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Specification tests for partially identified models defined by moment inequalities

Author

Listed:
  • Federico A. Bugni

    (Institute for Fiscal Studies and Duke University)

  • Ivan A. Canay

    (Institute for Fiscal Studies and Northwestern University)

  • Xiaoxia Shi

    (Institute for Fiscal Studies)

Abstract

This paper studies the problem of specifi cation testing in partially identi fied models defi ned by a fi nite number of moment equalities and inequalities (i.e. (in)equalities). Under the null hypothesis, there is at least one parameter value that simultaneously satis fies all of the moment (in)equalities whereas under the alternative hypothesis there is no such parameter value. This problem has not been directly addressed in the literature (except in particular cases), although several papers have suggested a test based on checking whether con fidence sets for the parameters of interest are empty or not, referred to as Test BP. We propose two new speci fication tests, denoted Tests RS and RC, that achieve uniform asymptotic size control and dominate Test BP in terms of power in any finite sample and in the asymptotic limit. Test RC is particularly convenient to implement because it requires little additional work beyond the con fidence set construction. Test RS requires a separate procedure to compute, but has the best power. The separate procedure is computationally easier than confi dence set construction in typical cases.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2014. "Specification tests for partially identified models defined by moment inequalities," CeMMAP working papers CWP19/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:19/14
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    References listed on IDEAS

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    20. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    21. Federico A. Bugni & Ivan A. Canay & Patrik Guggenberger, 2012. "Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models," Econometrica, Econometric Society, vol. 80(4), pages 1741-1768, July.
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    Cited by:

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    2. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    3. Kristin F. Butcher & Kyung H. Park & Anne Morrison Piehl, 2017. "Comparing Apples to Oranges: Differences in Women’s and Men’s Incarceration and Sentencing Outcomes," Journal of Labor Economics, University of Chicago Press, vol. 35(S1), pages 201-234.
    4. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    5. Ivan A. Canay & Azeem M. Shaikh, 2016. "Practical and theoretical advances in inference for partially identified models," CeMMAP working papers CWP05/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Russell Davidson & Victoria Zinde-Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics, Canadian Economics Association, vol. 50(5), pages 1595-1631, December.
    7. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    8. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    9. Fan, Yanqin & Liu, Ruixuan, 2018. "Partial identification and inference in censored quantile regression," Journal of Econometrics, Elsevier, vol. 206(1), pages 1-38.
    10. Dovonon, Prosper & Gonçalves, Sílvia, 2017. "Bootstrapping the GMM overidentification test under first-order underidentification," Journal of Econometrics, Elsevier, vol. 201(1), pages 43-71.
    11. JoonHwan Cho & Thomas M. Russell, 2018. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Papers 1810.03180, arXiv.org, revised Dec 2020.
    12. Arkadiusz Szydlowski, 2015. "Endogenous Censoring in the Mixed Proportional Hazard Model with an Application to Optimal Unemployment Insurance," Discussion Papers in Economics 15/06, Division of Economics, School of Business, University of Leicester.
    13. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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