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Inference on sets in finance

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  • Victor Chernozhukov
  • Emre Kocatulum
  • Konrad Menzel

Abstract

We consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include the Hansen–Jagannathan sets of admissible stochastic discount factors, Markowitz–Fama mean–variance sets for asset portfolio returns, and the set of structural elasticities in Chetty's (2012) analysis of demand with optimization frictions. The econometric structure of the problem allows us to construct convenient and powerful confidence regions based on the weighted likelihood ratio and weighted Wald statistics. Our statistics differ from existing statistics in that they enforce either exact or first‐order equivariance to transformations of parameters, making them especially appealing in the target applications. We show that the resulting inference procedures are more powerful than the structured projection methods. Last, our framework is also useful for analyzing intersection bounds, namely sets defined as solutions to multiple smooth inequalities, since multiple inequalities can be conservatively approximated by a single smooth inequality. We present two empirical examples showing how the new econometric methods are able to generate sharp economic conclusions.

Suggested Citation

  • Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2015. "Inference on sets in finance," Quantitative Economics, Econometric Society, vol. 6(2), pages 309-358, July.
  • Handle: RePEc:wly:quante:v:6:y:2015:i:2:p:309-358
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    Cited by:

    1. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.
    2. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
    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. 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.
    5. Christian Bontemps & Rohit Kumar, 2019. "A Geometric Approach to Inference in Set-Identified Entry Games," Working Papers hal-02137356, HAL.
    6. Liao, Yuan & Simoni, Anna, 2019. "Bayesian inference for partially identified smooth convex models," Journal of Econometrics, Elsevier, vol. 211(2), pages 338-360.
    7. Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2016. "On the properties of the constrained Hansen–Jagannathan distance," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 121-150.
    8. 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.
    9. Hiroaki Kaido & Jiaxuan Li & Marc Rysman, 2018. "Moment inequalities in the context of simulated and predicted variables," CeMMAP working papers CWP26/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    11. 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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