This paper considers estimation of the function g in the model Yt = g(Xt) + εt when E(εt|Xt) ≠ 0 with nonzero probability. We assume the existence of an instrumental variable Zt that is independent of εt, and of an innovation ηt = Xt - E(Xt|Zt). We use a nonparametric regression of Xt on Zt to obtain residuals η̂t, 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty