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. 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.
    8. Allen, Jason & Gregory, Allan W. & Shimotsu, Katsumi, 2011. "Empirical likelihood block bootstrapping," Journal of Econometrics, Elsevier, vol. 161(2), pages 110-121, April.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    17. Sun, Yiguo, 2016. "Functional-coefficient spatial autoregressive models with nonparametric spatial weights," Journal of Econometrics, Elsevier, vol. 195(1), pages 134-153.
    18. 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. 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.
    5. 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.
    6. Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    7. 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.
    8. repec:esx:essedp:772 is not listed on IDEAS
    9. 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.
    10. 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.
    11. 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).
    12. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.
    13. 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.
    14. 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.
    15. Bogui Li & Jianbao Chen & Shuangshuang Li, 2023. "Estimation of Fixed Effects Partially Linear Varying Coefficient Panel Data Regression Model with Nonseparable Space-Time Filters," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    16. Konstantinidi, Antri & Kourtellos, Andros & Sun, Yiguo, 2023. "Social threshold regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 2057-2081.
    17. Cheng, Suli & Chen, Jianbao, 2023. "GMM estimation of partially linear additive spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    18. Gupta, Abhimanyu & Robinson, Peter M., 2015. "Inference on higher-order spatial autoregressive models with increasingly many parameters," Journal of Econometrics, Elsevier, vol. 186(1), pages 19-31.
    19. Mustafa Koroglu & Yiguo Sun, 2016. "Functional-Coefficient Spatial Durbin Models with Nonparametric Spatial Weights: An Application to Economic Growth," Econometrics, MDPI, vol. 4(1), pages 1-16, February.
    20. 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.
    21. Zhang Yuanqing, 2014. "Estimation of Partially Specified Spatial Autoregressive Model," Journal of Systems Science and Information, De Gruyter, vol. 2(3), pages 226-235, June.

    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.