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Efficient Estimation of Spatial Autoregressive Models

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  • Théophile AZOMAHOU
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    Abstract

    This paper considers estimating general spatial autoregressive models using the generalized method of moments (GMM). I propose nonparametric estimates of the optimal instruments based on conditional second moment restrictions. I show that these instruments are optimal over all possible instruments, especially over those usually suggested in a spatial context. I provide a nonparametric estimator of sample autocovariances function for irregularly spaced spatial processes, and I show that this estimator converges in probability. I then derive the consistency in norm L_2 of the resulting asymptotic variance matrix estimator. Finally, the asymptotic distribution of the GMM estimator is stated.

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    File URL: http://www.beta-umr7522.fr/productions/publications/2001/2001-05.pdf
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    Bibliographic Info

    Paper provided by Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg in its series Working Papers of BETA with number 2001-05.

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    Date of creation: 2001
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    Handle: RePEc:ulp:sbbeta:2001-05

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    Keywords: Instrumental variables; Spatial dependence; Nonparametric estimation;

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    References

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    1. Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers 341, Princeton, Department of Economics - Econometric Research Program.
    2. Hautsch, Nikolaus & Klotz, Stefan, 2003. "Estimating the neighborhood influence on decision makers: theory and an application on the analysis of innovation decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 52(1), pages 97-113, September.
    3. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    4. 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.
    5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    6. 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.
    7. Théophile AZOMAHOU & Agénor LAHATTE, 2000. "On the Inconsistency of the Ordinary Least Squares Estimator for Spatial Autoregressive Processes," Working Papers of BETA 2000-12, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    8. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
    9. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
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