Using mixtures in econometric models: a brief review and some new results

This paper is concerned with applications of mixture models in econometrics. Focused attention is given to semiparametric and nonparametric models that incorporate mixture distributions, where important issues about model specifications arise. For example, there is a significant difference between a finite mixture and a continuous mixture in terms of model identifiability. Likewise, the dimension of the latent mixing variables is a critical issue, in particular when a continuous mixture is used. We present applications of mixture models to address various problems in econometrics, such as unobserved heterogeneity and multiple equilibria. New nonparametric identification results are developed for finite mixture models with testable exclusion restrictions without relying on an identification-at-infinity assumption on covariates. The results apply to mixtures with both continuous and discrete covariates, delivering point identification under weak conditions.