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Testing Many Moment Inequalities

Author

Listed:
  • Victor Chernozhukov

    (Institute for Fiscal Studies and MIT)

  • Denis Chetverikov

    (Institute for Fiscal Studies and UCLA)

  • Kengo Kato

    (Institute for Fiscal Studies)

Abstract

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by p, is possibly much larger than the sample size n. There are a variety of economic applications where the problem of testing many moment inequalities appears; a notable example is the entry model of Ciliberto and Tamer (2009) where p=2m+1 with m being the number of firms. We consider the test statistics given by the maximum of p Studentized (or t-type) statistics, and analyze various ways to compute critical values for the test. Specifically, we consider critical values based upon (i) the union (Bonferroni) bound combined with a moderate deviation inequality for self-normalized sums, (ii) the multiplier bootstrap. We also consider two step variants of (i) and (ii) by incorporating moment selection. We prove validity of these methods, showing that under mild conditions, they lead to tests with error in size decreasing polynomially in n while allowing for p being much larger than n; indeed p can be of order exp(nc) for some c>0. Importantly, all these results hold without any restriction on correlation structure between p Studentized statistics, and also hold uniformly with respect to suitably wide classes of underlying distributions. We also show that all the tests developed in this paper are asymptotically minimax optimal when p grows with n.

Suggested Citation

  • Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing Many Moment Inequalities," CeMMAP working papers CWP65/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:65/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp651313.pdf
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    Cited by:

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    3. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    4. 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.
    5. Victor Chernozhukov & Wolfgang Härdle & Chen Huang & Weining Wang, 2018. "LASSO-driven inference in time and space," CeMMAP working papers CWP36/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers 63/15, Institute for Fiscal Studies.
    7. Bontemps, Christian & Kumar, Rohit, 2020. "A geometric approach to inference in set-identified entry games," Journal of Econometrics, Elsevier, vol. 218(2), pages 373-389.
    8. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    9. Li, Jia & Liao, Zhipeng, 2020. "Uniform nonparametric inference for time series," Journal of Econometrics, Elsevier, vol. 219(1), pages 38-51.
    10. 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.
    11. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    12. Allen, Roy, 2018. "Testing moment inequalities: Selection versus recentering," Economics Letters, Elsevier, vol. 162(C), pages 124-126.
    13. Baris Ata & Alexandre Belloni & Ozan Candogan, 2018. "Latent Agents in Networks: Estimation and Targeting," Papers 1808.04878, arXiv.org, revised Jan 2022.
    14. Guber, Raphael, 2018. "Instrument Validity Tests with Causal Trees: With an Application to the Same-sex Instrument," MEA discussion paper series 201805, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    15. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," Journal of Econometrics, Elsevier, vol. 206(1), pages 57-82.
    17. Chang, Jinyuan & Qiu, Yumou & Yao, Qiwei & Zou, Tao, 2018. "Confidence regions for entries of a large precision matrix," LSE Research Online Documents on Economics 87513, London School of Economics and Political Science, LSE Library.

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