Local identification in nonseparable models

Conditions are derived under which there is local nonparametric identification of values of structural functions and of their derivatives in potentially nonlinear nonseparable models. The attack on this problem is via conditional quantile functions and exploits local quantile independence conditions. The identification conditions include local analogues of the order and rank conditions familiar in the analysis of linear simultaeous equations models. The derivatives whose identification is sought are derivatives of structural equations at a point defined by values of covariates and quantiles of the distributions of the stochastic drivers of the system. These objects convey information about the distribution of the exogenous impact of changes in variables potentially endogenous in the data generating process. The identification conditions point directly to analogue estimators of derivatives of structural functions which are functionals of quantile regression function estimators.