GMM Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances
We consider a spatial econometric model containing a spatial lag in the dependent variable and the disturbance term with an unknown form of heteroskedasticity in innovations. We first prove that the maximum likelihood (ML) estimator for spatial autoregressive models is generally inconsistent when heteroskedasticity is not taken into account in the estimation. We show that the necessary condition for the consistency of the ML estimator of spatial autoregressive parameters depends on the structure of the spatial weight matrices. Then, we extend the robust generalized method of moment (GMM) estimation approach in Lin and Lee (2010) for the spatial model allowing for a spatial lag not only in the dependent variable but also in the disturbance term. We show the consistency of the robust GMM estimator and determine its asymptotic distribution. Finally, through a comprehensive Monte Carlo simulation, we compare finite sample properties of the robust GMM estimator with other estimators proposed in the literature.
|Date of creation:||16 Dec 2013|
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- Harry H. Kelejian & Ingmar R. Prucha & Yevgeny Yuzefovich, 2006. "Estimation Problems In Models With Spatial Weighting Matrices Which Have Blocks Of Equal Elements," Journal of Regional Science, Wiley Blackwell, vol. 46(3), pages 507-515.
- Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
- White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(01), pages 187-230, February.
- Irani Arraiz & David M. Drukker & Harry H. Kelejian & Ingmar R. Prucha, 2010.
"A Spatial Cliff-Ord-Type Model With Heteroskedastic Innovations: Small And Large Sample Results,"
Journal of Regional Science,
Wiley Blackwell, vol. 50(2), pages 592-614.
- Irani Arraiz & David M. Drukker & Harry H. Kelejian & Ingmar R. Prucha, 2008. "A Spatial Cliff-Ord-type Model with Heteroskedastic Innovations: Small and Large Sample Results," CESifo Working Paper Series 2485, CESifo Group Munich.
- Olivier Parent & James Lesage, 2005.
"Bayesian Model Averaging for Spatial Econometric Models,"
- Olivier Parent & James P. Lesage, 2007. "Bayesian Model Averaging for Spatial Econometric Models ," University of Cincinnati, Economics Working Papers Series 2007-02, University of Cincinnati, Department of Economics.
- Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
- repec:cup:cbooks:9780521822893 is not listed on IDEAS
- Harry H. Kelejian & Ingmar R. Prucha, 1997.
"A Generalized Spatial Two Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances,"
Electronic Working Papers
97-002, University of Maryland, Department of Economics, revised Aug 1997.
- Kelejian, Harry H & Prucha, Ingmar 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, Springer, vol. 17(1), pages 99-121, July.
- Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
- James P. Lesage, 1997. "Bayesian Estimation of Spatial Autoregressive Models," International Regional Science Review, SAGE Publishing, vol. 20(1-2), pages 113-129, April.
- Pace, R. Kelley & LeSage, James P., 2004. "Chebyshev approximation of log-determinants of spatial weight matrices," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 179-196, March.
- J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
- Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, December.
- Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
- Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
- Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
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