Babii, Andrii and Florens, Jean-Pierre (2017) Are unobservables separable? TSE Working Paper, n. 17-802, Toulouse

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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 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.