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Estimation of Spatial Regression Models with Autoregressive Errors by Two-Stage Least Squares Procedures: A Serious Problem

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  • Harry H. Kelejian

    (Department of Economics, University of Maryland, College Park, MD 20742 USA, kelejian@econ.umd.edu)

  • Ingmar R. Prucha

    (Department of Economics, University of Maryland, College Park, MD 20742 USA, prucha@econ.umd.edu)

Abstract

Time series regression models that have autoregressive errors are often estimated by two-stage procedures which are based on the Cochrane-Orcutt (1949) transformation. It seems natural to also attempt the estimation of spatial regression models whose error terms are autoregressive in terms of an analogous transformation. Various two-stage least squares procedures suggest themselves in this context, including an analog to Durbin's (1960) procedure. Indeed, these procedures are so suggestive and computationally convenient that they are quite "tempting." Unfortunately, however, as shown in this paper, these two-stage least squares procedures are generally, in a typical cross-sectional spatial context, not consistent and therefore should not be used.

Suggested Citation

  • Harry H. Kelejian & Ingmar R. Prucha, 1997. "Estimation of Spatial Regression Models with Autoregressive Errors by Two-Stage Least Squares Procedures: A Serious Problem," International Regional Science Review, , vol. 20(1-2), pages 103-111, April.
  • Handle: RePEc:sae:inrsre:v:20:y:1997:i:1-2:p:103-111
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    References listed on IDEAS

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    1. Dubin, Robin A, 1988. "Estimation of Regression Coefficients in the Presence of Spatially Autocorrelated Error Terms," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 466-474, August.
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    3. Blommestein, Hans J., 1983. "Specification and estimation of spatial econometric models : A discussion of alternative strategies for spatial economic modelling," Regional Science and Urban Economics, Elsevier, vol. 13(2), pages 251-270, May.
    4. P Burridge, 1981. "Testing for a Common Factor in a Spatial Autoregression Model," Environment and Planning A, , vol. 13(7), pages 795-800, July.
    5. Benedikt M. Pötscher & Ingmar R. Prucha, 1999. "Basic Elements of Asymptotic Theory," Electronic Working Papers 99-001, University of Maryland, Department of Economics.
    6. Anselin, Luc, 1990. "Some robust approaches to testing and estimation in spatial econometrics," Regional Science and Urban Economics, Elsevier, vol. 20(2), pages 141-163, September.
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    Citations

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    Cited by:

    1. Julie Le Gallo, 2002. "Économétrie spatiale : l'autocorrélation spatiale dans les modèles de régression linéaire," Économie et Prévision, Programme National Persée, vol. 155(4), pages 139-157.
    2. Gupta, Abhimanyu & Robinson, Peter M., 2018. "Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension," Journal of Econometrics, Elsevier, vol. 202(1), pages 92-107.
    3. 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.
    4. Basile, Roberto & Durbán, María & Mínguez, Román & María Montero, Jose & Mur, Jesús, 2014. "Modeling regional economic dynamics: Spatial dependence, spatial heterogeneity and nonlinearities," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 229-245.
    5. Kazuhiko Kakamu & Hajime Wago, 2008. "Small-sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood MethodsAn earlier version of this paper was presented at the 2007 Fall meeting of Japa," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(3), pages 305-319.
    6. Agostini, Claudio A. & Brown, Philip H. & Zhang, Xiaobo, 2010. "Neighbor effects in the provision of public goods in a young democracy: Evidence from China," IFPRI discussion papers 1027, International Food Policy Research Institute (IFPRI).
    7. Christian Helmers & Manasa Patnam, 2014. "Does the rotten child spoil his companion? Spatial peer effects among children in rural India," Quantitative Economics, Econometric Society, vol. 5, pages 67-121, March.
    8. Anselin, Luc, 2002. "Under the hood : Issues in the specification and interpretation of spatial regression models," Agricultural Economics, Blackwell, vol. 27(3), pages 247-267, November.
    9. Liu, Shuangzhe & Ma, Tiefeng & Polasek, Wolfgang, 2014. "Spatial system estimators for panel models: A sensitivity and simulation study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 101(C), pages 78-102.
    10. Di Fang & Timothy J. Richards, 2018. "New Maize Variety Adoption in Mozambique: A Spatial Approach," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 66(3), pages 469-488, September.
    11. Julie Le Gallo, 2000. "Spatial econometrics (1, Spatial autocorrelation)
      [Econométrie spatiale (1, Autocorrélation spatiale)]
      ," Working Papers hal-01527290, HAL.
    12. Sylvain Barde, 2008. "The spatial structure of French wages : Investigating the robustness of two-stage least squares estimations of spatial autoregressive models," Sciences Po publications 2008-03, Sciences Po.
    13. Christian Helmers & Manasa Patnam, 2014. "Does the rotten child spoil his companion? Spatial peer effects among children in rural India," Quantitative Economics, Econometric Society, vol. 5, pages 67-121, 03.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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