Bias Reduction for Linearized Nonlinear Regression Models by Simulation Estimations

Abstract

Nonlinear models are commonly linearized by a Taylor series expansion approximation. The conventional ordinary least squares (OLS) estimator for the linearized regression equation is known to suffer from a bias due to the linearization approximation. That is, though OLS is unbiased for the linearized regression, the estimates are biased for the true underlying nonlinear model. A simulation estimation technique is developed here to eliminate or reduce the linearization bias. The new technique is shown to reduce the OLS linearization bias through a series of Monte Carlo sampling experiments. The technique is also applied to a nonlinear consumption function for the U.S.