EC3SLS Estimator for a Simultaneous System of Spatial Autoregressive Equations with Random Effects

Abstract

This article derives a 3SLS estimator for a simultaneous system of spatial autoregressive equations with random effects which can therefore handle endoegeneity, spatial lag dependence, heterogeneity as well as cross equation correlation. This is done by utilizing the Kelejian and Prucha (1998 Kelejian , H. H. , Prucha , I. R. ( 1998 ). A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances . The Journal of Real Estate Finance and Economics 17 ( 1 ): 99 – 121 .[Crossref], [Web of Science ®] , [Google Scholar]) and Lee (2003 Lee , L. ( 2003 ). Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances . Econometric Reviews 22 ( 4 ): 307 – 335 .[Taylor & Francis Online] , [Google Scholar]) type instruments from the cross-section spatial autoregressive literature and marrying them to the error components 3SLS estimator derived by Baltagi (1981 Baltagi , B.H. ( 1981 ). Simultaneous equations with error components . Journal of Econometrics 17 ( 2 ): 189 – 200 .[Crossref], [Web of Science ®] , [Google Scholar]) for a system of simultaneous panel data equations. Our Monte Carlo experiments indicate that, for the single equation spatial error components 2SLS estimators, there is a slight gain in efficiency when Lee (2003 Lee , L. ( 2003 ). Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances . Econometric Reviews 22 ( 4 ): 307 – 335 .[Taylor & Francis Online] , [Google Scholar]) type rather than Kelejian and Prucha (1998 Kelejian , H. H. , Prucha , I. R. ( 1998 ). A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances . The Journal of Real Estate Finance and Economics 17 ( 1 ): 99 – 121 .[Crossref], [Web of Science ®] , [Google Scholar]) instruments are used. However, there is not much difference in efficiency between these instruments for spatial error components 3SLS estimators.

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