Identification of Mixture Models Using Support Variations

We consider the issue of identifying nonparametrically mixture models. In thesemodels, all observed variables depend on a common and unobserved component,but are mutually independent conditional on it. Such models are important in themeasurement error, auction and matching literatures. Traditional approaches relyon parametric assumptions or strong functional restrictions. We show that thesemodels are actually identified nonparametrically if a moving support assumption issatisfied. More precisely, we suppose that the supports of the observed variables movewith the true value of the unobserved component. We show that this assumption istheoretically grounded, empirically relevant and testable. Finally, we compare ourapproach with the diagonalization technique introduced by Hu and Schennach (2008),which allows to obtain similar results.