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One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data

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  • Fang Lu

    (Hunan Normal University)

  • Jing Yang

    (Hunan Normal University)

  • Xuewen Lu

    (University of Calgary)

Abstract

Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention. Motivated by a Boston housing price data analysis, this paper studies the sparse inference of varying coefficient partially linear spatial autoregressive model, which is quite valuable in econometrics with high-dimensional data. A novel, efficient and convenient one-step variable selection procedure is proposed by using a twofold penalty for simultaneous estimation and variable selection of the parametric components and varying coefficient functions, in which the varying coefficient functions are approximated by the B-spline basis. Under some regularity conditions, asymptotic properties of the resulting estimators are established, including consistency, asymptotic normality and the oracle property. Besides, the optimal choices of the tuning parameters are discussed and a practical iterative algorithm based on the locally quadratic approximation approach is presented for implementation. Finally, extensive numerical simulations and a Boston housing price data analysis are conducted to confirm the finite sample performance and theoretical findings of the new method.

Suggested Citation

  • Fang Lu & Jing Yang & Xuewen Lu, 2022. "One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data," Empirical Economics, Springer, vol. 62(6), pages 2645-2671, June.
    • Handle: RePEc:spr:empeco:v:62:y:2022:i:6:d:10.1007_s00181-021-02118-z
    DOI: 10.1007/s00181-021-02118-z
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    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Heng Lian, 2012. "Semiparametric Estimation of Additive Quantile Regression Models by Two-Fold Penalty," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 337-350, March.
    3. Sun, Yanqing & Zhang, Yuanqing & Huang, Jianhua Z., 2019. "Estimation of a semiparametric varying-coefficient mixed regressive spatial autoregressive model," Econometrics and Statistics, Elsevier, vol. 9(C), pages 140-155.
    4. 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.
    5. 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.
    6. Wang, Dewei & Kulasekera, K.B., 2012. "Parametric component detection and variable selection in varying-coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 117-129.
    7. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    8. Peixin Zhao & Liugen Xue, 2012. "Variable selection in semiparametric regression analysis for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 213-231, February.
    9. Xu, Xingbai & Lee, Lung-fei, 2015. "A spatial autoregressive model with a nonlinear transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 186(1), pages 1-18.
    10. 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.
    11. Yueqin Wu & Yan Sun, 2017. "Shrinkage estimation of the linear model with spatial interaction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 51-68, January.
    12. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    13. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    14. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    15. Tianfa Xie & Ruiyuan Cao & Jiang Du, 2020. "Variable selection for spatial autoregressive models with a diverging number of parameters," Statistical Papers, Springer, vol. 61(3), pages 1125-1145, June.
    16. Yang, Zhenlin & Li, Chenwei & Tse, Y.K., 2006. "Functional form and spatial dependence in dynamic panels," Economics Letters, Elsevier, vol. 91(1), pages 138-145, April.
    17. Noh, Hohsuk & Chung, Kwanghun & Van Keilegom, Ingrid, 2012. "Variable Selection of Varying Coefficient Models in Quantile Regression," LIDAM Discussion Papers ISBA 2012020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Pal, Amresh Bahadur & Dubey, Ashutosh Kumar & Chaturvedi, Anoop, 2016. "Shrinkage estimation in spatial autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 362-373.
    19. 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.
    20. 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.
    21. 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.
    22. Wei, Chuanhua & Guo, Shuang & Zhai, Shufen, 2017. "Statistical inference of partially linear varying coefficient spatial autoregressive models," Economic Modelling, Elsevier, vol. 64(C), pages 553-559.
    23. Yan Sun & Yueqin Wu, 2018. "Estimation and testing for a partially linear single-index spatial regression model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(4), pages 473-489, October.
    24. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    25. Roberto BASILE & Bernard GRESS, 2005. "Semi-Parametric Spatial Auto-Covariance Models Of Regional Growth In Europe," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 21, pages 93-118.
    26. Badi H. Baltagi & Dong Li, 2001. "LM Tests for Functional Form and Spatial Error Correlation," International Regional Science Review, , vol. 24(2), pages 194-225, April.
    27. Philip Kostov, 2009. "A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(1), pages 53-72.
    28. 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.
    29. Pace, R Kelley & Gilley, Otis W, 1997. "Using the Spatial Configuration of the Data to Improve Estimation," The Journal of Real Estate Finance and Economics, Springer, vol. 14(3), pages 333-340, May.
    30. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    31. Noh, Hohsuk & Chung, Kwanghun & Van Keilegom, Ingrid, 2012. "Variable selection of varying coefficient models in quantile regression," LIDAM Reprints ISBA 2012008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    32. Sun, Yan, 2017. "Estimation of single-index model with spatial interaction," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 36-45.
    33. 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.
    34. 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.
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