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) + 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 η̂_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.