Partial identification of finite mixtures in econometric models

• 成果类型: Article
• 署名作者: Henry, Marc; Kitamura, Yuichi; Salanie, Bernard
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Yale University; Columbia University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE170
• 发表日期: 2014
• 页码: 123-144
• 关键词: partial identification; finite mixture models; C24

摘要

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.