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Partial identification of finite mixtures in econometric models

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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. D’Haultfœuille, Xavier & Février, Philippe, 2015. "Identification of mixture models using support variations," Journal of Econometrics, Elsevier, vol. 189(1), pages 70-82.
    2. repec:bla:ecinqu:v:56:y:2018:i:2:p:895-913 is not listed on IDEAS
    3. 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.
    4. repec:wly:emjrnl:v:19:y:2016:i:3:p:c95-c127 is not listed on IDEAS
    5. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2017. "Nonparametric Estimation in Case of Endogenous Selection," Rationality and Competition Discussion Paper Series 58, CRC TRR 190 Rationality and Competition.
    6. 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.
    7. 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, revised Aug 2018.
    8. 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.
    9. 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.
    10. repec:eee:econom:v:201:y:2017:i:2:p:249-268 is not listed on IDEAS
    11. repec:eee:econom:v:202:y:2018:i:2:p:268-285 is not listed on IDEAS
    12. repec:bla:ecinqu:v:57:y:2019:i:2:p:1215-1230 is not listed on IDEAS

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