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Finite-Sample Bias Of The Qmle In Spatial Autoregressive Models

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  • Bao, Yong

Abstract

We investigate the finite-sample bias of the quasi-maximum likelihood estimator (QMLE) in spatial autoregressive models with possible exogenous regressors. We derive the approximate bias result of the QMLE in terms of model parameters and also the moments (up to order 4) of the error distribution, and thus a feasible bias-correction procedure is directly applicable. In some special cases, the analytical bias result can be significantly simplified. Our Monte Carlo results demonstrate that the feasible bias-correction procedure works remarkably well.

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  • Bao, Yong, 2013. "Finite-Sample Bias Of The Qmle In Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 68-88, February.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:01:p:68-88_00
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    Cited by:

    1. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    2. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, vol. 3(2), pages 1-36, May.
    3. Yang, Zhenlin & Yu, Jihai & Liu, Shew Fan, 2016. "Bias correction and refined inferences for fixed effects spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 61(C), pages 52-72.
    4. Yong Bao & Aman Ullah & Yun Wang & Jun Yu, 2013. "Bias in the Mean Reversion Estimator in Continuous-Time Gaussian and Lévy Processes," Working Papers 02-2013, Singapore Management University, School of Economics.
    5. Kyriacou, Maria & Phillips, Peter C.B. & Rossi, Francesca, 2023. "Continuously Updated Indirect Inference In Heteroskedastic Spatial Models," Econometric Theory, Cambridge University Press, vol. 39(1), pages 107-145, February.
    6. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
    7. Rossi, Francesca & Robinson, Peter M., 2023. "Higher-order least squares inference for spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 244-269.
    8. Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    9. Yu, Dalei & Bai, Peng & Ding, Chang, 2015. "Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 116-135.
    10. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    11. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers 44/13, Institute for Fiscal Studies.
    12. Kripfganz, Sebastian, 2014. "Unconditional Transformed Likelihood Estimation of Time-Space Dynamic Panel Data Models," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100604, Verein für Socialpolitik / German Economic Association.
    13. Bao, Yong & Ullah, Aman & Wang, Yun & Yu, Jun, 2015. "Bias in the estimation of mean reversion in continuous-time Lévy processes," Economics Letters, Elsevier, vol. 134(C), pages 16-19.
    14. Francesca Rossi & Peter M. Robinson, 2020. "Higher-Order Least Squares Inference for Spatial Autoregressions," Working Papers 04/2020, University of Verona, Department of Economics.
    15. Christoph Strumann, 2019. "Hodges–Lehmann Estimation of Static Panel Models with Spatially Correlated Disturbances," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 141-168, January.
    16. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers CWP44/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.
    18. Kyoo Il Kim, 2016. "Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency," Econometrics, MDPI, vol. 4(4), pages 1-19, December.
    19. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1249-1280, December.
    20. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
    21. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.

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