Nonparametric two‐step regression estimation when regressors and error are dependent

This is the authors' abstract. We don't add key points for this paper.

This paper considers estimation of the function g in the model Y t = g ( X t ) + ϵ t when E(ϵ t | X t ) ≠ 0 with nonzero probability. We assume the existence of an instrumental variable Z t that is independent of ϵ t , and of an innovation η t = X t — E ( X t | Z t ). We use a nonparametric regression of X t on Z t to obtain residuals η t , which in turn are used to obtain a consistent estimator of g . The estimator was first analyzed by Newey, Powell & Vella (1999) under the assumption that the observations are independent and identically distributed. Here we derive a sample mean‐squared‐error convergence result for independent identically distributed observations as well as a uniform‐convergence result under time‐series dependence.