标题： 不可观测变量的识别 显示英文标题

标题： Identification of Unobservables in Observations

摘要： 在实证研究中，数据通常不包括经济模型中的所有感兴趣变量。 本文展示了在总体观测中未观察到的变量的识别。 当可观测变量在每次观测中各不相同时，存在从可观测变量到不可观测变量的函数映射。 这种函数保证了每次观测中潜在值的独特性。 关键在于从可观测变量的分布识别可观测变量和不可观测变量的联合分布。 然后，可观测变量和不可观测变量的联合分布揭示了每次观测中的潜在值。 讨论了这一结果的三个例子。 显示英文摘要

摘要： In empirical studies, the data usually don't include all the variables of interest in an economic model. This paper shows the identification of unobserved variables in observations at the population level. When the observables are distinct in each observation, there exists a function mapping from the observables to the unobservables. Such a function guarantees the uniqueness of the latent value in each observation. The key lies in the identification of the joint distribution of observables and unobservables from the distribution of observables. The joint distribution of observables and unobservables then reveal the latent value in each observation. Three examples of this result are discussed.