Before revision:  The test is based on verifying the independence condition between residuals of the NPIV estimator and the instrument and can distinguish between the non-separable and the separable specification under endogeneity .
After revision:  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 .