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Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach

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  • Doğan, Osman
  • Taşpınar, Süleyman

Abstract

Most of the estimators suggested for the estimation of spatial autoregressive models are generally inconsistent in the presence of an unknown form of heteroskedasticity in the disturbance term. The estimators formulated from the generalized method of moments (GMM) and the Bayesian Markov Chain Monte Carlo (MCMC) frameworks can be robust to unknown forms of heteroskedasticity. In this study, the finite sample properties of the robust GMM estimator are compared with the estimators based on the Bayesian MCMC approach for the spatial autoregressive models with heteroskedasticity of an unknown form. A Monte Carlo simulation study provides evaluation of the performance of the heteroskedasticity robust estimators. Our results indicate that the MLE and the Bayesian estimators impose relatively greater bias on the spatial autoregressive parameter when there is negative spatial dependence in the model. In terms of finite sample efficiency, the Bayesian estimators perform better than the robust GMM estimator. In addition, two empirical applications are provided to evaluate relative performance of heteroskedasticity robust estimators.

Suggested Citation

  • Doğan, Osman & Taşpınar, Süleyman, 2014. "Spatial autoregressive models with unknown heteroskedasticity: A comparison of Bayesian and robust GMM approach," Regional Science and Urban Economics, Elsevier, vol. 45(C), pages 1-21.
    • Handle: RePEc:eee:regeco:v:45:y:2014:i:c:p:1-21
    DOI: 10.1016/j.regsciurbeco.2013.12.003
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    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. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649, Elsevier.
    3. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    4. Olivier Parent & James P. LeSage, 2008. "Using the variance structure of the conditional autoregressive spatial specification to model knowledge spillovers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 235-256.
    5. 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.
    6. Kristian Behrens & Cem Ertur & Wilfried Koch, 2012. "‘Dual’ Gravity: Using Spatial Econometrics To Control For Multilateral Resistance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 773-794, August.
    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. Irani Arraiz & David M. Drukker & Harry H. Kelejian & Ingmar R. Prucha, 2010. "A Spatial Cliff‐Ord‐Type Model With Heteroskedastic Innovations: Small And Large Sample Results," Journal of Regional Science, Wiley Blackwell, vol. 50(2), pages 592-614, May.
    9. Gilley, Otis W. & Pace, R. Kelley, 1996. "On the Harrison and Rubinfeld Data," Journal of Environmental Economics and Management, Elsevier, vol. 31(3), pages 403-405, November.
    10. 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.
    11. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, September.
    12. 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.
    13. Olivier Parent & James Lesage, 2005. "Bayesian Model Averaging for Spatial Econometric Models," Post-Print hal-00375489, HAL.
    14. 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.
    15. James P. Lesage, 1997. "Bayesian Estimation of Spatial Autoregressive Models," International Regional Science Review, , vol. 20(1-2), pages 113-129, April.
    16. 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.
    17. Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2007. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9780521671736, June.
    18. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    19. Geweke, John & Keane, Michael, 2001. "Computationally intensive methods for integration in econometrics," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 56, pages 3463-3568, Elsevier.
    20. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    21. 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.
    22. Chan,Joshua & Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2019. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9781108423380, September.
    23. McCallum, John, 1995. "National Borders Matter: Canada-U.S. Regional Trade Patterns," American Economic Review, American Economic Association, vol. 85(3), pages 615-623, June.
    24. Harald Badinger & Peter Egger, 2011. "Estimation of higher‐order spatial autoregressive cross‐section models with heteroscedastic disturbances," Papers in Regional Science, Wiley Blackwell, vol. 90(1), pages 213-235, March.
    25. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    26. 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.
    27. 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.
    28. Chan,Joshua & Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2019. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9781108437493, September.
    29. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    30. L Anselin, 1982. "A Note on Small Sample Properties of Estimators in a First-Order Spatial Autoregressive Model," Environment and Planning A, , vol. 14(8), pages 1023-1030, August.
    31. 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.
    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. 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.
    34. 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.
    35. 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.
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    2. Dogan, Osman & Taspinar, Suleyman, 2016. "Bayesian Inference in Spatial Sample Selection Models," MPRA Paper 82829, University Library of Munich, Germany.
    3. Agovino, Massimiliano & Aprile, Maria Carmela & Garofalo, Antonio & Mariani, Angela, 2018. "Cancer mortality rates and spillover effects among different areas: A case study in Campania (southern Italy)," Social Science & Medicine, Elsevier, vol. 204(C), pages 67-83.

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    More about this item

    Keywords

    Spatial autoregressive models; Unknown heteroskedasticity; Robustness; GMM; Asymptotics; MLE; Markov Chain Monte Carlo (MCMC);
    All these keywords.

    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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