Identifying Heterogeneity in Economic Choice and Selection Models Using Mixtures

independence of a class of economic choice models. We state an economic property known as reducibility and prove that reducibility ensures linear independence and hence identification. Reducibility makes verifying the identification of nonlinear models easy. We use our mixtures framework to prove identification in three classes of economic models: 1) continuous outcomes including simultaneous equations, 2) multinomial discrete choice, and 3) selection and mixed continuous-discrete choice. We rely on linear independence, not identification at infinity. For selection, we allow for essential heterogeneity in both the selection and outcome equations and fully identify the joint distribution of outcomes.