Identification of mixture models using support variations

We consider the issue of identifying nonparametrically continuous mixture models. In these models, all observed variables depend on a common and unobserved component, but are mutually independent conditional on it. Such a structure applies for instance to measurement error, matching and auction models. Traditional approaches rely on parametric assumptions or strong functional restrictions. We show that these models are actually identified nonparametrically if the supports of the observed variables move with the value of the unobserved component. Moreover, this assumption is testable nonparametrically, using tools from extreme value theory. We develop an appropriate test and derive its asymptotic properties.