Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors

Let Y = mu*(X) + epsilon, where mu* is unknown and E vertical bar epsilon vertical bar X vertical bar not equal 0 with positive probability but there exist instrumental variables W such that E vertical bar epsilon vertical bar W vertical bar = 0 w.p.l. It is well known that such nonparametric regression models are generally "ill-posed" in the sense that the map from the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating certain linear functionals of mu* without assuming mu* itself to be identified. (C) 2012 Elsevier B.V. All rights reserved.