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Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities

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  • Hiroaki Kaido
  • Andres Santos

Abstract

This paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest. In such a setting, the identified set is itself convex and hence fully characterized by its support function. We provide conditions under which, despite being an infinite dimensional parameter, the support function admits √n‐consistent regular estimators. A semiparametric efficiency bound is then derived for its estimation, and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions. In addition, we show that the “plug‐in” estimator is efficient, and devise a consistent bootstrap procedure for estimating its limiting distribution. The setting we examine is related to an incomplete linear model studied in Beresteanu and Molinari (2008) and Bontemps, Magnac, and Maurin (2012), which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem.

Suggested Citation

  • Hiroaki Kaido & Andres Santos, 2014. "Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities," Econometrica, Econometric Society, vol. 82(1), pages 387-413, January.
  • Handle: RePEc:wly:emetrp:v:82:y:2014:i:1:p:387-413
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    File URL: http://hdl.handle.net/10.3982/ECTA10017
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    Citations

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    Cited by:

    1. 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.
    2. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    3. Yuan Liao & Anna Simoni, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," Papers 1212.3267, arXiv.org, revised Nov 2013.
    4. repec:taf:jnlasa:v:112:y:2017:i:519:p:1064-1075 is not listed on IDEAS
    5. Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2015. "Inference on sets in finance," Quantitative Economics, Econometric Society, vol. 6(2), pages 309-358, July.
    6. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    7. Yu-Wei Hsieh & Xiaoxia Shi & Matthew Shum, 2017. "Inference on Estimators defined by Mathematical Programming," Papers 1709.09115, arXiv.org.
    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. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
    10. 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.
    11. 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.
    12. Magnac, Thierry, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258, Décembre.
    13. repec:cup:etheor:v:33:y:2017:i:05:p:1218-1241_00 is not listed on IDEAS
    14. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(05), pages 1218-1241, October.
    15. Kaido, Hiroaki, 2016. "A dual approach to inference for partially identified econometric models," Journal of Econometrics, Elsevier, vol. 192(1), pages 269-290.
    16. Kline Patrick & Santos Andres, 2012. "A Score Based Approach to Wild Bootstrap Inference," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 23-41, August.
    17. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    18. David Pacini, 2012. "Least Square Linear Prediction with Two-Sample Data," Bristol Economics Discussion Papers 12/631, Department of Economics, University of Bristol, UK.
    19. Yuan Liao & Anna Simoni, 2016. "Bayesian Inference for Partially Identified Convex Models: Is it Valid for Frequentist Inference?," Departmental Working Papers 201607, Rutgers University, Department of Economics.

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