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Efficient Estimation of Spatial Autoregressive Models

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  • Théophile AZOMAHOU

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.

Suggested Citation

  • Théophile AZOMAHOU, 2001. "Efficient Estimation of Spatial Autoregressive Models," Working Papers of BETA 2001-05, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2001-05
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    File URL: http://www.beta-umr7522.fr/productions/publications/2001/2001-05.pdf
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    References listed on IDEAS

    as
    1. 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 509-533, May.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    4. 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.
    5. 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.
    6. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    7. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    8. 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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    More about this item

    Keywords

    Instrumental variables; Spatial dependence; Nonparametric estimation;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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