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Specification tests for partially identified models defined by moment inequalities

Author

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  • 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 specification testing in partially identified models defined by a finite number of moment equalities and inequalities (i.e., (in)equalities). Under the null hypothesis, there is at least one parameter value that simultaneously satisfies all of the moment (in)equalities whereas under the alternative hypothesis there is no such parameter value. While this problem has not been directly addressed in the literature (except in particular cases), several papers have suggested implementing this inferential problem by checking whether confidence intervals for the parameters of interest are empty or not. We propose two hypothesis tests that use the infimum of the sample criterion function over the parameter space as the test statistic together with two different critical values. We obtain two main results. First, we show that the two tests we propose are asymptotically size correct in a uniform sense. Second we show our tests are more powerful than the test that checks whether the confidence set for the parameters of interest is empty or not.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2013. "Specification tests for partially identified models defined by moment inequalities," CeMMAP working papers CWP01/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:01/13
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    References listed on IDEAS

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    3. Gualdani, Cristina, 2018. "An Econometric Model of Network Formation with an Application to Board Interlocks between Firms," TSE Working Papers 17-898, Toulouse School of Economics (TSE), revised Jul 2019.
    4. 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.
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    6. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    7. 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.
    8. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    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. Jorg Stoye, 2020. "A Simple, Short, but Never-Empty Confidence Interval for Partially Identified Parameters," Papers 2010.10484, 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. Levon Barseghyan & Maura Coughlin & Francesca Molinari & Joshua C. Teitelbaum, 2021. "Heterogeneous Choice Sets and Preferences," Econometrica, Econometric Society, vol. 89(5), pages 2015-2048, September.
    14. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    15. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    16. Matias D. Cattaneo & Xinwei Ma & Yusufcan Masatlioglu & Elchin Suleymanov, 2020. "A Random Attention Model," Journal of Political Economy, University of Chicago Press, vol. 128(7), pages 2796-2836.
    17. Ashesh Rambachan, 2022. "Identifying Prediction Mistakes in Observational Data," NBER Chapters, in: Economics of Artificial Intelligence, National Bureau of Economic Research, Inc.
    18. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    19. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    21. JoonHwan Cho & Thomas M. Russell, 2018. "Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments," Papers 1810.03180, arXiv.org, revised Nov 2021.
    22. Matthew A. Masten & Alexandre Poirier, 2021. "Salvaging Falsified Instrumental Variable Models," Econometrica, Econometric Society, vol. 89(3), pages 1449-1469, May.
    23. 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

    Keywords

    Partial Identification; Moment Inequalities; Specification Tests; Hypothesis Testing.;
    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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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