Large Sample Properties of The Matrix Exponential Spatial Specification with an application to FDI

Abstract

This paper considers the large sample properties of the matrix exponential spatial specification (MESS) and compares its properties with those of the spatial autoregressive (SAR) model. We find that the quasimaximum likelihood estimator (QMLE) for the MESS is consistent under heteroskedasticity, a property not shared by the QMLE of the SAR model. For the MESS in both homoskedastic and heteroskedastic cases, consistency is proved and asymptotic distributions are derived. We also consider properties of the generalized method of moments estimator (GMME). In the homoskedastic case, we derive a best GMME that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the QMLE under non-normality. In the heteroskedastic case, an optimal GMME can be more efficient than the QMLE asymptotically and the possible best GMME is also discussed. For the general model that has MESS in both the dependent variable and disturbances, labeled MESS(1,1), the QMLE can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two MESS processes are commutative. Also, properties of the QMLE and GMME for the general model are considered. The QML approach for the MESS model has the computational advantage over that of a SAR model. The computational simplicity carries over to MESS models with any finite order of spatial matrices. No parameter range needs to be imposed in order for the model to be stable. Furthermore, the Delta method is used to derive test statistics for the impacts of exogenous variables on the dependent variable. Results of Monte Carlo experiments for finite sample properties of the estimators are reported. Finally, the MESS(1,1) is applied to Belgium's outward FDI data and we observe that the dominant motivation of Belgium's outward FDI lies in finding cheaper factor inputs. Keywords: Spatial autocorrelation, MESS, QML, GMM, Heteroskedasticity, Delta method, FDI JEL Classification: C12, C13, C21, F14, F21