Global estimation of finite mixture and misclassi fication models with an application to multiple equilibria

We show that the identi fication results of fi nite mixture and misclassifi cation models are equivalent in a widely-used scenario except an extra ordering assumption. In the misclassi fication model, an ordering condition is imposed to pin down the precise values of the latent variable, which are also of researchers' interests and need to be identifi ed. In contrast, the identifi cation of fi nite mixture models is usually up to permutations of a latent index. This local identifi cation is satisfactory because the latent index does not convey any economic meaning. However, reaching global identi fication is important for estimation, especially, when researchers use bootstrap to estimate standard errors, which may be wrong without a global estimator. We provide a theoretical framework and Monte Carlo evidences to show that imposing an ordering condition to achieve a global estimator innocuously improves the estimation of fi nite mixture models. As a natural application, we show that games with multiple equilibria fi t in our framework and the global estimator with ordering assumptions provides more reliable estimates.