Nonparametric Identifiability of Finite Mixtures

Finite mixture models are useful in applied econometrics. They can be used to model unobserved heterogeneity, which plays major roles in labor economics, industrial organization and other fields. Mixtures are also convenient in dealing with contaminated sampling models and models with multiple equilibria. Most of the currently available estimation methods for mixtures are entirely parametric; or, at least they usually employ parametric “type-specific” likelihood functions. This paper develops nonparametric/semiparametric treatments of these models. First, it presents some new nonparametric identification results. It is shown that finite mixture models are identified under weak assumptions that are plausible in economic applications. Next, it shows how to carry out semiparametric maximum likelihood estimation for these models. A practical EM-type algorithm is proposed.