Partially Linear Models under Data Combination

Xavier D'Haultfoeuille, Christophe Gaillac and Arnaud Maurel

No 15230, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: We consider the identification of and inference on a partially linear model, 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. Finally, we apply our methodology to study intergenerational income mobility over the period 1850-1930 in the United States. Our method allows to relax the exclusion restrictions used in earlier work while delivering confidence regions that are informative.

Keywords: partial identification; data combination; partially linear model; intergenerational mobility (search for similar items in EconPapers)
JEL-codes: C14 C21 J62 (search for similar items in EconPapers)
Pages: 64 pages
Date: 2022-04
New Economics Papers: this item is included in nep-lab
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Published - published online in: Review of Economic Studies , 29 March 2024

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Related works:
Journal Article: Partially Linear Models under Data Combination (2025)
Working Paper: Partially Linear Models under Data Combination (2023)
Working Paper: Partially Linear Models under Data Combination (2022)
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