We develop a uniform asymptotic expansion for the empirical distribution function of residuals in the nonparametric IV regression. Such expansion opens a door for construction of a broad range of residual-based specification tests in nonparametric IV models. Building on obtained result, we develop a test for the separability of unobservables in econometric models with endogeneity. 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.
separability test; distribution of residuals; nonparametric instrumental regression; Sobolev scales;
- C12: Hypothesis Testing: General
- C14: Semiparametric and Nonparametric Methods: General
TSE Working Paper, n. 17-802, May 2017