ARE UNOBSERVABLES SEPARABLE?
针对实证研究中常用的可观测与不可观测变量可加可分离假设，基于非可分离工具变量模型开发了一种新的非参数可分离性检验，并应用于2015年美国消费者支出调查数据，发现部分商品的恩格尔曲线中不可观测变量不可分离。
It is common to assume in empirical research that observables and unobservables are additively separable, especially when the former are endogenous. This is 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 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 U.S. Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for some commodities.