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Identifying Finite Mixtures in Econometric Models

Marc Henry; Yuichi Kitamura; Bernard Salanie

Title:
Identifying Finite Mixtures in Econometric Models
Author(s):
Henry, Marc
Kitamura, Yuichi
Salanie, Bernard
Date:
Type:
Working papers
Department:
Economics
Permanent URL:
Series:
Department of Economics Discussion Papers
Publisher:
Columbia University, Department of Economics
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):
Economic theory
Item views:
265
Metadata:
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