Large sample properties of the matrix exponential spatial specification with an application to FDI

This paper studies large sample properties of the matrix exponential spatial specification (MESS). We find that the quasi-maximum likelihood estimator (QMLE) for the MESS is consistent under heteroskedasticity, a property not shared by the QMLE of the SAR model. 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. We also consider 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. 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. 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.