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Identifying Finite Mixtures in Econometric Models

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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 Salanie, 2010. "Identifying Finite Mixtures in Econometric Models," Cowles Foundation Discussion Papers 1767, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.
  • Handle: RePEc:cwl:cwldpp:1767
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    Cited by:

    1. Hoderlein, Stefan & Nesheim, Lars & Simoni, Anna, 2017. "Semiparametric Estimation Of Random Coefficients In Structural Economic Models," Econometric Theory, Cambridge University Press, vol. 33(06), pages 1265-1305, December.

    More about this item

    Keywords

    Misclassified regressors; Nonparametric identification;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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