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


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  • Osman Dogan

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

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    In this study, we investigate the necessary condition for the consistency of the maximum like- lihood estimator (MLE) of spatial models that have a spatial moving average process in the disturbance term (for short SARMA(1,1)). We show that the maximum likelihood estimator (MLE) of the spatial autoregressive and spatial moving average parameters is generally incon- sistent when heteroskedasticity is not considered in the estimation. The necessary condition for the consistency of the MLE depends on the structure of the spatial weight matrices. We also show that the inconsistency of the spatial autoregressive and spatial moving average parameters contaminates the MLE of the parameters of the exogenous variables. A Monte Carlo simulation study provides evaluation of the performance of the MLE in the presence of heteroskedastic innovations. The simulation results indicate that the MLE imposes substantial amount of bias on both autoregressive and moving average parameters. However, they also show that the MLE imposes almost no bias on the parameters of the exogenous variables in moderate sample sizes.

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    Bibliographic Info

    Paper provided by City University of New York Graduate Center, Ph.D. Program in Economics in its series Working Papers with number 002.

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    Length: 33
    Date of creation: 16 Dec 2013
    Date of revision:
    Handle: RePEc:cgc:wpaper:002

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

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    1. 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.
    2. Arnold, Matthias & Wied, Dominik, 2010. "Improved GMM estimation of the spatial autoregressive error model," Economics Letters, Elsevier, vol. 108(1), pages 65-68, July.
    3. 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.
    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. 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. 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.
    7. 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.
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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.


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