Open AccessPartial identification of finite mixtures in econometric models
Author(s) -
Henry Marc,
Kitamura Yuichi,
Salanié Bernard
Publication year - 2014
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe170
Subject(s) - observable , mathematics , component (thermodynamics) , a priori and a posteriori , identification (biology) , econometrics , econometric model , outcome (game theory) , statistics , mathematical economics , physics , botany , biology , philosophy , epistemology , quantum mechanics , thermodynamics
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.