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Inference for functions of partially identified parameters in moment inequality models

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 introduces a bootstrap-based inference method for functions of the parameter vector in a moment (in)equality model. As a special case, our method yields marginal confidence sets for individual coordinates of this parameter vector. Our inference method controls asymptotic size uniformly over a large class of data distributions. The current literature describes only two other procedures that deliver uniform size control for this type of problem: projection-based and subsampling inference. Relative to projection-based procedures, our method presents three advantages: (i) it weakly dominates in terms of finite sample power, (ii) it strictly dominates in terms of asymptotic power, and (iii) it is typically less computationally demanding. Relative to subsampling, our method presents two advantages: (i) it strictly dominates in terms of asymptotic power (for reasonable choices of subsample size), and (ii) it appears to be less sensitive to the choice of its tuning parameter than subsampling is to the choice of subsample size.

Suggested Citation

  • Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2015. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers CWP54/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:54/15
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    References listed on IDEAS

    as
    1. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(03), pages 669-709, June.
    2. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    3. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    4. 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.
    5. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
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    7. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    8. 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.
    9. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    10. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2014. "A Practical Two‐Step Method for Testing Moment Inequalities," Econometrica, Econometric Society, vol. 82(5), pages 1979-2002, September.
    11. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    12. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    13. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    14. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
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    17. Donald W. K. Andrews & Sukjin Han, 2009. "Invalidity of the bootstrap and the m out of n bootstrap for confidence interval endpoints defined by moment inequalities," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 172-199, January.
    18. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
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    20. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    21. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    22. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, March.
    23. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    24. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
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    Citations

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    Cited by:

    1. 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.
    2. Ho, Katherine & Rosen, Adam M., 2015. "Partial Identification in Applied Research: Benefits and Challenges," CEPR Discussion Papers 10883, C.E.P.R. Discussion Papers.
    3. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    4. 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.
    5. Battey, Heather & Feng, Qiang & Smith, Richard J., 2016. "Improving confidence set estimation when parameters are weakly identified," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 117-123.
    6. 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.
    7. Lee, Y-Y. & Bhattacharya, D., 2018. "Applied Welfare Analysis for Discrete Choice with Interval-data on Income," Cambridge Working Papers in Economics 1882, Faculty of Economics, University of Cambridge.
    8. 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.
    9. Fack, Gabrielle & Grenet, Julien & He, Yinghua, 2015. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice," CEPR Discussion Papers 10907, C.E.P.R. Discussion Papers.
    10. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. repec:hal:cesptp:halshs-01215998 is not listed on IDEAS

    More about this item

    Keywords

    Partial identification; moment inequalities; subvector inference; hypothesis testing;

    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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