Linear Regressions with Combined Data

Xavier D'Haultfoeuille (), Christophe Gaillac () and Arnaud Maurel ()
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Xavier D'Haultfoeuille: CREST
Christophe Gaillac: University of Oxford
Arnaud Maurel: Duke University

No 18276, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: We study linear regressions 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, with the sharp bounds taking a simple form. We obtain tighter bounds when variables observed in both datasets, but not included in the regression of interest, are available, even if these variables are not subject to specific restrictions. We develop computationally simple and asymptotically normal estimators of the bounds. Finally, we apply our methodology to estimate racial disparities in patent approval rates and to evaluate the effect of patience and risk-taking on educational performance.

Keywords: partial identification; best linear prediction; data combination (search for similar items in EconPapers)
JEL-codes: C14 C21 (search for similar items in EconPapers)
Date: 2025-11
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