IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4606-d1277822.html
   My bibliography  Save this article

Statistical Inference for Partially Linear Varying Coefficient Spatial Autoregressive Panel Data Model

Author

Listed:
  • Sanying Feng

    (School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China)

  • Tiejun Tong

    (Department of Mathematics, Hong Kong Baptist University, Hong Kong)

  • Sung Nok Chiu

    (Department of Mathematics, Hong Kong Baptist University, Hong Kong)

Abstract

This paper studies the estimation and inference of a partially linear varying coefficient spatial autoregressive panel data model with fixed effects. By means of the basis function approximations and the instrumental variable methods, we propose a two-stage least squares estimation procedure to estimate the unknown parametric and nonparametric components, and meanwhile study the asymptotic properties of the proposed estimators. Together with an empirical log-likelihood ratio function for the regression parameters, which follows an asymptotic chi-square distribution under some regularity conditions, we can further construct accurate confidence regions for the unknown parameters. Simulation studies show that the finite sample performance of the proposed methods are satisfactory in a wide range of settings. Lastly, when applied to the public capital data, our proposed model can also better reflect the changing characteristics of the US economy compared to the parametric panel data models.

Suggested Citation

  • Sanying Feng & Tiejun Tong & Sung Nok Chiu, 2023. "Statistical Inference for Partially Linear Varying Coefficient Spatial Autoregressive Panel Data Model," Mathematics, MDPI, vol. 11(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4606-:d:1277822
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4606/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4606/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Alicia H. Munnell, 1990. "Why has productivity growth declined? Productivity and public investment," New England Economic Review, Federal Reserve Bank of Boston, issue Jan, pages 3-22.
    3. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    4. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    5. Zongwu Cai & Huaiyu Xiong, 2012. "Partially varying coefficient instrumental variables models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(2), pages 85-110, May.
    6. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    7. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    8. 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.
    9. Allen, Jason & Gregory, Allan W. & Shimotsu, Katsumi, 2011. "Empirical likelihood block bootstrapping," Journal of Econometrics, Elsevier, vol. 161(2), pages 110-121, April.
    10. Baltagi, Badi H & Pinnoi, Nat, 1995. "Public Capital Stock and State Productivity Growth: Further Evidence from an Error Components Model," Empirical Economics, Springer, vol. 20(2), pages 351-359.
    11. Rodriguez-Poo, Juan M. & Soberón, Alexandra, 2015. "Nonparametric estimation of fixed effects panel data varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 95-122.
    12. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    13. 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.
    14. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    15. Degui Li & Jia Chen & Jiti Gao, 2011. "Non‐parametric time‐varying coefficient panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 387-408, October.
    16. Sanying Feng & Gaorong Li & Tiejun Tong & Shuanghua Luo, 2020. "Testing for heteroskedasticity in two-way fixed effects panel data models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(1), pages 91-116, January.
    17. 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.
    18. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    19. Sun, Yiguo, 2016. "Functional-coefficient spatial autoregressive models with nonparametric spatial weights," Journal of Econometrics, Elsevier, vol. 195(1), pages 134-153.
    20. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xuan Liang & Jiti Gao & Xiaodong Gong, 2022. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1784-1802, October.
    2. Xuan Liang & Jiti Gao & Xiaodong Gong, 2019. "Time-Varying Coefficient Spatial Autoregressive Panel Data Model with Fixed Effects," Monash Econometrics and Business Statistics Working Papers 26/19, Monash University, Department of Econometrics and Business Statistics.
    3. Luo, Guowang & Wu, Mixia & Pang, Zhen, 2022. "Estimation of spatial autoregressive models with covariate measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    4. 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.
    5. 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.
    6. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.
    7. Zhang, Yuanqing & Sun, Yanqing, 2015. "Estimation of partially specified dynamic spatial panel data models with fixed-effects," Regional Science and Urban Economics, Elsevier, vol. 51(C), pages 37-46.
    8. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.
    9. Ruiqin Tian & Miaojie Xia & Dengke Xu, 2024. "Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects," Statistical Papers, Springer, vol. 65(8), pages 5109-5143, October.
    10. Tizheng Li & Xiaojuan Kang, 2022. "Variable selection of higher-order partially linear spatial autoregressive model with a diverging number of parameters," Statistical Papers, Springer, vol. 63(1), pages 243-285, February.
    11. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    12. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    13. Alberto Gude & Inmaculada Álvarez & Luis Orea, 2018. "Heterogeneous spillovers among Spanish provinces: a generalized spatial stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 50(3), pages 155-173, December.
    14. Zhang, Xinyu & Yu, Jihai, 2018. "Spatial weights matrix selection and model averaging for spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 203(1), pages 1-18.
    15. repec:esx:essedp:772 is not listed on IDEAS
    16. 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.
    17. Liu, Yu & Zhuang, Xiaoyang, 2023. "Shrinkage estimation of semi-parametric spatial autoregressive panel data model with fixed effects," Statistics & Probability Letters, Elsevier, vol. 194(C).
    18. Su, Liangjun & Yang, Zhenlin, 2015. "QML estimation of dynamic panel data models with spatial errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 230-258.
    19. 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.
    20. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    21. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4606-:d:1277822. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.