QML estimation of the matrix exponential spatial specification panel data model with fixed effects and heteroskedasticity

Abstract This paper studies a spatial panel data model with fixed effects and heteroskedasticity, where the spatial effects in the dependent variable and disturbances are in the form of matrix exponential spatial specification (MESS). The asymptotic properties of quasi maximum likelihood (QML) estimators with large n and finite or large T are established. We show that the QML estimator (QMLE) can be consistent and asymptotically normal under unknown heteroskedasticity when the spatial weights matrices in the two MESS processes are commutative. We provide a consistent estimator for the standard deviation of the QMLE under regularity conditions, which can be used for inference.