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A dual approach to inference for partially identified econometric models

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  • Kaido, Hiroaki

Abstract

This paper considers inference for the set ΘI of parameter values that minimize a criterion function. Chernozhukov et al. (2007) (CHT) develop a general theory of estimation and inference using the level-set of a criterion function. We establish a dual relationship between the level-set estimator and its support function and show that the properly normalized support function provides alternative Wald-type inference methods. These methods can be used to obtain confidence sets for ΘI and points inside it. For models with finitely many moment inequalities, we show that our Wald-type statistic is asymptotically equivalent to CHT’s statistic under regularity conditions.

Suggested Citation

  • Kaido, Hiroaki, 2016. "A dual approach to inference for partially identified econometric models," Journal of Econometrics, Elsevier, vol. 192(1), pages 269-290.
  • Handle: RePEc:eee:econom:v:192:y:2016:i:1:p:269-290
    DOI: 10.1016/j.jeconom.2015.12.017
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    Citations

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    Cited by:

    1. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
    2. Madeira, João & Palma, Nuno, 2018. "Measuring monetary policy deviations from the Taylor rule," Economics Letters, Elsevier, vol. 168(C), pages 25-27.
    3. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    4. 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.
    5. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    6. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers CWP43/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Lee, Ying-Ying & Bhattacharya, Debopam, 2019. "Applied welfare analysis for discrete choice with interval-data on income," Journal of Econometrics, Elsevier, vol. 211(2), pages 361-387.
    8. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    9. 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.
    10. Li, Tong & Oka, Tatsushi, 2015. "Set identification of the censored quantile regression model for short panels with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 363-377.
    11. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    12. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2019. "Best linear approximations to set identified functions: with an application to the gender wage gap," CeMMAP working papers CWP09/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Matthew A. Masten & Alexandre Poirier, 2020. "Inference on breakdown frontiers," Quantitative Economics, Econometric Society, vol. 11(1), pages 41-111, January.
    14. 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.
    15. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. 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.
    17. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    More about this item

    Keywords

    Partial identification; Criterion function; Support function;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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