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Identifying Finite Mixtures in Econometric Models

Bernard Salanie; Marc Henry; Yuichi Kitamura

Title:
Identifying Finite Mixtures in Econometric Models
Author(s):
Salanie, Bernard
Henry, Marc
Kitamura, Yuichi
Date:
Type:
Reports
Department(s):
Economics
Persistent URL:
Series:
Department of Economics discussion papers
Part Number:
0910-20
Publisher:
Department of Economics, Columbia University
Publisher Location:
New York
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.
Subject(s):
Economics
Item views
385
Metadata:
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Suggested Citation:
Bernard Salanie, Marc Henry, Yuichi Kitamura, , Identifying Finite Mixtures in Econometric Models, Columbia University Academic Commons, .

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