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Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

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  • Harry H. Kelejian
  • Ingmar R. Prucha
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    Abstract

    One important goal of this study is to develop a methodology of inference for a widely used Cliff-Ord type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first generalize the generalized moments (GM) estimator suggested in Kelejian and Prucha (1998, 1999) for the spatial autoregressive parameter in the disturbance process. We prove the consistency of our estimator; unlike in our earlier paper we also determine its asymptotic distribution, and discuss issues of efficiency. We then define instrumental variable (IV) estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GM estimator under reasonable conditions. Much of the theory is kept general to cover a wide range ofsettings. We note the estimation theory developed by Kelejian and Prucha (1998, 1999) for GM and IV estimators and by Lee (2004) for the quasi-maximum likelihood estimator under the assumption of homoskedastic innovations does not carry over to the case of heteroskedastic innovations. The paper also provides a critical discussion of the usual specification of the parameter space.

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    File URL: http://www.cesifo-group.de/portal/page/portal/DocBase_Content/WP/WP-CESifo_Working_Papers/wp-cesifo-2008/wp-cesifo-2008-11/cesifo1_wp2448.pdf
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    Bibliographic Info

    Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 2448.

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    Date of creation: 2008
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    Handle: RePEc:ces:ceswps:_2448

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    Related research

    Keywords: spatial dependence; heteroskedasticity; Cliff-Ord model; two-stage least squares; generalized moments estimation; asymptotics;

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    References

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    1. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    2. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    3. 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.
    4. Kathleen P. Bell & Nancy E. Bockstael, 2000. "Applying the Generalized-Moments Estimation Approach to Spatial Problems Involving Microlevel Data," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 72-82, February.
    5. Badi H. Baltagi & Seuck Heun Song & Won Koh, 2002. "Testing Panel Data Regression Models with Spatial Error Correlation," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B6-4, International Conferences on Panel Data.
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    7. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    8. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2005. "Estimating Models of Complex FDI: Are There Third-Country Effects?," Center for Policy Research Working Papers 73, Center for Policy Research, Maxwell School, Syracuse University.
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    17. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-33, May.
    18. Badi Baltagi & Dong Li, 2006. "Prediction in the Panel Data Model with Spatial Correlation: the Case of Liquor," Spatial Economic Analysis, Taylor & Francis Journals, vol. 1(2), pages 175-185.
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    26. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
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    Cited by:
    1. Moscone, Francesco & Tosetti, Elisa, 2009. "GMM estimation of spatial panels," MPRA Paper 16327, University Library of Munich, Germany.
    2. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2012. "A Generalized Spatial Panel Data Model with Random Effects," CESifo Working Paper Series 3930, CESifo Group Munich.
    3. Lenka Šťastná, 2009. "Spatial Interdependence of Local Public Expenditures: Selected Evidence from the Czech Republic," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 3(1), pages 007-025, March.
    4. Harald Badinger & Peter Egger, 2008. "GM Estimation of Higher Order Spatial Autoregressive Processes in Panel Data Error Component Models," CESifo Working Paper Series 2301, CESifo Group Munich.
    5. Fingleton, Bernard & Palombi, Silvia, 2013. "Spatial panel data estimation, counterfactual predictions, and local economic resilience among British towns in the Victorian era," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 649-660.
    6. Steven N. Durlauf & Yannis M. Ioannides, 2009. "Social Interactions," Discussion Papers Series, Department of Economics, Tufts University 0739, Department of Economics, Tufts University.
    7. Harald Badinger & Peter Egger, 2009. "Estimation of Higher-Order Spatial Autoregressive Panel Data Error Component Models," CESifo Working Paper Series 2556, CESifo Group Munich.
    8. Harald Badinger & Peter Egger, 2008. "GM Estimation of Higher-Order Spatial Autoregressive Processes in Cross-Section Models with Heteroskedastic Disturbances," CESifo Working Paper Series 2356, CESifo Group Munich.
    9. Moscone, Francesco & Tosetti, Elisa, 2010. "GMM estimation of Spatial Panels with Fixed Effects," MPRA Paper 20152, University Library of Munich, Germany.

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