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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
    Date of revision:
    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. Case, Anne C. & Rosen, Harvey S. & Hines, James Jr., 1993. "Budget spillovers and fiscal policy interdependence : Evidence from the states," Journal of Public Economics, Elsevier, vol. 52(3), pages 285-307, October.
    2. Baltagi, Badi H. & Egger, Peter & Pfaffermayr, Michael, 2007. "Estimating models of complex FDI: Are there third-country effects?," Journal of Econometrics, Elsevier, vol. 140(1), pages 260-281, September.
    3. Badi Baltagi & Dong Li, 2001. "Double Length Artificial Regressions For Testing Spatial Dependence," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 31-40.
    4. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    5. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
    6. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    7. Baltagi, Badi H. & Heun Song, Seuck & Cheol Jung, Byoung & Koh, Won, 2007. "Testing for serial correlation, spatial autocorrelation and random effects using panel data," Journal of Econometrics, Elsevier, vol. 140(1), pages 5-51, September.
    8. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    9. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
    10. Jeffrey P. Cohen & Catherine J. Morrison Paul, 2004. "Public Infrastructure Investment, Interstate Spatial Spillovers, and Manufacturing Costs," The Review of Economics and Statistics, MIT Press, vol. 86(2), pages 551-560, May.
    11. Holtz-Eakin, Douglas, 1994. "Public-Sector Capital and the Productivity Puzzle," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 12-21, February.
    12. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    13. Badi H. Baltagi & Dong Li, 2006. "Prediction in the Panel Data Model with Spatial Correlation: The Case of Liquor," Center for Policy Research Working Papers 84, Center for Policy Research, Maxwell School, Syracuse University.
    14. 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.
    15. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
    16. Eric A. Hanushek & John F. Kain & Jacob M. Markman & Steven G. Rivkin, 2001. "Does Peer Ability Affect Student Achievement?," NBER Working Papers 8502, National Bureau of Economic Research, Inc.
    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, 2000. "LM Tests for Functional Form and Spatial Correlation," Econometric Society World Congress 2000 Contributed Papers 0099, Econometric Society.
    19. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    20. Shroder, Mark, 1995. "Games the States Don't Play: Welfare Benefits and the Theory of Fiscal Federalism," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 183-91, February.
    21. 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.
    22. 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.
    23. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
    24. 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.
    25. Pinkse, Joris & Slade, Margaret E., 1998. "Contracting in space: An application of spatial statistics to discrete-choice models," Journal of Econometrics, Elsevier, vol. 85(1), pages 125-154, July.
    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.
    27. Topa, Giorgio, 2001. "Social Interactions, Local Spillovers and Unemployment," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 261-95, April.
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    Citations

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    Cited by:
    1. 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.
    2. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2013. "A Generalized Spatial Panel Data Model with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 650-685, August.
    3. Steven N. Durlauf & Yannis M. Ioannides, 2009. "Social Interactions," Discussion Papers Series, Department of Economics, Tufts University 0739, Department of Economics, Tufts University.
    4. Moscone, Francesco & Tosetti, Elisa, 2010. "GMM estimation of Spatial Panels with Fixed Effects," MPRA Paper 20152, University Library of Munich, Germany.
    5. 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.
    6. Harald Badinger & Peter Egger, 2009. "Estimation of Higher-Order Spatial Autoregressive Panel Data Error Component Models," CESifo Working Paper Series 2556, CESifo Group Munich.
    7. Moscone, Francesco & Tosetti, Elisa, 2009. "GMM estimation of spatial panels," MPRA Paper 16327, University Library of Munich, Germany.
    8. 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.
    9. 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.

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