Partially Linear Models under Data Combination

• 成果类型: Article
• 署名作者: D'Haultfoeuille, X.; Gaillac, C.; Maurel, A.
• 署名单位: Institut Polytechnique de Paris; ENSAE Paris; Institut Polytechnique de Paris; University of Oxford; University of Oxford; Duke University; National Bureau of Economic Research
• 刊物名称: REVIEW OF ECONOMIC STUDIES
• ISSN/ISSBN: 0034-6527
• DOI: 10.1093/restud/rdae022
• 发表日期: 2024
• 页码: 238-267
• 关键词: set identification; inference; regressions; bounds

摘要

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.