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Modified QML Estimation of Spatial Autoregressive Models with Unknown Heteroskedasticity and Nonnormality

Author

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  • Shew Fan Liu

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

  • Zhenlin Yang

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

Abstract

In the presence of heteroskedasticity, Lin and Lee (2010) show that the quasi maximum likelihood (QML) estimators of spatial autoregressive models (SAR) can be inconsistent as a ‘necessary’ condition for consistency can be violated, and thus propose robust GMM estimators for the model. In this paper, we first show that this condition may hold in many practical situations and when it does the regular QML estimators can be consistent. In cases where this condition is violated, we propose a modified QML estimation method robust against heteroskedasticity of unknown form. In both cases, asymptotic distributions of the estimators are derived, and methods for estimating robust variances are given, leading to robust inferences for the model. Extensive Monte Carlo results show that the modified QML estimator outperforms the GMM estimators, and the regular QML estimator even when it is consistent. The proposed robust inference methods can also be easily applied.

Suggested Citation

  • Shew Fan Liu & Zhenlin Yang, 2014. "Modified QML Estimation of Spatial Autoregressive Models with Unknown Heteroskedasticity and Nonnormality," Working Papers 14-2014, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:14-2014
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Zhenlin Yang, 2018. "Bootstrap LM tests for higher-order spatial effects in spatial linear regression models," Empirical Economics, Springer, vol. 55(1), pages 35-68, August.
    2. Maria Kyriacou & Peter C.B. Phillips & Francesca Rossi, 2019. "Continuously Updated Indirect Inference in Heteroskedastic Spatial Models," Cowles Foundation Discussion Papers 2208, Cowles Foundation for Research in Economics, Yale University.
    3. Gupta, Abhimanyu & Kokas, Sotirios & Michaelides, Alexander, 2017. "Credit Market Spillovers: Evidence from a Syndicated Loan Market Network," CEPR Discussion Papers 12424, C.E.P.R. Discussion Papers.
    4. Nicolas DEBARSY & Cem ERTUR, 2016. "Interaction matrix selection in spatial econometrics with an application to growth theory," LEO Working Papers / DR LEO 2172, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    5. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, Open Access Journal, vol. 3(2), pages 1-36, May.
    6. Debarsy, Nicolas & Ertur, Cem, 2019. "Interaction matrix selection in spatial autoregressive models with an application to growth theory," Regional Science and Urban Economics, Elsevier, vol. 75(C), pages 49-69.
    7. Jin, Fei & Lee, Lung-fei, 2020. "Asymptotically efficient root estimators for spatial autoregressive models with spatial autoregressive disturbances," Economics Letters, Elsevier, vol. 194(C).
    8. Jin, Fei & Lee, Lung-fei, 2018. "Outer-product-of-gradients tests for spatial autoregressive models," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 35-57.
    9. Jakub Olejnik & Alicja Olejnik, 2017. "Improved asymptotic analysis of Gaussian QML estimators in spatial models," Lodz Economics Working Papers 9/2017, University of Lodz, Faculty of Economics and Sociology.
    10. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    11. Shi, Wei & Lee, Lung-fei, 2017. "Spatial dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 197(2), pages 323-347.
    12. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    13. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.
    14. Li, Liyao & Yang, Zhenlin, 2020. "Estimation of fixed effects spatial dynamic panel data models with small T and unknown heteroskedasticity," Regional Science and Urban Economics, Elsevier, vol. 81(C).

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    More about this item

    Keywords

    Spatial dependence; Unknown heteroskedasticity; Nonnormality; Modified QML estimator; Robust standard error;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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

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