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Partial identification of finite mixtures in econometric models

Author

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  • Marc Henry
  • Yuichi Kitamura
  • Bernard Salanié

Abstract

We consider partial identification of finite mixture models in the presence of an observable source of variation in the mixture weights that leaves component distributions unchanged, as is the case in large classes of econometric models. We first show that when the number J of component distributions is known a priori, the family of mixture models compatible with the data is a subset of a J(J−1)‐dimensional space. When the outcome variable is continuous, this subset is defined by linear constraints, which we characterize exactly. Our identifying assumption has testable implications, which we spell out for J = 2. We also extend our results to the case when the analyst does not know the true number of component distributions and to models with discrete outcomes.

Suggested Citation

  • Marc Henry & Yuichi Kitamura & Bernard Salanié, 2014. "Partial identification of finite mixtures in econometric models," Quantitative Economics, Econometric Society, vol. 5, pages 123-144, March.
    • Handle: RePEc:wly:quante:v:5:y:2014:i::p:123-144
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    File URL: http://hdl.handle.net/10.1111/quan.2014.5.issue-1.x
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    Cited by:

    1. Li Gan & Manuel A. Hernandez & Yanyan Liu, 2018. "Group Lending With Heterogeneous Types," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 895-913, April.
    2. Rasmus Lentz & Suphanit Piyapromdee & Jean-Marc Robin, 2018. "On Worker and Firm Heterogeneity in Wages and Employment Mobility: Evidence from Danish Register Data," PIER Discussion Papers 91, Puey Ungphakorn Institute for Economic Research.
    3. Jason Abaluck & Abi Adams, 2017. "What Do Consumers Consider Before They Choose? Identification from Asymmetric Demand Responses," NBER Working Papers 23566, National Bureau of Economic Research, Inc.
    4. Hajimoladarvish , Narges, 2021. "Explaining Heterogeneity in Risk Preferences Using a Finite Mixture Model," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(4), pages 533-554, December.
    5. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    6. Despoina Makariou & Pauline Barrieu & George Tzougas, 2021. "A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures," Risks, MDPI, vol. 9(6), pages 1-25, June.
    7. Gan, Li & Hernandez, Manuel A. & Zhang, Shuoxun, 2021. "Insurance or deliberate use of the bankruptcy law for financial gain? Testing for heterogeneous filing behaviors in the United States," Economic Modelling, Elsevier, vol. 105(C).
    8. Higgins, Ayden & Jochmans, Koen, 2023. "Identification of mixtures of dynamic discrete choices," Journal of Econometrics, Elsevier, vol. 237(1).
    9. Jason Abaluck & Abi Adams, 2017. "What do consumers consider before they choose? Identification from asymmetric demand responses," IFS Working Papers W17/09, Institute for Fiscal Studies.
    10. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    11. Krasnokutskaya, Elena & Song, Kyungchul & Tang, Xun, 2022. "Estimating unobserved individual heterogeneity using pairwise comparisons," Journal of Econometrics, Elsevier, vol. 226(2), pages 477-497.
    12. Diego Escobari & Manuel A. Hernandez, 2019. "Separating Between Unobserved Consumer Types: Evidence From Airlines," Economic Inquiry, Western Economic Association International, vol. 57(2), pages 1215-1230, April.
    13. Kedagni, Desire, 2018. "Identifying Treatment Effects in the Presence of Confounded Types," ISU General Staff Papers 201809110700001056, Iowa State University, Department of Economics.
    14. Jochmans, Koen & Henry, Marc & Salanié, Bernard, 2017. "Inference On Two-Component Mixtures Under Tail Restrictions," Econometric Theory, Cambridge University Press, vol. 33(3), pages 610-635, June.
    15. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    16. Yannick V. Markhof, 2020. "Divide to Conquer? Latent Preference Types and Country-level Heterogeneity," CSAE Working Paper Series 2020-05, Centre for the Study of African Economies, University of Oxford.
    17. Giovanni Compiani & Yuichi Kitamura, 2016. "Using mixtures in econometric models: a brief review and some new results," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 95-127, October.
    18. Marcia C Castro & Mathieu Maheu-Giroux & Christinah Chiyaka & Burton H Singer, 2016. "Malaria Incidence Rates from Time Series of 2-Wave Panel Surveys," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-26, August.
    19. Xi Wu & Li Gan, 2023. "Multiple dimensions of private information in life insurance markets," Empirical Economics, Springer, vol. 65(5), pages 2145-2180, November.
    20. Erhao Xie, 2018. "Inference in Games Without Nash Equilibrium: An Application to Restaurants, Competition in Opening Hours," Staff Working Papers 18-60, Bank of Canada.
    21. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.

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