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Inference Based on Many Conditional Moment Inequalities

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Abstract

In this paper, we construct confidence sets for models defined by many conditional moment inequalities/equalities. The conditional moment restrictions in the models can be finite, countably infinite, or uncountably infinite. To deal with the complication brought about by the vast number of moment restrictions, we exploit the manageability (Pollard (1990)) of the class of moment functions. We verify the manageability condition in five examples from the recent partial identification literature. The proposed confidence sets are shown to have correct asymptotic size in a uniform sense and to exclude parameter values outside the identified set with probability approaching one. Monte Carlo experiments for a conditional stochastic dominance example and a random-coefficients binary-outcome example support the theoretical results.

Suggested Citation

  • Donald W.K. Andrews & Xiaoxia Shi, 2015. "Inference Based on Many Conditional Moment Inequalities," Cowles Foundation Discussion Papers 2010, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2010
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    1. Armstrong, Timothy B., 2015. "Asymptotically exact inference in conditional moment inequality models," Journal of Econometrics, Elsevier, vol. 186(1), pages 51-65.
    2. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    3. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    4. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    5. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    6. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
    7. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    8. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Comparison and anti-concentration bounds for maxima of Gaussian random vectors," CeMMAP working papers CWP71/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
    10. Armstrong, Timothy B. & Chan, Hock Peng, 2016. "Multiscale adaptive inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 194(1), pages 24-43.
    11. 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.
    12. Amit Gandhi Gandhi & Zhentong Lu & Xiaoxia Shi, 2013. "Estimating demand for differentiated products with error in market shares," CeMMAP working papers CWP03/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2009. "Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions," Econometrica, Econometric Society, vol. 77(4), pages 1193-1227, July.
    14. Armstrong, Timothy B., 2014. "Weighted KS statistics for inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 181(2), pages 92-116.
    15. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
    16. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    17. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    18. Chesher, Andrew & Smolinski, Konrad, 2012. "IV models of ordered choice," Journal of Econometrics, Elsevier, vol. 166(1), pages 33-48.
    19. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    20. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    21. Garry F. Barrett & Stephen G. Donald & Debopam Bhattacharya, 2014. "Consistent Nonparametric Tests for Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 1-13, January.
    22. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
    23. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    24. A. Pakes & J. Porter & Kate Ho & Joy Ishii, 2015. "Moment Inequalities and Their Application," Econometrica, Econometric Society, vol. 83, pages 315-334, January.
    25. Andrew Chesher & Adam M. Rosen, 2014. "An instrumental variable random‐coefficients model for binary outcomes," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 1-19, June.
    26. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    27. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    28. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    29. 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.
    30. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    31. Beare, Brendan K. & Moon, Jong-Myun, 2015. "Nonparametric Tests Of Density Ratio Ordering," Econometric Theory, Cambridge University Press, vol. 31(3), pages 471-492, June.
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    Cited by:

    1. Mikkel Plagborg-M{o}ller & Christian K. Wolf, 2020. "Instrumental Variable Identification of Dynamic Variance Decompositions," Papers 2011.01380, arXiv.org, revised Jul 2021.
    2. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    3. Hsu, Yu-Chin & Shen, Shu, 2019. "Testing treatment effect heterogeneity in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 208(2), pages 468-486.
    4. Xavier D'Haultf{oe}uille & Christophe Gaillac & Arnaud Maurel, 2022. "Partially Linear Models under Data Combination," Papers 2204.05175, arXiv.org.
    5. Lok, Thomas M. & Tabri, Rami V., 2021. "An improved bootstrap test for restricted stochastic dominance," Journal of Econometrics, Elsevier, vol. 224(2), pages 371-393.
    6. Xavier D'Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2021. "Rationalizing rational expectations: Characterizations and tests," Quantitative Economics, Econometric Society, vol. 12(3), pages 817-842, July.
    7. Parker, Thomas, 2019. "Asymptotic inference for the constrained quantile regression process," Journal of Econometrics, Elsevier, vol. 213(1), pages 174-189.
    8. Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Robust inference in deconvolution," Quantitative Economics, Econometric Society, vol. 12(1), pages 109-142, January.
    9. Rami V. Tabri & Christopher D. Walker, 2020. "Inference for Moment Inequalities: A Constrained Moment Selection Procedure," Papers 2008.09021, arXiv.org, revised Aug 2020.
    10. Yonghong An & Pengfei Liu, 2020. "Eliciting Information from Sensitive Survey Questions," Papers 2009.01430, arXiv.org.
    11. Fakih, Ali & Makdissi, Paul & Marrouch, Walid & Tabri, Rami V. & Yazbeck, Myra, 2022. "A stochastic dominance test under survey nonresponse with an application to comparing trust levels in Lebanese public institutions," Journal of Econometrics, Elsevier, vol. 228(2), pages 342-358.
    12. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.
    13. Yu‐Chin Hsu & Shu Shen, 2021. "Testing monotonicity of conditional treatment effects under regression discontinuity designs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(3), pages 346-366, April.

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    More about this item

    Keywords

    Asymptotic size; Conditional moment inequalities; Confidence set; Many moments; Multiple equilibria; Partial identification; Random coefficients; Stochastic dominance; Test;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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