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A note on 2SLS estimation of the mixed regressive spatial autoregressive model

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  • Liu, Long

Abstract

This paper considers the mixed regressive spatial autoregressive model in an important special case where the spatially lag term is collinear with the regressors. The asymptotic properties of the two-stage least square (2SLS) estimator suggested by Kelejian and Prucha (1998) are derived under such a circumstance. Although the coefficients of the spatial effect cannot be consistently estimated, the coefficients of regressors may still be consistently estimated with a regular n speed of convergence, for example, when all instruments are irrelevant. Furthermore, when the coefficient of the spatial effect is close to 1, it could be also consistently estimated.

Suggested Citation

  • Liu, Long, 2015. "A note on 2SLS estimation of the mixed regressive spatial autoregressive model," Economics Letters, Elsevier, vol. 134(C), pages 49-52.
    • Handle: RePEc:eee:ecolet:v:134:y:2015:i:c:p:49-52
    DOI: 10.1016/j.econlet.2015.06.007
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    References listed on IDEAS

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    1. 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.
    2. Lung-Fei Lee & Jihai Yu, 2013. "Near Unit Root in the Spatial Autoregressive Model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 314-351, September.
    3. 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.
    4. Badi H. Baltagi & Chihwa Kao & Long Liu, 2013. "The Estimation and Testing of a Linear Regression with Near Unit Root in the Spatial Autoregressive Error Term," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 241-270, September.
    5. 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.
    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.
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    Cited by:

    1. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    2. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-31, March.

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    More about this item

    Keywords

    Spatial lag model; Two-stage least square; Instrument variables;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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