiscal Studies.

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    More about this item

    Keywords

    Bootstrap; conditional moment inequalities; kernel estimation; local poly-nomial estimation; Lp norm; nonparametric testing; partial identi cation; Poissonization; quantile regression; uniform asymptotics;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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