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Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

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  • Bartolucci, Francesco
  • Nigro, Valentina

Abstract

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.

Suggested Citation

  • Bartolucci, Francesco & Nigro, Valentina, 2012. "Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data," Journal of Econometrics, Elsevier, vol. 170(1), pages 102-116.
    • Handle: RePEc:eee:econom:v:170:y:2012:i:1:p:102-116
    DOI: 10.1016/j.jeconom.2012.03.004
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    Cited by:

    1. Pauline Givord & Lionel Wilner, 2015. "When Does the Stepping‐Stone Work? Fixed‐Term Contracts Versus Temporary Agency Work in Changing Economic Conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 787-805, August.
    2. Manuel Arellano & Stéphane Bonhomme, 2017. "Nonlinear Panel Data Methods for Dynamic Heterogeneous Agent Models," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 471-496, September.
    3. Lucchetti, Riccardo & Pigini, Claudia, 2017. "DPB: Dynamic Panel Binary Data Models in gretl," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i08).
    4. Carlos Fernández-Loría & Maxime C. Cohen & Anindya Ghose, 2023. "Evolution of Referrals over Customers’ Life Cycle: Evidence from a Ride-Sharing Platform," Information Systems Research, INFORMS, vol. 34(2), pages 698-720, June.
    5. Yoshitsugu Kitazawa, 2017. "DFEL-RTN, a set of TSP programs for root-N consistent estimations of dynamic fixed effects logit models," Discussion Papers 81, Kyushu Sangyo University, Faculty of Economics.
    6. Francesco Bartolucci & Valentina Nigro & Claudia Pigini, 2018. "Testing for state dependence in binary panel data with individual covariates by a modified quadratic exponential model," Econometric Reviews, Taylor & Francis Journals, vol. 37(1), pages 61-88, January.
    7. Lionel WILNER, 2019. "The Dynamics of Individual Happiness," Working Papers 2019-18, Center for Research in Economics and Statistics.
    8. Majid M. Al-Sadoon & Tong Li & M. Hashem Pesaran, 2017. "Exponential class of dynamic binary choice panel data models with fixed effects," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 898-927, October.
    9. Pigini, Claudia & Bartolucci, Francesco, 2022. "Conditional inference for binary panel data models with predetermined covariates," Econometrics and Statistics, Elsevier, vol. 23(C), pages 83-104.
    10. Bartolucci, Francesco & Nigro, Valentina & Pigini, Claudia, 2013. "Testing for state dependence in binary panel data with individual covariates," MPRA Paper 48233, University Library of Munich, Germany.
    11. 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.
    12. Lee Myoung-jae, 2015. "Panel conditional and multinomial logit with time-varying parameters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(3), pages 317-337, June.
    13. Miranda, Alfonso & Trivedi, Pravin K., 2020. "Econometric Models of Fertility," GLO Discussion Paper Series 574, Global Labor Organization (GLO).
    14. Francesco Bartolucci & Claudia Pigini, 2017. "Granger causality in dynamic binary short panel data models," Working Papers 421, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    15. Brown, Sarah & Ghosh, Pulak & Taylor, Karl, 2014. "The existence and persistence of household financial hardship: A Bayesian multivariate dynamic logit framework," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 285-298.
    16. Hugo Kruiniger, 2021. "Root-n-consistent Conditional ML estimation of dynamic panel logit models with fixed effects," Papers 2103.04973, arXiv.org, revised Apr 2021.
    17. Miriam Koning & Gerard Mertens & Peter Roosenboom, 2018. "Drivers of institutional change around the world: The case of IFRS," Journal of International Business Studies, Palgrave Macmillan;Academy of International Business, vol. 49(3), pages 249-271, April.
    18. F. Bartolucci & R. Bellio & A. Salvan & N. Sartori, 2016. "Modified Profile Likelihood for Fixed-Effects Panel Data Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(7), pages 1271-1289, August.
    19. Bartolucci, Francesco & Pigini, Claudia, 2017. "cquad: An R and Stata Package for Conditional Maximum Likelihood Estimation of Dynamic Binary Panel Data Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 78(i07).
    20. 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.
    21. Francesco Bartolucci & Claudia Pigini, 2018. "Partial effects estimation for fixed-effects logit panel data models," Working Papers 431, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    22. Yoshitsugu Kitazawa, 2013. "Exploration of dynamic fixed effects logit models from a traditional angle," Discussion Papers 60, Kyushu Sangyo University, Faculty of Economics.

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    More about this item

    Keywords

    Log-linear models; Longitudinal data; Pseudo likelihood inference; Quadratic exponential distribution;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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

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