On estimating finite mixtures of multivariate regression and simultaneous equation models

We propose a maximum likelihood framework for estimating finite mixtures of multivariate regression and simultaneous equation models with multiple endogenous variables. The proposed "semi-parametric" approach posits that the sample of endogenous observations arises from a finite mixture of components (or latent-classes) of unknown proportions with multiple structural relations implied by the specified model for each latent-class. We devise an Expectation-Maximization algorithm in a maximum likelihood framework to simultaneously estimate the class proportions, the class-specific structural parameters, and posterior probabilities of membership of each observation into each latent-class. The appropriate number of classes can be chosen using various information-theoretic heuristics. A data set entailing cross-sectional observations for a diverse sample of businesses is used to illustrate the proposed approach.