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A More Efficient Best Spatial Three-stage Least Squares Estimator for Spatial Autoregressive Models

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  • Zhengyu Zhang

    (Research Center of Econometrics, Shanghai Academy of Social Sciences)

  • Pingfang Zhu

    (Research Center of Econometrics, Shanghai Academy of Social Sciences)

Abstract

Lee (2003) proposed for spatial autoregressive (SAR) model the best spatial two-stage least squares estimator (BS2SLSE) as an improvement on Kelejian and Prucha (1998)¡¯s S2SLSE. In this paper, we show that one more step iteration based on BS2SLSE gives a spatial counterpart of the three-stage least squares estimator for a system of J equations. This estimator, named BS3SLSE, is shown to be equivalent to BS2SLSE under normality and more efficient under non-normality. The proposed BS3SLSE can be interpreted as a GMM estimator where the number of moments increases with the sample size n at some slow rate. The asymptotic efficiency of BS3SLSE relative to other previously proposed estimators such as MLE (Lee, 2004) and GMME (Lee, 2007a) is also discussed. As an empirical illustration, we apply these estimation procedures to re-examining the presence of environmental ¡°race-to-the-bottom¡± effect in competition for FDI across China municipal governments.

Suggested Citation

  • Zhengyu Zhang & Pingfang Zhu, 2010. "A More Efficient Best Spatial Three-stage Least Squares Estimator for Spatial Autoregressive Models," Annals of Economics and Finance, Society for AEF, vol. 11(1), pages 155-184, May.
    • Handle: RePEc:cuf:journl:y:2010:v:11:i:1:p:155-184
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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.
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    3. Werner Antweiler & Brian R. Copeland & M. Scott Taylor, 2001. "Is Free Trade Good for the Environment?," American Economic Review, American Economic Association, vol. 91(4), pages 877-908, September.
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    5. 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.
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    7. Wheeler, David, 2001. "Racing to the bottom : foreign investment and air pollution in developing countries," Policy Research Working Paper Series 2524, The World Bank.
    8. 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.
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    11. 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.
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    1. Marius C. O. Amba & Taoufiki Mbratana & Julie Gallo, 2023. "Spatial panel simultaneous equations models with error components," Empirical Economics, Springer, vol. 65(3), pages 1149-1196, September.

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    More about this item

    Keywords

    Spatial autoregressive model; 3SLSE; GMME; Relative asymptotic efficiency;
    All these keywords.

    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
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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