HIGHER-ORDER APPROXIMATION OF IV ESTIMATORS WITH INVALID INSTRUMENTS

This paper analyzes the higher-order approximation of instrumental variable (IV) estimators in a linear homoskedastic IV regression model when large set instruments with potential invalidity is present. We establish theoretical results on mean-squared error (MSE) two-stage least-squares (2SLS), limited information maximum likelihood (LIML), Fuller (FULL), bias-adjusted 2SLS, and jackknife version LIML FULL by allowing for local violations instrument exogeneity conditions. Based to MSE, we consider selection criteria that can be used choose among available instruments. demonstrate asymptotic optimality procedure proposed Donald Newey (2001, Econometrica 69, 1161–1191) presence locally (faster than $N^{-1/2}$ ) invalid sense dominant term MSE chosen asymptotically equivalent infeasible optimum. Furthermore, propose procedures sets conservative (known) valid potentially ( based considering bias-variance trade-off.