Partially Linear Models under Data Combination

X D’Haultfœuille, Christophe Gaillac and Arnaud Maurel

The Review of Economic Studies, 2025, vol. 92, issue 1, 238-267

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.

Keywords: Partially linear model; Data combination; Partial identification; Intergenerational mobility (search for similar items in EconPapers)
Date: 2025
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Related works:
Working Paper: Partially Linear Models under Data Combination (2023)
Working Paper: Partially Linear Models under Data Combination (2022)
Working Paper: Partially Linear Models under Data Combination (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:oup:restud:v:92:y:2025:i:1:p:238-267.

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