Are unobservables separable?

It is common to assume in the empirical practice that the observables are additively separable from the unobservables, 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 the nonseparable IV model, where the IV is independent of the unobservable, we develop a novel nonparametric test for the separability of unobservables. The test relies on the estimation of the separable IV model and the verification of the independence restriction between the residual and the instrumental variable imposed by the non-separable model. To obtain a large-sample approximation to the test statistics, we develop a novel uniform asymptotic expansion of the empirical distribution function of residuals that lead to a Donsker-type central limit theorem. 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.