IDEAS home Printed from https://ideas.repec.org/p/wrk/warwec/1531.html

Fixed Effects Nonlinear Panel Models with Heterogeneous Slopes : Identification and Consistency

Author

Listed:
  • Mugnier, Martin

    (Paris School of Economics)

  • Wang, Ao

    (University of Warwick and CAGE Research Centre)

Abstract

We study a class of two-way fixed effects index function models with a nonparametric link function and individual- (or time-) specific slopes. Our model alleviates potential misspecification errors due to the common practice of specifying a known link function such as Gaussian and its tail behavior. It also enables to incorporate richer unobserved heterogeneity in the marginal effects of covariates via heterogeneous slopes across individuals. We show the identification of the link function as well as the slopes and fixed effects parameters when both individual and time dimensions are large. We propose a nonparametric consistency result for the fixed effects sieve maximum likelihood estimators. Finally, we apply our method to the study of establishing exportation and illustrate the consequences of imposing Gaussian link function and homogeneity on the slope of distance.

Suggested Citation

  • Mugnier, Martin & Wang, Ao, 2024. "Fixed Effects Nonlinear Panel Models with Heterogeneous Slopes : Identification and Consistency," The Warwick Economics Research Paper Series (TWERPS) 1531, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:1531
    as

    Download full text from publisher

    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2024/twerp_1531-_wang.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    2. Luis E. Candelaria, 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," Papers 2007.05403, arXiv.org, revised Aug 2020.
    3. Candelaria, Luis E., 2020. "A Semiparametric Network Formation Model with Unobserved Linear Heterogeneity," The Warwick Economics Research Paper Series (TWERPS) 1279, University of Warwick, Department of Economics.
    4. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    5. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    6. Boneva, L. & Linton, O., 2017. "A Discrete Choice Model For Large Heterogeneous Panels with Interactive Fixed Effects with an Application to the Determinants of Corporate Bond Issuance," Cambridge Working Papers in Economics 1703, Faculty of Economics, University of Cambridge.
    7. Lihua Lei & Brad Ross, 2023. "Estimating Counterfactual Matrix Means with Short Panel Data," Papers 2312.07520, arXiv.org, revised Dec 2025.
    8. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    9. Gao, Wayne Yuan, 2020. "Nonparametric identification in index models of link formation," Journal of Econometrics, Elsevier, vol. 215(2), pages 399-413.
    10. Karyne B. Charbonneau, 2017. "Multiple fixed effects in binary response panel data models," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 1-13, October.
    11. Lena Boneva & Oliver Linton, 2017. "A discrete†choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1226-1243, November.
    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. Mugnier, Martin & Wang, Ao, 2022. "Identification and (Fast) Estimation of Large Nonlinear Panel Models with Two-Way Fixed Effects," The Warwick Economics Research Paper Series (TWERPS) 1422, University of Warwick, Department of Economics.
    2. David W. Hughes, 2022. "A jackknife bias correction for nonlinear network data models with fixed effects," Papers 2203.15603, arXiv.org, revised Nov 2025.
    3. David W. Hughes, 2021. "Estimating Nonlinear Network Data Models with Fixed Effects," Boston College Working Papers in Economics 1058, Boston College Department of Economics.
    4. Candelaria, Luis E. & Ura, Takuya, 2023. "Identification and inference of network formation games with misclassified links," Journal of Econometrics, Elsevier, vol. 235(2), pages 862-891.
    5. Francesco Bartolucci & Claudia Pigini & Francesco Valentini, 2024. "MCMC conditional maximum likelihood for the two-way fixed-effects logit," Econometric Reviews, Taylor & Francis Journals, vol. 43(6), pages 379-404, July.
    6. Chernozhukov, Victor & Fernández-Val, Iván & Weidner, Martin, 2024. "Network and panel quantile effects via distribution regression," Journal of Econometrics, Elsevier, vol. 240(2).
    7. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    8. Ando, Tomohiro & Bai, Jushan, 2021. "Large-scale generalized linear longitudinal data models with grouped patterns of unobserved heterogeneity," MPRA Paper 111431, University Library of Munich, Germany.
    9. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2025. "Grouped fixed effects regularization for binary choice models," Papers 2502.06446, arXiv.org, revised Nov 2025.
    10. Federico Crippa, 2025. "Identification, Estimation, and Inference in Two-Sided Interaction Models," Papers 2510.22884, arXiv.org.
    11. Gao, Wayne Yuan & Li, Ming & Xu, Sheng, 2023. "Logical differencing in dyadic network formation models with nontransferable utilities," Journal of Econometrics, Elsevier, vol. 235(1), pages 302-324.
    12. Ando, Tomohiro & Bai, Jushan & Li, Kunpeng, 2022. "Bayesian and maximum likelihood analysis of large-scale panel choice models with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 230(1), pages 20-38.
    13. Alejandro Sanchez-Becerra, 2022. "The Network Propensity Score: Spillovers, Homophily, and Selection into Treatment," Papers 2209.14391, arXiv.org.
    14. Ming Li & Zhentao Shi & Yapeng Zheng, 2024. "Bagging the Network," Papers 2410.23852, arXiv.org, revised Sep 2025.
    15. Arturas Juodis & Simon Reese, 2018. "The Incidental Parameters Problem in Testing for Remaining Cross-section Correlation," Papers 1810.03715, arXiv.org, revised Feb 2021.
    16. Valeria Costantini & Valerio Leone Sciabolazza & Elena Paglialunga, 2023. "Network-driven positive externalities in clean energy technology production: the case of energy efficiency in the EU residential sector," The Journal of Technology Transfer, Springer, vol. 48(2), pages 716-748, April.
    17. Jie Wei & Yonghui Zhang, 2022. "Panel Probit Models with Time‐Varying Individual Effects: Reestimating the Effects of Fertility on Female Labour Participation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 799-829, August.
    18. Weidner, Martin & Zylkin, Thomas, 2021. "Bias and consistency in three-way gravity models," Journal of International Economics, Elsevier, vol. 132(C).
    19. Ye, Xiaoqing & Xu, Juan & Wu, Xiangjun, 2018. "Estimation of an unbalanced panel data Tobit model with interactive effects," Journal of choice modelling, Elsevier, vol. 28(C), pages 108-123.
    20. Qiuping Wang & Yuan Zhang & Ting Yan, 2023. "Asymptotic theory in network models with covariates and a growing number of node parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 369-392, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

    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:wrk:warwec:1531. 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: Margaret Nash (email available below). General contact details of provider: https://edirc.repec.org/data/dewaruk.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.