# Are Unobservables Separable?

## TL;DR

This paper develops a novel nonparametric test for the separability of unobservables in models with endogenous observables, using a nonseparable IV framework and applying it to US expenditure data.

## Contribution

It introduces a new nonparametric test for unobservables separability based on a nonseparable IV model with a novel Donsker-type CLT for residuals.

## Key findings

- Test rejects separability in Engel curves for most commodities.
- Proposes a nonstandard distribution for the test statistic.
- Uses a dataset from the 2015 US Consumer Expenditure Survey.

## 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, 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.