IDEAS home Printed from https://ideas.repec.org/a/spr/lsprsc/v5y2012i3p119-135.html
   My bibliography  Save this article

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

Author

Listed:
  • Lung-fei Lee
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s12076-012-0077-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s12076-012-0077-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    2. 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.
    3. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    4. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    6. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    7. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
    8. 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.
    9. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    10. 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.
    11. Cosslett, Stephen R. & Lee, Lung-Fei, 1985. "Serial correlation in latent discrete variable models," Journal of Econometrics, Elsevier, vol. 27(1), pages 79-97, January.
    12. 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.
    13. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    14. 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.
    15. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    16. 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.
    17. 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(1), pages 187-230, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rossi, Francesca & Robinson, Peter M., 2023. "Higher-order least squares inference for spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 244-269.
    2. Jungyoon Lee & Peter C.B. Phillips & Francesca Rossi, 2020. "Consistent Misspecification Testing in Spatial Autoregressive Models," Cowles Foundation Discussion Papers 2256, Cowles Foundation for Research in Economics, Yale University.
    3. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1249-1280, December.
    4. Taşpınar, Süleyman & Doğan, Osman & Bera, Anil K., 2017. "GMM gradient tests for spatial dynamic panel data models," Regional Science and Urban Economics, Elsevier, vol. 65(C), pages 65-88.
    5. Jin, Fei & Lee, Lung-fei, 2018. "Outer-product-of-gradients tests for spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 35-57.
    6. Francesca Rossi & Peter M. Robinson, 2020. "Higher-Order Least Squares Inference for Spatial Autoregressions," Working Papers 04/2020, University of Verona, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    2. Jin, Fei & Lee, Lung-fei, 2012. "Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 446-458.
    3. Jin, Fei & Lee, Lung-fei, 2018. "Outer-product-of-gradients tests for spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 35-57.
    4. Yong Bao & Xiaotian Liu & Lihong Yang, 2020. "Indirect Inference Estimation of Spatial Autoregressions," Econometrics, MDPI, vol. 8(3), pages 1-26, September.
    5. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    6. Debarsy, Nicolas & Jin, Fei & Lee, Lung-fei, 2015. "Large sample properties of the matrix exponential spatial specification with an application to FDI," Journal of Econometrics, Elsevier, vol. 188(1), pages 1-21.
    7. Zhengyu Zhang, 2013. "A Pairwise Difference Estimator for Partially Linear Spatial Autoregressive Models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(2), pages 176-194, June.
    8. Cynthia Fan Yang, 2021. "Common factors and spatial dependence: an application to US house prices," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 14-50, January.
    9. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    10. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    11. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    12. Jin, Fei & Lee, Lung-fei, 2020. "Asymptotically efficient root estimators for spatial autoregressive models with spatial autoregressive disturbances," Economics Letters, Elsevier, vol. 194(C).
    13. Osman Doğan, 2015. "Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with a Moving Average Disturbance Term," Econometrics, MDPI, vol. 3(1), pages 1-27, February.
    14. Wang, Wei & Lee, Lung-Fei & Bao, Yan, 2018. "GMM estimation of the spatial autoregressive model in a system of interrelated networks," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 167-198.
    15. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, vol. 3(2), pages 1-36, May.
    16. Doğan, Osman & Taşpınar, Süleyman, 2014. "Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach," Regional Science and Urban Economics, Elsevier, vol. 45(C), pages 1-21.
    17. Bing Su & Fukang Zhu & Ke Zhu, 2023. "Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables," Papers 2301.06658, arXiv.org.
    18. Doğan, Osman & Taşpınar, Süleyman, 2013. "GMM estimation of spatial autoregressive models with moving average disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(6), pages 903-926.
    19. David M. Drukker & Peter Egger & Ingmar R. Prucha, 2013. "On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 686-733, August.
    20. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.

    More about this item

    Keywords

    C(α) test; Gradient test; Generalized method of moments; Spatial dependence; C12; C23;
    All these keywords.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:lsprsc:v:5:y:2012:i:3:p:119-135. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.