Title: Distribution of residuals in the nonparametric IV model with application to separability testing,
Abstract: 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.