The second-order bias and mean squared error of nonlinear estimators

Despite the now widespread use of nonlinear estimators, their finite-sample properties have received very little attention in either the statistics or econometrics literature. We partially redress this problem by deriving and examining the second-order bias and mean squared error of a fairly wide class of nonlinear estimators which includes Nonlinear Least Squares, Maximum Likelihood, and many Generalized Method of Moments estimators as special cases. A number of examples are provided. The results from a Monte Carlo exercise demonstrate how the results can be applied for improved inferences.