• Open Access

Partial identification of finite mixtures in econometric models


  • Marc Henry,

    1. Economics Department, The Pennsylvania State University; marc.henry@psu.edu
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  • Yuichi Kitamura,

    1. Economics Department, Yale University; yuichi.kitamura@yale.edu
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  • Bernard Salanié

    1. Economics Department, Columbia University; bs2237@columbia.edu
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    • Parts of this paper were written while Henry was visiting the University of Tokyo Graduate School of Economics and Salanié was visiting the Toulouse School of Economics; they both thank their respective hosts, the CIRJE, and the Georges Meyer endowment for their support. Support from the NSF (Grants SES-0551271, SES-0851759, and SES-1156266) and the SSHRC (Grant 410-2010-242) is also gratefully acknowledged. The authors thank Koen Jochmans, Ismael Mourifié, Elie Tamer, and three anonymous referees for their very helpful comments and suggestions.


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.