IDEAS home Printed from https://ideas.repec.org/p/siu/wpaper/03-2013.html
   My bibliography  Save this paper

LM Tests of Spatial Dependence Based on Bootstrap Critical Values

Author

Listed:
  • Zhenlin Yang

    () (School of Economics, Singapore Management University)

Abstract

To test the existence of spatial dependence in an econometric model, a convenient test is the Lagrange Multiplier (LM) test. However, evidence shows that, infinite samples, the LM test referring to asymptotic critical values may suffer from the problems of size distortion and low power, which become worse with a denser spatial weight matrix. In this paper, residual-based bootstrap methods are introduced for asymptotically refined approximations to the finite sample critical values of the LM statistics. Conditions for their validity are clearly laid out and formal justifications are given in general, and in details under several popular spatial LM tests using Edgeworth expansions. Monte Carlo results show that when the conditions are not fully met, bootstrap may lead to unstable critical values that change significantly with the alternative, whereas when all conditions are met, bootstrap critical values are very stable, approximate much better the finite sample critical values than those based on asymptotics, and lead to significantly improved size and power. The methods are further demonstrated using more general spatial LM tests, in connection with local misspecification and unknown heteroskedasticity.

Suggested Citation

  • Zhenlin Yang, 2013. "LM Tests of Spatial Dependence Based on Bootstrap Critical Values," Working Papers 03-2013, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:03-2013
    as

    Download full text from publisher

    File URL: https://mercury.smu.edu.sg/rsrchpubupload/20295/03-2013.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Kuan-Pin Lin & Zhi-He Long & Bianling Ou, 2011. "The Size and Power of Bootstrap Tests for Spatial Dependence in a Linear Regression Model," Computational Economics, Springer;Society for Computational Economics, vol. 38(2), pages 153-171, August.
    2. Yang, Zhenlin, 2010. "A robust LM test for spatial error components," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 299-310, September.
    3. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, pages 162-169.
    4. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    5. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, pages 421-441.
    6. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    7. Badi H. Baltagi & Zhenlin Yang, 2013. "Standardized LM tests for spatial error dependence in linear or panel regressions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 103-134, February.
    8. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    9. van Giersbergen, Noud P. A. & Kiviet, Jan F., 2002. "How to implement the bootstrap in static or stable dynamic regression models: test statistic versus confidence region approach," Journal of Econometrics, Elsevier, vol. 108(1), pages 133-156, May.
    10. Peter Burridge & Bernard Fingleton, 2010. "Bootstrap Inference in Spatial Econometrics: the J-test," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 93-119.
    11. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
    12. 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.
    13. Anselin, Luc & Moreno, Rosina, 2003. "Properties of tests for spatial error components," Regional Science and Urban Economics, Elsevier, vol. 33(5), pages 595-618, September.
    14. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.
    15. Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
    16. Anselin, Luc & Bera, Anil K. & Florax, Raymond & Yoon, Mann J., 1996. "Simple diagnostic tests for spatial dependence," Regional Science and Urban Economics, Elsevier, vol. 26(1), pages 77-104, February.
    17. Cameron,A. Colin & Trivedi,Pravin K., 2008. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9787111235767, December.
    18. Benjamin Born & Jörg Breitung, 2011. "Simple regression‐based tests for spatial dependence," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 330-342, July.
    19. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, pages 361-376.
    20. 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.
    21. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
    22. Peter Burridge, 2012. "Improving the J Test in the SARAR Model by Likelihood-based Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 75-107, March.
    23. 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.
    24. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    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. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1249-1280, December.

    More about this item

    Keywords

    Asymptotic refinements; Bootstrap; Edgeworth expansion; LM Tests; Spatial dependence; Size; Power; Local misspecification; heteroskedasticity; Wild bootstrap.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:siu:wpaper:03-2013. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (QL THor). General contact details of provider: http://edirc.repec.org/data/sesmusg.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.