IDEAS home Printed from https://ideas.repec.org/p/siu/wpaper/15-2014.html
   My bibliography  Save this paper

Asymptotic Distribution and Finite-Sample Bias Correction of QML Estimators for Spatial Error Dependence Model

Author

Listed:
  • Shew Fan Liu

    () (School of Economics, Singapore Management University, Singapore, 178903)

  • Zhenlin Yang

    () (School of Economics, Singapore Management University, Singapore, 178903)

Abstract

In studying the asymptotic and finite-sample properties of quasi-maximum likelihood (QML) estimators for the spatial linear regression models, much attention has been paid to the spatial lag dependence (SLD) model; little has been given to its companion, the spatial error dependence (SED) model. In particular, the effect of spatial dependence on the convergence rate of the QML estimators has not been formally studied, and methods for correcting finite-sample bias of the QML estimators have not been given. This paper fills in these gaps. Of the two, bias correction is particularly important to the application of this model. Contrary to the common perceptions, both the large and small sample behaviors of the QML estimators for the SED model can be different from those for the SLD model in terms of the rate of convergence and the magnitude of bias. Monte Carlo results show that the bias can be severe and the proposed bias correction procedure is very effective.

Suggested Citation

  • Shew Fan Liu & Zhenlin Yang, 2014. "Asymptotic Distribution and Finite-Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Working Papers 15-2014, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:15-2014
    as

    Download full text from publisher

    File URL: https://mercury.smu.edu.sg/rsrchpubupload/24859/15-2014.pdf
    Download Restriction: no

    Other versions of this item:

    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.
    2. Martellosio, Federico, 2010. "Power Properties Of Invariant Tests For Spatial Autocorrelation In Linear Regression," Econometric Theory, Cambridge University Press, vol. 26(01), pages 152-186, February.
    3. Bun, Maurice J.G. & Carree, Martin A., 2005. "Bias-Corrected Estimation in Dynamic Panel Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 200-210, April.
    4. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    5. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    6. 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.
    7. 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.
    8. Bao, Yong, 2013. "Finite-Sample Bias Of The Qmle In Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 29(01), pages 68-88, February.
    9. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, March.
    10. Bernard Fingleton, 2008. "A generalized method of moments estimator for a spatial model with moving average errors, with application to real estate prices," Empirical Economics, Springer, vol. 34(1), pages 35-57, February.
    11. 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.
    12. Baltagi, Badi H. & Yang, Zhenlin, 2013. "Heteroskedasticity and non-normality robust LM tests for spatial dependence," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 725-739.
    13. 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.
    14. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    15. Bao, Yong & Ullah, Aman, 2007. "Finite sample properties of maximum likelihood estimator in spatial models," Journal of Econometrics, Elsevier, vol. 137(2), pages 396-413, April.
    16. Liu, Shew Fan & Yang, Zhenlin, 2015. "Modified QML estimation of spatial autoregressive models with unknown heteroskedasticity and nonnormality," Regional Science and Urban Economics, Elsevier, vol. 52(C), pages 50-70.
    17. 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.
    18. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    19. Luc Anselin, 2003. "Spatial Externalities, Spatial Multipliers, And Spatial Econometrics," International Regional Science Review, , vol. 26(2), pages 153-166, April.
    20. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
    21. 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.
    22. Kiviet, Jan F., 1995. "On bias, inconsistency, and efficiency of various estimators in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 68(1), pages 53-78, July.
    23. Magnus, J.R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Other publications TiSEM 388c2c25-0925-4b56-834a-7, Tilburg University, School of Economics and Management.
    24. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 252-277, April.
    25. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    26. James LeSage & R. Kelley Pace, 2010. "Spatial Econometrics," Book Chapters,in: Web Book of Regional Science Regional Research Institute, West Virginia University.
    27. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    28. Magnus, Jan R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Journal of Econometrics, Elsevier, vol. 7(3), pages 281-312, April.
    29. 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.
    30. Bao, Yong, 2013. "Finite Sample Bias Of The Qmle In Spatial Autoregressive Models – Erratum," Econometric Theory, Cambridge University Press, vol. 29(01), pages 89-89, February.
    31. J. Barkley Rosser, 2009. "Introduction," Chapters,in: Handbook of Research on Complexity, chapter 1 Edward Elgar Publishing.
    32. 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.
    33. 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.
    34. 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.
    35. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    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. Yang, Zhenlin & Yu, Jihai & Liu, Shew Fan, 2016. "Bias correction and refined inferences for fixed effects spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 61(C), pages 52-72.
    2. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.

    More about this item

    Keywords

    Asymptotics; Bias Correction; Bootstrap; Concentrated estimating equation; Monte Carlo; Spatial layout; Stochastic expansion;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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:15-2014. 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.