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Partially Linear Models under Data Combination

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  • Xavier D'Haultfoeuille
  • Christophe Gaillac
  • Arnaud Maurel

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.

Suggested Citation

  • Xavier D'Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2022. "Partially Linear Models under Data Combination," NBER Working Papers 29953, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:29953
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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • J62 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Job, Occupational and Intergenerational Mobility; Promotion

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