Partially Linear Models under Data Combination
研究了结果变量和部分协变量分别来自两个无法链接的数据集时的部分线性模型，利用最优传输理论刻画了尖锐识别集，并开发了基于其几何特性的推断方法，应用于1850-1930年美国代际收入流动性分析。
Abstract We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics. Using recent tools from optimal transport theory, we derive a constructive characterization of the sharp identified set. We then build on this result and develop a novel inference method that exploits the specific geometric properties of the identified set. Our method exhibits good performances in finite samples, while remaining very tractable. We apply our approach to study intergenerational income mobility over the period 1850–1930 in the U.S. Our method allows us to relax the exclusion restrictions used in earlier work, while delivering confidence regions that are informative.