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Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

Author

Listed:
  • Francesco Bartolucci

    (University of Perugia)

  • Francesco Valentini

    (Marche Polytechnic University)

  • Claudia Pigini

    (Marche Polytechnic University)

Abstract

We propose a general recursive algorithm for the computation of the conditional probability function of the quadratic exponential model for binary panel data given the total of the responses, which is a sufficient statistic for the individual intercept parameter. This recursion permits to implement conditional and pseudo-conditional maximum likelihood estimators of the parameters of this model, and related models such as the dynamic logit model, even when one or more statistical units are observed at many occasions. In this way we solve a typical problem in dealing with distributions with a complex normalizing constant. The advantage in terms of computational load with respect to standard techniques is assessed by simulation and illustrated by an application based on a popular dataset about brand loyalty.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:2:d:10.1007_s10614-021-10218-2
    DOI: 10.1007/s10614-021-10218-2
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    1. 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.
    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. Gregori Baetschmann & Kevin E. Staub & Rainer Winkelmann, 2015. "Consistent estimation of the fixed effects ordered logit model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 685-703, June.
    4. Francesco Bartolucci & Valentina Nigro, 2010. "A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a √n-Consistent Conditional Estimator," Econometrica, Econometric Society, vol. 78(2), pages 719-733, March.
    5. Zhang, Daowen & Davidian, Marie, 2004. "Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 90-106, October.
    6. Arellano, Manuel & Honore, Bo, 2001. "Panel data models: some recent developments," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 53, pages 3229-3296, Elsevier.
    7. Carro, Jesus M., 2007. "Estimating dynamic panel data discrete choice models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 503-528, October.
    8. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    9. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    10. Jain, Dipak C & Vilcassim, Naufel J & Chintagunta, Pradeep K, 1994. "A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 317-328, July.
    11. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    12. Francesco Bartolucci & Fulvia Pennoni, 2007. "On the approximation of the quadratic exponential distribution in a latent variable context," Biometrika, Biometrika Trust, vol. 94(3), pages 745-754.
    13. D. R. Cox, 1972. "The Analysis of Multivariate Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 21(2), pages 113-120, June.
    14. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    15. 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.
    16. Manuel Arellano & Jinyong Hahn, 2016. "A likelihood-Based Approximate Solution to the Incidental Parameter Problem in Dynamic Nonlinear Models with Multiple Effects," Global Economic Review, Taylor & Francis Journals, vol. 45(3), pages 251-274, July.
    17. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    18. 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).
    19. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers 08/17, Institute for Fiscal Studies.
    20. 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.
    21. Chintagunta, Pradeep & Kyriazidou, Ekaterini & Perktold, Josef, 2001. "Panel data analysis of household brand choices," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 111-153, July.
    22. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    23. 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.
    24. 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.
    25. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    26. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1152-1191, December.
    27. Bester, C. Alan & Hansen, Christian, 2009. "A Penalty Function Approach to Bias Reduction in Nonlinear Panel Models with Fixed Effects," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 131-148.
    28. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
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