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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
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    File URL: http://wfs.gc.cuny.edu/Economics/RePEc/cgc/wpaper/CUNYGC-WP002R.pdf
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    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. 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. Bernard Fingleton, 2008. "A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(1), pages 27-44.
    4. 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.
    5. L W Hepple, 1995. "Bayesian Techniques in Spatial and Network Econometrics: 2. Computational Methods and Algorithms," Environment and Planning A, , vol. 27(4), pages 615-644, April.
    6. Bernard Fingleton, 2009. "A generalized method of moments estimator for a spatial model with moving average errors, with application to real estate prices," Studies in Empirical Economics, in: Giuseppe Arbia & Badi H. Baltagi (ed.), Spatial Econometrics, pages 35-57, Springer.
    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. 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.
    9. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, November.
    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. 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.
    12. Harry H. Kelejian & Dennis P. Robinson, 1993. "A Suggested Method Of Estimation For Spatial Interdependent Models With Autocorrelated Errors, And An Application To A County Expenditure Model," Papers in Regional Science, Wiley Blackwell, vol. 72(3), pages 297-312, July.
    13. 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.
    14. Manfred M. Fischer & Peter Nijkamp (ed.), 2014. "Handbook of Regional Science," Springer Books, Springer, edition 127, number 978-3-642-23430-9, March.
    15. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    16. L W Hepple, 1995. "Bayesian Techniques in Spatial and Network Econometrics: 1. Model Comparison and Posterior Odds," Environment and Planning A, , vol. 27(3), pages 447-469, March.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. James P. Lesage, 1997. "Bayesian Estimation of Spatial Autoregressive Models," International Regional Science Review, , vol. 20(1-2), pages 113-129, April.
    23. 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.
    24. 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.
    25. Lung-fei Lee & Xiaodong Liu & Xu Lin, 2010. "Specification and estimation of social interaction models with network structures," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 145-176, July.
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    Cited by:

    1. Otto, Philipp & Sibbertsen, Philipp, 2023. "Spatial autoregressive fractionally integrated moving average model," Hannover Economic Papers (HEP) dp-712, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    2. 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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    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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