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The C(α)-type gradient test for spatial dependence in spatial autoregressive models

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  • Lung-fei Lee

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  • Jihai Yu

    ()

Abstract

This paper proposes the C(α)-type test in the GMM framework to test the possible presence of spatial correlation through the spatial lag in the spatial autoregressive (SAR) model. This test statistics is especially useful for the SAR model with disturbances under unknown heteroskedasticity. We provide analytical justification of its asymptotic distribution and also investigate its performance via various Monte Carlo simulations. We show that the C(α) test is computationally simple and has satisfactory finite sample performance. Copyright Springer-Verlag 2012

Suggested Citation

  • Lung-fei Lee & Jihai Yu, 2012. "The C(α)-type gradient test for spatial dependence in spatial autoregressive models," Letters in Spatial and Resource Sciences, Springer, vol. 5(3), pages 119-135, October.
  • Handle: RePEc:spr:lsprsc:v:5:y:2012:i:3:p:119-135
    DOI: 10.1007/s12076-012-0077-0
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    References listed on IDEAS

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    1. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
    2. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    3. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    4. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. 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.
    7. 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.
    8. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    9. Lee, Lung-fei & Liu, Xiaodong, 2010. "Efficient Gmm Estimation Of High Order Spatial Autoregressive Models With Autoregressive Disturbances," Econometric Theory, Cambridge University Press, vol. 26(01), pages 187-230, February.
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    Citations

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    Cited by:

    1. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1249-1280, December.
    2. repec:eee:regeco:v:65:y:2017:i:c:p:65-88 is not listed on IDEAS
    3. repec:eee:regeco:v:72:y:2018:i:c:p:35-57 is not listed on IDEAS

    More about this item

    Keywords

    C(α) test; Gradient test; Generalized method of moments; Spatial dependence; C12; C23;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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