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Identifying Finite Mixtures in Econometric Models

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  • Marc Henry

    ()
    (Université de Montréal - Département de sciences économiques)

  • Yuichi Kitamura

    ()
    (Yale University - Department of Economics)

  • Bernard Salanié

    ()
    (Columbia University - Department of Economics)

Abstract

Mixtures of distributions are present in many econometric models, such as models with unobserved heterogeneity. It is thus crucial to have a general approach to identify them nonparametrically. Yet the literature so far only contains isolated examples, applied to specific models. We derive the identifying implications of a conditional independence assumption in finite mixture models. It applies for instance to models with unobserved heterogeneity, regime switching models, and models with mismeasured discrete regressors. Under this assumption, we derive sharp bounds on the mixture weights and components. For models with two mixture components, we show that if in addition the components behave differently in the tails of their distributions, then components and weights are fully nonparametrically identified. We apply our findings to the nonparametric identification and estimation of outcome distributions with a misclassified binary regressor. This provides a simple estimator that does not require instrumental variables, auxiliary data, symmetric error distributions or other shape restrictions.

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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0910-20.

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Date of creation: 2010
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Handle: RePEc:clu:wpaper:0910-20

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Cited by:
  1. Stefan Hoderlein & Lars Nesheim & Anna Simoni, 2012. "Semiparametric estimation of random coefficients in structural economic models," CeMMAP working papers CWP09/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Spindler, Martin, 2013. "“They do know what they are doing... at least most of them.” Asymmetric Information in the (private) Disability Insurance," MEA discussion paper series 12260, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.

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