IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/113568.html

Threshold spatial autoregressive model

Author

Listed:
  • Li, Kunpeng

Abstract

This paper considers the estimation and inferential issues of threshold spatial autoregressive model, which is a hybrid of threshold model and spatial autoregressive model. We consider using the quasi maximum likelihood (QML) method to estimate the model. We prove the tightness and the H\'{a}jek-R\'{e}nyi type inequality for a quadratic form, and establish a full inferential theory of the QML estimator under the setup that threshold effect shrinks to zero along with an increasing sample size. We consider the hypothesis testing on the presence of threshold effect. Three super-type statistics are proposed to perform this testing. Their asymptotic behaviors are studied under the Pitman local alternatives. A bootstrap procedure is proposed to obtain the asymptotically correct critical value. We also consider the hypothesis testing on the threshold value equal to some prespecified one. We run Monte carlo simulations to investigate the finite sample performance of the QML estimators and find that the QML estimators have good performance.

Suggested Citation

  • Li, Kunpeng, 2022. "Threshold spatial autoregressive model," MPRA Paper 113568, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:113568
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/113568/1/MPRA_paper_113568.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    3. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2008. "Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large," Journal of Econometrics, Elsevier, vol. 146(1), pages 118-134, September.
    4. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(5), pages 813-843, October.
    5. 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.
    6. F. Pukelshim, 1980. "Multilinear estimation of skewness and kutosis in linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 27(1), pages 103-113, December.
    7. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    8. Deng, Ying, 2018. "Estimation for the spatial autoregressive threshold model," Economics Letters, Elsevier, vol. 171(C), pages 172-175.
    9. Bramoullé, Yann & Djebbari, Habiba & Fortin, Bernard, 2009. "Identification of peer effects through social networks," Journal of Econometrics, Elsevier, vol. 150(1), pages 41-55, May.
    10. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    11. Marcucci, Juri & Quagliariello, Mario, 2009. "Asymmetric effects of the business cycle on bank credit risk," Journal of Banking & Finance, Elsevier, vol. 33(9), pages 1624-1635, September.
    12. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1239-1267.
    13. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    14. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    15. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    16. Li, Kunpeng, 2018. "Spatial panel data models with structural change," MPRA Paper 85388, University Library of Munich, Germany.
    17. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 531-542.
    18. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    19. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    20. Winford H. Masanjala & Chris Papageorgiou, 2004. "The Solow model with CES technology: nonlinearities and parameter heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(2), pages 171-201.
    21. 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.
    22. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
    23. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.
    24. Lee, Sokbae & Seo, Myung Hwan & Shin, Youngki, 2011. "Testing for Threshold Effects in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 220-231.
    25. 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.
    26. Xu Lin, 2010. "Identifying Peer Effects in Student Academic Achievement by Spatial Autoregressive Models with Group Unobservables," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 825-860, October.
    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. Li, Kunpeng & Lin, Wei, 2024. "Threshold spatial autoregressive model," Journal of Econometrics, Elsevier, vol. 244(1).
    2. Wang, Luya & Li, Kunpeng, 2025. "Spatial panel data models with structural change," Journal of Econometrics, Elsevier, vol. 251(C).
    3. Li, Kunpeng, 2018. "Spatial panel data models with structural change," MPRA Paper 85388, University Library of Munich, Germany.
    4. Bai, Jushan & Li, Kunpeng, 2021. "Dynamic spatial panel data models with common shocks," Journal of Econometrics, Elsevier, vol. 224(1), pages 134-160.
    5. Konstantinidi, Antri & Kourtellos, Andros & Sun, Yiguo, 2023. "Social threshold regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 2057-2081.
    6. Kwok, Hon Ho, 2019. "Identification and estimation of linear social interaction models," Journal of Econometrics, Elsevier, vol. 210(2), pages 434-458.
    7. Gibbons, Steve & Overman, Henry G. & Patacchini, Eleonora, 2015. "Spatial Methods," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 115-168, Elsevier.
    8. 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.
    9. 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.
    10. Houndetoungan, Aristide & Kouame, Cristelle & Vlassopoulos, Michael, 2024. "Identifying Peer Effects in Networks with Unobserved Effort and Isolated Students," IZA Discussion Papers 16998, IZA Network @ LISER.
    11. Patacchini, Eleonora & Hsieh, Chih-Sheng & Lin, Xu, 2019. "Social Interaction Methods," CEPR Discussion Papers 14141, C.E.P.R. Discussion Papers.
    12. Herrera Gómez, Marcos, 2017. "Fundamentos de Econometría Espacial Aplicada [Fundamentals of Applied Spatial Econometrics]," MPRA Paper 80871, University Library of Munich, Germany.
    13. Jiankun Chen & Yanli Lin & Yang Yang, 2025. "Modeling and Estimating Two-Layer Network Interactions with Unknown Heteroskedasticity," Economics Discussion / Working Papers 25-03, The University of Western Australia, Department of Economics.
    14. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.
    15. Rainone, Edoardo, 2020. "The network nature of over-the-counter interest rates," Journal of Financial Markets, Elsevier, vol. 47(C).
    16. Philipp Otto & Wolfgang Schmid, 2018. "Spatiotemporal analysis of German real-estate prices," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 60(1), pages 41-72, January.
    17. Jonathan Pratschke & Giovanni Abbiati, 2023. "“Like with like” or “do like?” Modeling peer effects in the classroom," Social Science Quarterly, Southwestern Social Science Association, vol. 104(3), pages 265-280, May.
    18. 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.
    19. Kuersteiner, Guido M. & Prucha, Ingmar R. & Zeng, Ying, 2023. "Efficient peer effects estimators with group effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 2155-2194.
    20. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:113568. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.