Working paper

Are unobservables separable?

Andrii Babii, and Jean-Pierre Florens


It is common to assume in empirical research that observables and unobservables are additively separable, especially, when the former are endogenous. This is done 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 novel Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals. Using a dataset drawn from the 2015 US Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for most of the commodities.


unobservables; endogeneity; separability test; nonparametric IV regression; nonparametric IV residuals; Engel curves.;

JEL codes

  • C12: Hypothesis Testing: General
  • C14: Semiparametric and Nonparametric Methods: General
  • C26: Instrumental Variables (IV) Estimation


Andrii Babii, and Jean-Pierre Florens, Are unobservables separable?, TSE Working Paper, n. 17-802, May 2017, revised January 2020.

See also

Published in

TSE Working Paper, n. 17-802, May 2017, revised January 2020