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Nonparametric identification and estimation of random coefficients in multinomial choice models
Author(s) -
Fox Jeremy T.,
Gandhi Amit
Publication year - 2016
Publication title -
the rand journal of economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.687
H-Index - 108
eISSN - 1756-2171
pISSN - 0741-6261
DOI - 10.1111/1756-2171.12125
Subject(s) - multinomial distribution , nonparametric statistics , estimator , consistency (knowledge bases) , identification (biology) , class (philosophy) , econometrics , mathematics , product (mathematics) , distribution (mathematics) , discrete choice , statistics , computer science , artificial intelligence , mathematical analysis , botany , biology , geometry
We show how to nonparametrically identify the distribution of unobservables, such as random coefficients, that characterizes the heterogeneity among consumers in multinomial choice models. We provide general identification conditions for a class of nonlinear models and then verify these conditions using the primitives of the multinomial choice model. We require that the distribution of unobservables lie in the class of all distributions with finite support, which under our most general assumptions, resembles a product space where some of the product members are function spaces. We show how identification leads to the consistency of a nonparametric estimator.