  Latent variable models are widely used to account for unobserved determinants
of economic behavior. Traditional nonparametric methods to estimate latent
heterogeneity do not scale well into multidimensional settings. Distributional
restrictions alleviate tractability concerns but may impart non-trivial
misspecification bias. Motivated by these concerns, this paper introduces a
quasi-Bayes approach to estimate a large class of multidimensional latent
variable models. Our approach to quasi-Bayes is novel in that we center it
around relating the characteristic function of observables to the distribution
of unobservables. We propose a computationally attractive class of priors that
are supported on Gaussian mixtures and derive contraction rates for a variety
of latent variable models.

Econometrics;Methodology