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Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with Moving Average Disturbance Term

Author

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  • Osman Dogan

    () (Ph.D. Program in Economics, City University of New York Graduate Center)

Abstract

In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. I provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters.

Suggested Citation

  • Osman Dogan, 2013. "Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with Moving Average Disturbance Term," Working Papers 2, City University of New York Graduate Center, Ph.D. Program in Economics.
    • Handle: RePEc:cgc:wpaper:002
    as

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    File URL: http://wfs.gc.cuny.edu/Economics/RePEc/cgc/wpaper/CUNYGC-WP002R.pdf
    File Function: Revised version, December 2014
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    References listed on IDEAS

    as
    1. Arnold, Matthias & Wied, Dominik, 2010. "Improved GMM estimation of the spatial autoregressive error model," Economics Letters, Elsevier, vol. 108(1), pages 65-68, July.
    2. 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.
    3. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, May.
    4. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
    5. Baltagi, Badi H. & Liu, Long, 2011. "An improved generalized moments estimator for a spatial moving average error model," Economics Letters, Elsevier, vol. 113(3), pages 282-284.
    6. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    7. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    8. Osman Dogan & Suleyman Taspinar, 2013. "GMM Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances," Working Papers 1, City University of New York Graduate Center, Ph.D. Program in Economics.
    9. James P. Lesage, 1997. "Bayesian Estimation of Spatial Autoregressive Models," International Regional Science Review, , vol. 20(1-2), pages 113-129, April.
    10. 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.
    11. 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.
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    Cited by:

    1. 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.

    More about this item

    Keywords

    spatial dependence; spatial moving average; spatial autoregressive; maximum likelihood estimator; MLE; asymptotics; heteroskedasticity; SARMA(1; 1);

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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