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Multiscale Adaptive Inference on Conditional Moment Inequalities

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Abstract

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple analytic formula, and to prove the asymptotic validity of a modified bootstrap procedure. The asymptotic distribution is extreme value, and the proof uses new techniques to overcome several technical obstacles. The test detects local alternatives that approach the identified set at the best rate in a broad class of models, and is adaptive to the smoothness properties of the data generating process. Our results also have implications for the use of moment selection procedures in this setting. We provide a monte carlo study and an empirical illustration to inference in a regression model with endogenously censored and missing data.

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  • Timothy B. Armstrong & Hock Peng Chan, 2013. "Multiscale Adaptive Inference on Conditional Moment Inequalities," Cowles Foundation Discussion Papers 1885R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2014.
  • Handle: RePEc:cwl:cwldpp:1885r
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    Cited by:

    1. Yoichi Arai & Yu‐Chin Hsu & Toru Kitagawa & Ismael Mourifié & Yuanyuan Wan, 2022. "Testing identifying assumptions in fuzzy regression discontinuity designs," Quantitative Economics, Econometric Society, vol. 13(1), pages 1-28, January.
    2. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2018. "The identification power of smoothness assumptions in models with counterfactual outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 617-642, July.
    3. Chen, Le-Yu & Lee, Sokbae, 2019. "Breaking the curse of dimensionality in conditional moment inequalities for discrete choice models," Journal of Econometrics, Elsevier, vol. 210(2), pages 482-497.
    4. Madeira, João & Palma, Nuno, 2018. "Measuring monetary policy deviations from the Taylor rule," Economics Letters, Elsevier, vol. 168(C), pages 25-27.
    5. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    6. Timothy B Armstrong & Michal Kolesár, 2018. "A Simple Adjustment for Bandwidth Snooping," Review of Economic Studies, Oxford University Press, vol. 85(2), pages 732-765.
    7. Armstrong, Timothy B., 2018. "On the choice of test statistic for conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 203(2), pages 241-255.
    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. Vogt, Michael & Linton, Oliver, 2020. "Multiscale clustering of nonparametric regression curves," Journal of Econometrics, Elsevier, vol. 216(1), pages 305-325.
    10. Toru Kitagawa, 2013. "A bootstrap test for instrument validity in heterogeneous treatment effect models," CeMMAP working papers CWP53/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. 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.
    12. Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    13. Toru Kitagawa, 2013. "A bootstrap test for instrument validity in heterogeneous treatment effect models," CeMMAP working papers 53/13, Institute for Fiscal Studies.
    14. Victor Chernozhukov & Wooyoung Kim & Sokbae Lee & Adam M. Rosen, 2015. "Implementing intersection bounds in Stata," Stata Journal, StataCorp LP, vol. 15(1), pages 21-44, March.
    15. Shi, Chengchun & Luo, Shikai & Zhu, Hongtu & Song, Rui, 2021. "An online sequential test for qualitative treatment effects," LSE Research Online Documents on Economics 112521, London School of Economics and Political Science, LSE Library.
    16. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    17. Nicky L. Grant & Richard J. Smith, 2018. "GEL-based inference with unconditional moment inequality restrictions," CeMMAP working papers 23/18, Institute for Fiscal Studies.
    18. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    19. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    20. Timothy B. Armstrong & Michal Koles'ar & Soonwoo Kwon, 2020. "Bias-Aware Inference in Regularized Regression Models," Papers 2012.14823, arXiv.org.
    21. Nicky L. Grant & Richard J. Smith, 2018. "GEL-based inference with unconditional moment inequality restrictions," CeMMAP working papers CWP23/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    22. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Nick Koning & Paul Bekker, 2019. "Exact Testing of Many Moment Inequalities Against Multiple Violations," Papers 1904.12775, arXiv.org, revised Jun 2020.
    24. Harold D. Chiang & Kengo Kato & Yuya Sasaki, 2020. "Inference for high-dimensional exchangeable arrays," Papers 2009.05150, arXiv.org, revised Jul 2021.
    25. Nicky L. Grant & Richard J. Smith, 2018. "GEL-Based Inference from Unconditional Moment Inequality Restrictions," Economics Discussion Paper Series 1802, Economics, The University of Manchester.

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    More about this item

    Keywords

    Moment inequalities; Set inference; Adaptive inference;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

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