Modifying the linear two-step Windmeijer correction for the presence of spatial error dependence

Abstract

The aim in the paper is to show how the presence of spatial dependence affects the often-adopted Windmeijer (J Econom 126:25–51, 2005) finite sample correction (For example it is an option facilitating robust estimation in the software package Stata, which is used by many applied econometricians and data analysts.), which corrects the downward bias in estimated parameter standard errors. Windmeijer (2005) explains why, with numerous instruments, the estimated asymptotic standard errors of the efficient, two-step, GMM estimator are downward biased in small samples. GMM estimation is based on an estimated optimal weight matrix, which is the inverse of the covariance of the sample moments, and the bias results from the weight matrix being evaluated at estimated, rather than the true values of parameters. Hwang et al. (J Econom 229(2):276–298, 2022) provide a correction to the Windmeijer (2005) finite sample correction to allow for over-identification bias. The novel contribution of the current paper is to show how the Windmeijer (2005) correction can be modified given spatial dependence in the error term of a model with moments conditions that are linear in parameters estimated by GMM, leading to corrected standard errors and therefore more accurate inference. Monte Carlo simulations are used to demonstrate the effect of the modification and two examples using real data shows how inference may be affected by ignoring the effect of spatial error dependence.