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Linear Regressions with Combined Data

Author

Listed:
  • Xavier D’Haultfoeuille

    (CREST-ENSAE)

  • Christophe Gaillac

    (University of Geneva, GSEM-IEE)

  • Arnaud Maurel

    (Duke University and TSE, NBER and IZA)

Abstract

We study best linear predictions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often implicitly, on exclusion restrictions. We show that without such restrictions, coefficients of interest can still be partially identified and we derive a constructive characterization of the sharp identified set. We then build on this characterization to develop computationally simple and asymptotically normal estimators of the corresponding bounds. We show that these estimators exhibit good finite sample performances.

Suggested Citation

  • Xavier D’Haultfoeuille & Christophe Gaillac & Arnaud Maurel, 2025. "Linear Regressions with Combined Data," Working Papers 2025-04, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2025-04
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