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ARE UNOBSERVABLES SEPARABLE?

Published online by Cambridge University Press:  26 January 2024

Andrii Babii Open the ORCID record for Andrii Babii [Opens in a new window]  and
Jean-Pierre Florens Open the ORCID record for Jean-Pierre Florens [Opens in a new window]
Andrii Babii*
Affiliation:
University of North Carolina at Chapel Hill
Jean-Pierre Florens
Affiliation:
Toulouse School of Economics
*
Address correspondence to Andrii Babii, Department of Economics, University of North Carolina at Chapel Hill—Gardner Hall, CB 3305, Chapel Hill, NC 27599-3305, USA; e-mail: babii.andrii@gmail.com.
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Abstract

It is common to assume in empirical research that observables and unobservables are additively separable, especially when the former are endogenous. This is because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from a nonseparable IV model, where the instrumental variable is independent of unobservables, we develop a novel nonparametric test of separability of unobservables. The large-sample distribution of the test statistics is nonstandard and relies on a Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals, which may be of independent interest. Using a dataset drawn from the 2015 U.S. Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for some commodities.

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Type
ARTICLES
Information
Econometric Theory , Volume 41 , Issue 3 , June 2025 , pp. 551 - 583
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

This work was supported by the French National Research Agency under Grant ANR-19-CE40-0013-01/ExtremReg project. We thank the seminar participants at Yale University, and the editorial team for helpful comments. We also thank Ivan Canay, Xiaohong Chen, Tim Christensen, Elia Lapenta, Pascal Lavergne, Thierry Magnac, Nour Meddahi, Ingrid Van Keilegom, and Edward Vytlacil for insightful discussions. All remaining errors are ours.

References

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