Are Unobservables Separable?
46 Pages Posted: 4 May 2017 Last revised: 12 Jul 2021
Date Written: May 3, 2017
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, which may be of independent interest. 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.
Keywords: unobservables, endogeneity, separability test, Engel curves, heterogeneity in unobservables, distribution of nonparametric IV residuals
JEL Classification: C12, C14, C26
Suggested Citation: Suggested Citation