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

This paper considers estimation of the function g in the model Y_t = g(X_t ) + ?_t when E(?_t|Xt) ≠ 0 with nonzero probability. We assume the existence of an instrumental variable Z_t that is independent of ?_t, and of an innovation ηt = 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.