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A practical two-step method for testing moment inequalities

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  • Joseph P. Romano
  • Azeem M. Shaikh
  • Michael Wolf

Abstract

This paper considers the problem of testing a finite number of moment inequalities. We propose a two-step approach. In the first step, a confidence region for the moments is constructed. In the second step, this set is used to provide information about which moments are “negative.” A Bonferonni-type correction is used to account for the fact that with some probability the moments may not lie in the confidence region. It is shown that the test controls size uniformly over a large class of distributions for the observed data. An important feature of the proposal is that it remains computationally feasible, even when the number of moments is large. The finite-sample properties of the procedure are examined via a simulation study, which demonstrates, among other things, that the proposal remains competitive with existing procedures while being computationally more attractive.

Suggested Citation

  • Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2012. "A practical two-step method for testing moment inequalities," ECON - Working Papers 090, Department of Economics - University of Zurich, revised Apr 2014.
  • Handle: RePEc:zur:econwp:090
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    References listed on IDEAS

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    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, pages 669-709.
    2. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, pages 1331-1370.
    3. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
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    5. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    6. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    7. Bugni, Federico A., 2016. "Comparison Of Inferential Methods In Partially Identified Models In Terms Of Error In Coverage Probability," Econometric Theory, Cambridge University Press, vol. 32(01), pages 187-242, February.
    8. 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.
    9. 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.
    10. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, pages 2805-2826.
    11. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
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    Cited by:

    1. Boneva, Lena & Linton, Oliver & Vogt, Michael, 2015. "A semiparametric model for heterogeneous panel data with fixed effects," Journal of Econometrics, Elsevier, pages 327-345.
    2. Hiroaki Kaido & Francesca Molinari & Jorg Stoye, 2016. "Confidence intervals for projections of partially identified parameters," CeMMAP working papers CWP02/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, pages 103-129.
    4. Joel L. Horowitz & Sokbae Lee, 2015. "Nonparametric estimation and inference under shape restrictions," CeMMAP working papers CWP67/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Andres Aradillas-Lopez & Adam Rosen, 2014. "Inference in Ordered Response Games with Complete Information," CeMMAP working papers CWP36/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. John Asker & Chaim Fershtman & Jihye Jeon & Ariel Pakes, 2016. "The Competitive Effects of Information Sharing," NBER Working Papers 22836, National Bureau of Economic Research, Inc.
    7. Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
    8. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
    9. 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.
    10. repec:eee:econom:v:200:y:2017:i:1:p:17-35 is not listed on IDEAS
    11. repec:eee:econom:v:201:y:2017:i:1:p:108-126 is not listed on IDEAS
    12. 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.
    13. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey, 2016. "Locally Robust Semiparametric Estimation," Papers 1608.00033, arXiv.org.
    14. Federico A. Bugni & Mehmet Caner & Anders Bredahl Kock & Soumendra Lahiri, 2016. "Inference in partially identified models with many moment inequalities using Lasso," CREATES Research Papers 2016-12, Department of Economics and Business Economics, Aarhus University.
    15. Clément de Chaisemartin & Xavier d'Haultfoeuille, 2015. "Fuzzy differences-in-differences," CeMMAP working papers CWP69/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Andres Aradillas-Lopez & Adam Rosen, 2013. "Inference in ordered response games with complete information," CeMMAP working papers CWP33/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Matias D. Cattaneo & Xinwei Ma & Yusufcan Masatlioglu & Elchin Suleymanov, 2017. "A Random Attention Model," Papers 1712.03448, arXiv.org.
    18. Joseph P. Romano & Michael Wolf, 2017. "Multiple testing of one-sided hypotheses: combining Bonferroni and the bootstrap," ECON - Working Papers 254, Department of Economics - University of Zurich.
    19. Clément de Chaisemartin & Xavier d'Haultfoeuille, 2015. "Fuzzy differences-in-differences," CeMMAP working papers CWP69/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2015. "Supplement to Fuzzy Differences-in-Differences," The Warwick Economics Research Paper Series (TWERPS) 1066, University of Warwick, Department of Economics.
    21. Andreas Dzemski & Ryo Okui, 2017. "Confidence set for group membership," Papers 1801.00332, arXiv.org.
    22. Chenyu Yang, 2017. "Could Vertical Integration Increase Innovation?," 2017 Meeting Papers 908, Society for Economic Dynamics.

    More about this item

    Keywords

    Bonferonni inequality; bootstrap; moment inequalities; partial identification; uniform validity;

    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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