Global estimation of finite mixture and misclassification models with an application to multiple equilibria
证明了有限混合模型与误分类模型在常见场景下识别结果等价，但误分类模型通过排序条件实现全局识别，这对使用自助法估计标准误至关重要，并以多重均衡博弈为例展示了全局估计的可靠性。
We show that the identification results of finite mixture and misclassification models are equivalent in a widely used scenario except for an extra ordering assumption. In the misclassification model, an ordering condition is imposed to pin down the precise values of the latent variable, which are also of interest to researchers and need to be identified. In contrast, finite mixture models are usually identified up to permutations of a latent index, which results in local identification. This local identification is satisfactory because the latent index does not convey any economic meaning. However, reaching global identification is important for estimation, especially when researchers use bootstrap to estimate standard errors. This is because standard errors approximated by bootstrap may be incorrect without a global estimator. We demonstrate that games with multiple equilibria fit in our framework and the global estimator with ordering conditions provides more reliable estimates.