IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/110034.html
   My bibliography  Save this paper

MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit

Author

Listed:
  • Bartolucci, Francesco
  • Pigini, Claudia
  • Valentini, Francesco

Abstract

We propose a Markov chain Monte Carlo Conditional Maximum Likelihood (MCMC-CML) estimator for two-way fixed-effects logit models for dyadic data. The proposed MCMC approach, based on a Metropolis algorithm, allows us to overcome the computational issues of evaluating the probability of the outcome conditional on nodes in and out degrees, which are sufficient statistics for the incidental parameters. Under mild regularity conditions, the MCMC-CML estimator converges to the exact CML one and is asymptotically normal. Moreover, it is more efficient than the existing pairwise CML estimator. We study the finite sample properties of the proposed approach by means of a simulation study and three empirical applications, where we also show that the MCMC-CML estimator can be applied to binary logit models for panel data with both subject and time fixed effects. Results confirm the expected theoretical advantage of the proposed approach, especially with small and sparse networks or with rare events in panel data.

Suggested Citation

  • Bartolucci, Francesco & Pigini, Claudia & Valentini, Francesco, 2021. "MCMC Conditional Maximum Likelihood for the two-way fixed-effects logit," MPRA Paper 110034, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:110034
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/110034/1/MPRA_paper_110034.pdf
    File Function: original version
    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. Koen Jochmans, 2018. "Semiparametric Analysis of Network Formation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 705-713, October.
    3. 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.
    4. Orazio Attanasio & Abigail Barr & Juan Camilo Cardenas & Garance Genicot & Costas Meghir, 2012. "Risk Pooling, Risk Preferences, and Social Networks," American Economic Journal: Applied Economics, American Economic Association, vol. 4(2), pages 134-167, April.
    5. 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.
    6. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    7. Fafchamps, Marcel & Gubert, Flore, 2007. "The formation of risk sharing networks," Journal of Development Economics, Elsevier, vol. 83(2), pages 326-350, July.
    8. Caggiano, Giovanni & Calice, Pietro & Leonida, Leone & Kapetanios, George, 2016. "Comparing logit-based early warning systems: Does the duration of systemic banking crises matter?," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 104-116.
    9. repec:dau:papers:123456789/4392 is not listed on IDEAS
    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. repec:dau:papers:123456789/10840 is not listed on IDEAS
    12. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    13. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Systemic Risk and Stability in Financial Networks," American Economic Review, American Economic Association, vol. 105(2), pages 564-608, February.
    14. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    15. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    16. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(2), pages 441-487.
    17. Paolo Zacchia, 2020. "Knowledge Spillovers through Networks of Scientists," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(4), pages 1989-2018.
    18. Marcel Fafchamps & Flore Gubert, 2007. "Risk Sharing and Network Formation," American Economic Review, American Economic Association, vol. 97(2), pages 75-79, May.
    19. Yuguo Chen & Junyi Xie & Jun S. Liu, 2005. "Stopping‐time resampling for sequential Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 199-217, April.
    20. Pigini, Claudia, 2021. "Penalized maximum likelihood estimation of logit-based early warning systems," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1156-1172.
    21. Koen Jochmans & Taisuke Otsu, 2019. "Likelihood Corrections for Two-way Models," Annals of Economics and Statistics, GENES, issue 134, pages 227-242.
    22. Mr. Luc Laeven & Mr. Fabian Valencia, 2018. "Systemic Banking Crises Revisited," IMF Working Papers 2018/206, International Monetary Fund.
    23. Mario Cruz-Gonzalez & Iván Fernández-Val & Martin Weidner, 2017. "Bias corrections for probit and logit models with two-way fixed effects," Stata Journal, StataCorp LP, vol. 17(3), pages 517-545, September.
    24. Ting Yan & Binyan Jiang & Stephen E. Fienberg & Chenlei Leng, 2019. "Statistical Inference in a Directed Network Model With Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 857-868, April.
    25. 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.
    26. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
    27. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    28. Andreas Dzemski, 2019. "An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 763-776, December.
    29. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Francesco Bartolucci & Claudia Pigini & Francesco Valentini, 2023. "Conditional inference and bias reduction for partial effects estimation of fixed-effects logit models," Empirical Economics, Springer, vol. 64(5), pages 2257-2290, May.

    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. David W. Hughes, 2021. "Estimating Nonlinear Network Data Models with Fixed Effects," Boston College Working Papers in Economics 1058, Boston College Department of Economics.
    2. 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.
    3. 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.
    4. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    5. Andreas Dzemski, 2019. "An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 763-776, December.
    6. Xuan Leng & Jiaming Mao & Yutao Sun, 2023. "Debiased inference for dynamic nonlinear models with two-way fixed effects," Papers 2305.03134, arXiv.org, revised Oct 2023.
    7. Weidner, Martin & Zylkin, Thomas, 2021. "Bias and consistency in three-way gravity models," Journal of International Economics, Elsevier, vol. 132(C).
    8. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Francesco Bartolucci & Francesco Valentini & Claudia Pigini, 2023. "Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 529-557, February.
    10. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    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. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380, arXiv.org, revised Oct 2022.
    13. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2023. "Specification testing with grouped fixed effects," Papers 2310.01950, arXiv.org.
    14. Francesco Bartolucci & Claudia Pigini & Francesco Valentini, 2023. "Conditional inference and bias reduction for partial effects estimation of fixed-effects logit models," Empirical Economics, Springer, vol. 64(5), pages 2257-2290, May.
    15. Bryan S. Graham, 2014. "An econometric model of link formation with degree heterogeneity," NBER Working Papers 20341, National Bureau of Economic Research, Inc.
    16. Arturas Juodis & Simon Reese, 2018. "The Incidental Parameters Problem in Testing for Remaining Cross-section Correlation," Papers 1810.03715, arXiv.org, revised Feb 2021.
    17. Victor Chernozhukov & Ivan Fernandez-Val & Martin Weidner, 2018. "Network and panel quantile effects via distribution regression," CeMMAP working papers CWP21/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
    19. Carneiro, Anabela & Portugal, Pedro & Raposo, Pedro & Rodrigues, Paulo M.M., 2023. "The persistence of wages," Journal of Econometrics, Elsevier, vol. 233(2), pages 596-611.
    20. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.

    More about this item

    Keywords

    Directed network; Fixed effects; Link formation; Metropolis algorithm; Panel data;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    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:110034. 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.