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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.
Henry, Marc; Kitamura, Yuichi; and Salanié, Bernard, "Identifying Finite Mixtures in Econometric Models" (2010). Cowles Foundation Discussion Papers. 2104.