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Estimation of spatial autoregressive models with covariate measurement errors

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  • Luo, Guowang
  • Wu, Mixia
  • Pang, Zhen

Abstract

In this paper, linear spatial autoregressive (SAR) models with covariate measurement errors are studied. A three-stage least squares (3SLS) estimation method both with Berkson’s and classical types of instrumental variables is proposed and asymptotic normality of the proposed estimator using each type of instrumental variables is derived under mild conditions. Simulation studies are conducted to investigate the finite sample performance of the proposed estimator. A real data example is used to illustrate the developed method.

Suggested Citation

  • Luo, Guowang & Wu, Mixia & Pang, Zhen, 2022. "Estimation of spatial autoregressive models with covariate measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jmvana:v:192:y:2022:i:c:s0047259x22000872
    DOI: 10.1016/j.jmva.2022.105093
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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. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2012. "Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration," Journal of Econometrics, Elsevier, vol. 167(1), pages 16-37.
    3. Warren J. Straws & Raymond J. Carroll & Steven M. Bortnick & John R. Menkedick & Bradley D. Schultz, 2001. "Combining Datasets to Predict the Effects of Regulation of Environmental Lead Exposure in Housing Stock," Biometrics, The International Biometric Society, vol. 57(1), pages 203-210, March.
    4. Chunrong Ai & Yuanqing Zhang, 2017. "Estimation of partially specified spatial panel data models with fixed-effects," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 6-22, March.
    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. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    7. Datta, Gauri S. & Torabi, Mahmoud & Rao, J.N.K. & Liu, Benmei, 2018. "Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 49-59.
    8. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.
    9. Paul Gustafson, 2007. "Measurement error modelling with an approximate instrumental variable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 797-815, November.
    10. Liang Li & Tom Greene, 2008. "Varying Coefficients Model with Measurement Error," Biometrics, The International Biometric Society, vol. 64(2), pages 519-526, June.
    11. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
    12. Sun, Yiguo, 2016. "Functional-coefficient spatial autoregressive models with nonparametric spatial weights," Journal of Econometrics, Elsevier, vol. 195(1), pages 134-153.
    13. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    14. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2018. "Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 261-275.
    15. 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.
    16. Lung-fei Lee & Jihai Yu, 2012. "QML Estimation of Spatial Dynamic Panel Data Models with Time Varying Spatial Weights Matrices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 31-74, March.
    17. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    18. Raymond J. Carroll & David Ruppert & Ciprian M. Crainiceanu & Tor D. Tosteson & Margaret R. Karagas, 2004. "Nonlinear and Nonparametric Regression and Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 736-750, January.
    19. 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.
    20. 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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