Identifying Finite Mixtures In Econometric Models
Mixtures of distributions are present in many econometric models, such as models with unobserved heterogeneity. It is thus crucial to have a general approach to identify them nonparametrically. Yet the literature so far only contains isolated examples, applied to specific models. The authors derive the identifying implications of a conditional independence assumption infinite mixture models. It applies for instance to models with unobserved heterogeneity, regime switching models, and models with mismeasured discrete regressors. Under this assumption, they derive sharp bounds on the mixture weights and components. For models with two mixture components, they show that if in addition the components behave differently in the tails of their distributions, then components and weights are fully nonparametrically identified.