Generalized least squares with misspecified serial correlation structures

Abstract

The regression literature contains hundreds of studies on serially correlated disturbances. Most of these studies assume that the structure of the error covariance matrix Ω is known or can be estimated consistently from data. Surprisingly, few studies investigate the properties of estimated generalized least squares (GLS) procedures when the structure of Ω is incorrectly identified and the parameters are inefficiently estimated. We compare the finite sample efficiencies of ordinary least squares (OLS), GLS and incorrect GLS (IGLS) estimators. We also prove new theorems establishing theoretical efficiency bounds for IGLS relative to GLS and OLS. Results from an exhaustive simulation study are used to evaluate the finite sample performance and to demonstrate the robustness of IGLS estimates vis-à-vis OLS and GLS estimates constructed for models with known and estimated (but correctly identified) Ω. Some of our conclusions for finite samples differ from established asymptotic results.