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Advances in Maximum Likelihood Estimation of Fixed-Effects Binary Panel Data Models

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Trends and Challenges in Categorical Data Analysis

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

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Abstract

We review recent fixed-effects approaches to the formulation and estimation of models for binary panel data, measured at T time occasions. We offer a unified framework for the two main streams of literature dealing with the inconsistency of the Maximum Likelihood (ML) estimator due to incidental parameters, namely target-corrected and Conditional ML (CML) estimators, including a recent Pseudo CML (PCML) estimator. While the former ones are general and not model specific, they are not fixed-T consistent and, in particular, have a bias of order O(T−2). The finite sample behavior of the latest contributions is compared by means of an extensive simulation study for the dynamic logit model. It results that the PCML estimator outperforms target corrected estimators in finite samples, especially when T ≤ 8. Further, the comparison is extended to a real data application concerning female labor supply.

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References

  1. Akay, A.: Finite-sample comparison of alternative methods for estimating dynamic panel data models. J. Appl. Econ. 27, 1189–1204 (2012)

    Article  MathSciNet  Google Scholar 

  2. Alessie, R., Hochguertel, S., Van Soest, A.: Ownership of stocks and mutual funds: a panel data analysis. Rev. Econ. Stat. 86, 783–796 (2004)

    Article  Google Scholar 

  3. Andersen, E.B.: Asymptotic properties of conditional maximum-likelihood estimators. J. R. Stat. Soc. Ser. B 32, 283–301 (1970)

    MathSciNet  MATH  Google Scholar 

  4. Anderson, T.W., Hsiao, C.: Estimation of dynamic models with error components. J. Amer. Stat. Assoc. 76, 598–606 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  5. Arellano, M.: Panel Data Econometrics. Oxford University Press, New York (2003)

    Book  MATH  Google Scholar 

  6. Arellano, M.: Discrete choices with panel data. Invest, Econ. 27, 423–458 (2003)

    Google Scholar 

  7. Arellano, M., Bond, S.: Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Rev. Econ. Stud. 58, 277–297 (1991)

    Article  MATH  Google Scholar 

  8. Arellano, M., Bover, O.: Another look at the instrumental variable estimation of error-components models. J. Econ. 68, 29–51 (1995)

    Article  MATH  Google Scholar 

  9. Arellano, M., Hahn, J.: Understanding bias in nonlinear panel models: some recent developments. Econ. Soc. Monogr. 43, 381 (2007)

    MATH  Google Scholar 

  10. Arellano, M., Hahn, J.: A likelihood-based approximate solution to the incidental parameter problem in dynamic nonlinear models with multiple effects. Global Econ. Rev. 45, 251–274 (2016)

    Article  Google Scholar 

  11. Arulampalam, W., Stewart, M.B.: Simplified implementation of the Heckman estimator of the dynamic probit model and a comparison with alternative estimators. Oxf. Bull. Econ. Stat. 71, 659–681 (2009)

    Article  Google Scholar 

  12. Baetschmann, G., Staub, K.E., Winkelmann, R.: Consistent estimation of the fixed effects ordered logit model. J. R. Stat. Soc. Ser. A 178, 685–703 (2015)

    Article  MathSciNet  Google Scholar 

  13. Bandeen-Roche, K., Miglioretti, D.L., Zeger, S.L., Rathouz, P.J.: Latent variable regression for multiple discrete outcomes. J. Amer. Stat. Assoc. 92, 1375–1386 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  14. Bartolucci, F., Nigro, V.: A dynamic model for binary panel data with unobserved heterogeneity admitting a n-consistent conditional estimator. Econometrica 78, 719–733 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bartolucci, F., Nigro, V.: Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data. J. Econ. 170, 102–116 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bartolucci, F., Pennoni, F.: On the approximation of the quadratic exponential distribution in a latent variable context. Biometrika 94, 745–754 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Bartolucci, F., Pigini, C.: cquad: An R and Stata package for conditional maximum likelihood estimation of dynamic binary panel data models. J. Stat. Softw. 78, 1–26 (2017)

    Google Scholar 

  18. Bartolucci, F., Pigini, C.: Partial effects estimation for fixed-effects logit panel data models. Technical Report, MPRA Paper No. 92251 (2019)

    Google Scholar 

  19. Bartolucci, F., Bellio, R., Salvan, A., Sartori, N.: Modified profile likelihood for fixed-effects panel data models. Econ. Rev. 35, 1271–1289 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Bartolucci, F., Nigro, V., Pigini, C.: Testing for state dependence in binary panel data with individual covariates by a modified quadratic exponential model. Econ. Rev. 37, 61–88 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  21. Bartolucci, F., Pigini, C., Valentini, F.: CQUADR: Stata module to estimate Quadratic Exponential models running the cquad R package. Statistical Software Components, Boston College Department of Economics (2020)

    Google Scholar 

  22. Beaule, A., Campbell, F., Dascola, M., Insolera, N., et al.: PSID main interview user manual: Release 2021. Institute for Social Research, University of Michigan (2021)

    Google Scholar 

  23. Bester, C.A., Hansen, C.: A penalty function approach to bias reduction in nonlinear panel models with fixed effects. J. Business Econ. Stat. 27, 131–148 (2009)

    Article  MathSciNet  Google Scholar 

  24. Bettin, G., Lucchetti, R.: Steady streams and sudden bursts: persistence patterns in remittance decisions. J. Populat. Econ. 29, 263–292 (2016)

    Article  Google Scholar 

  25. Blundell, R., Bond, S.: Initial conditions and moment restrictions in dynamic panel data models. J. Econ. 87, 115–143 (1998)

    Article  MATH  Google Scholar 

  26. Broström, G.: glmmML: Generalized Linear Models with Clustering. R package version 1.1.1 (2020)

    Google Scholar 

  27. Brown, S., Ghosh, P., Taylor, K.: The existence and persistence of household financial hardship. Technical Report, Department of Economics, University of Sheffield (2012)

    Google Scholar 

  28. Cameron, A.C., Trivedi, P.K.: Microeconometrics: Methods and Applications. Cambridge University Press, New York (2005)

    Book  MATH  Google Scholar 

  29. Carro, J.M.: Estimating dynamic panel data discrete choice models with fixed effects. J. Econ. 140, 503–528 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Chamberlain, G.: Analysis of covariance with qualitative data. Rev. Econ. Stud. 47, 225–238 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  31. Chamberlain, G.: Feedback in panel data medels. Technical Report, Harvard-Institute of Economic Research (1993)

    Google Scholar 

  32. Cox, D.R.: The analysis of multivariate binary data. Appl. Stat. 21, 113–120 (1972)

    Article  Google Scholar 

  33. Cox, D.R., Reid, N.: Parameter orthogonality and approximate conditional inference. J. R. Stat. Soc. Ser. B 49, 1–39 (1987)

    MathSciNet  MATH  Google Scholar 

  34. Cox, D.R., Wermuth, N.: A note on the quadratic exponential binary distribution. Biometrika 81(2), 403–408 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  35. Cruz-Gonzalez, M., Fernandez-Val, I., Weidner, M.: LOGITFE: Stata module to compute analytical and jackknife bias corrections for fixed effects estimators of panel logit models with individual and time effects. Statistical Software Components, Boston College Department of Economics (2016)

    Google Scholar 

  36. Cruz-Gonzalez, M., Fernandez-Val, I., Weidner, M.: PROBITFE: Stata module to compute analytical and jackknife bias corrections for fixed effects estimators of panel probit models with individual and time effects. Statistical Software Components, Boston College Department of Economics (2016)

    Google Scholar 

  37. Dayton, C.M., Macready, G.B.: Concomitant-variable latent-class models. J. Amer. Stat. Assoc. 83, 173–178 (1988)

    Article  MathSciNet  Google Scholar 

  38. Dhaene, G., Jochmans, K.: Split-panel jackknife estimation of fixed-effect models. Rev. Econ. Stud. 82, 991–1030 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  39. Diggle, P.J., Heagerty, P., Liang, K.-Y., Zeger, S.: Analysis of Longitudinal Data. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  40. Fernández-Val, I.: Fixed effects estimation of structural parameters and marginal effects in panel probit models. J. Econ. 150, 71–85 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  41. Fernández-Val, I., Weidner, M.: Individual and time effects in nonlinear panel models with large N, T. J. Econ. 192, 291–312 (2016)

    Google Scholar 

  42. Fernández-Val, I., Weidner, M.: Fixed effects estimation of large-T panel data models. Ann. Rev. Econ. 10, 109–138 (2018)

    Article  Google Scholar 

  43. Fitzmaurice, G., Davidian, M., Verbeke, G., Molenberghs, G.: Longitudinal Data Analysis. CRC Press, Boca Raton (2008)

    Book  MATH  Google Scholar 

  44. Formann, A.K.: Mixture analysis of multivariate categorical data with covariates and missing entries. Comput. Stat. Data Analy. 51, 5236–5246 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  45. Giarda, E.: Persistency of financial distress amongst Italian households: evidence from dynamic models for binary panel data. J. Banking Finance 37, 3425–3434 (2013)

    Article  Google Scholar 

  46. Hahn, J., Kuersteiner, G.: Bias reduction for dynamic nonlinear panel models with fixed effects. Econ. Theory 27, 1152–1191 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  47. Hahn, J., Newey, W.: Jackknife and analytical bias reduction for nonlinear panel models. Econometrica 72, 1295–1319 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  48. Heckman, J.J.: Heterogeneity and state dependence. In Studies in Labor Markets, pp. 91–140. University of Chicago Press, Chicago (1981)

    Google Scholar 

  49. Heckman, J.J.: The incidental parameters problem and the problem of initial conditions in estimating a discrete time-discrete data stochastic process and some Monte Carlo evidence. In: Manski, C.F., McFadden, D. (eds.) Structural Analysis of Discrete Data with Economic Applications. MIT Press, Cambridge (1981)

    Google Scholar 

  50. Heckman, J.J., Borjas, G.J.: Does unemployment cause future unemployment? Definitions, questions and answers from a continuous time model of heterogeneity and state dependence. Economica 47, 247–283 (1980)

    Article  Google Scholar 

  51. Honoré, B.E., Kyriazidou, E.: Panel data discrete choice models with lagged dependent variables. Econometrica 68, 839–874 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  52. Hsiao, C.: Analysis of Panel Data. Cambridge University Press, New York (2014)

    Book  MATH  Google Scholar 

  53. Hyslop, D.R.: State dependence, serial correlation and heterogeneity in intertemporal labor force participation of married women. Econometrica 67, 1255–1294 (1999)

    Article  Google Scholar 

  54. Jiang, J., Nguyen, T.: Linear and Generalized Linear Mixed Models and Their Applications. Springer Nature, New York (2021)

    Book  MATH  Google Scholar 

  55. Lancaster, T.: The incidental parameter problem since 1948. J. Econ. 95, 391–413 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  56. Lucchetti, R., Pigini, C.: DPB: dynamic panel binary data models in gretl. J. Stat. Softw. 79, 1–33 (2017)

    Article  Google Scholar 

  57. McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman & Hall, Boca Raton (1989)

    Book  MATH  Google Scholar 

  58. McFadden, D.: Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (ed.) Frontiers in Econometrics, pp. 105–142. Academic, Cambridge (1974)

    Google Scholar 

  59. McLachlan, G.J., Peel, D.: Finite Mixture Models. Wiley, New York (2004)

    MATH  Google Scholar 

  60. Mundlak, Y.: On the pooling of time series and cross section data. Econometrica 46, 69–85 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  61. Neyman, J., Scott, E.L.: Consistent estimates based on partially consistent observations. Econometrica 16, 1–32 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  62. Pigini, C., Presbitero, A.F., Zazzaro, A.: State dependence in access to credit. J. Finan. Stab. 27, 17–34 (2016)

    Article  Google Scholar 

  63. Quenouille, M.H.: Notes on bias in estimation. Biometrika 43, 353–360 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  64. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2021)

    Google Scholar 

  65. Rabe-Hesketh, S., Skrondal, A.: Avoiding biased versions of Wooldridge’s simple solution to the initial conditions problem. Econ. Lett. 120, 346–349 (2013)

    Article  Google Scholar 

  66. Severini, T.A.: An approximation to the modified profile likelihood function. Biometrika 85, 403–411 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  67. Skrondal, A., Rabe-Hesketh, S.: Handling initial conditions and endogenous covariates in dynamic/transition models for binary data with unobserved heterogeneity. J. R. Stat. Soc. Ser. C 63, 211–237 (2014)

    Article  MathSciNet  Google Scholar 

  68. Stammann, A., Heiss, F., McFadden, D.: Estimating fixed effects logit models with large panel data. In: VfS Annual Conference 2016 (Augsburg): Demographic Change (2016)

    Google Scholar 

  69. Stroup, W.W.: Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. Taylor & Francis, Boca Raton (2012)

    Google Scholar 

  70. Sun, Y., Dhaene, G.: XTSPJ: Stata module for split-panel jackknife estimation. In: Statistical Software Components, Boston College Department of Economics (2019)

    Google Scholar 

  71. Therneau, T.M.: A Package for Survival Analysis in R. R package version 3.2-11 (2021)

    Google Scholar 

  72. Verbeke, G., Molenberghs, G.: Linear Mixed Models for Longitudinal Data. Springer, New York (2001)

    MATH  Google Scholar 

  73. Wedel, M.: Concomitant variables in finite mixture models. Statistica Neerlandica 56, 362–375 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  74. Wooldridge, J.M.: Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. J. Appl. Econ. 20, 39–54 (2005)

    Article  MathSciNet  Google Scholar 

  75. Wooldridge, J.M.: Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambidge (2010)

    MATH  Google Scholar 

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Acknowledgements

F. Bartolucci acknowledges the financial support from the grant “Partial effects in econometric models for binary longitudinal data based on quadratic exponential distributions” of the University of Perugia (RICBASE2018).

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Authors and Affiliations

  1. Department of Economics and Social Sciences, Marche Polytechnic University, Ancona, Italy

    Francesco Valentini & Claudia Pigini

  2. Department of Economics, University of Perugia, Perugia, Italy

    Francesco Bartolucci

Authors
  1. Francesco Valentini
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  2. Claudia Pigini
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  3. Francesco Bartolucci
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Correspondence to Francesco Valentini .

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Editors and Affiliations

  1. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Maria Kateri

  2. Department of Statistics, London School of Econ. & Polit. Science, London, UK

    Irini Moustaki

Appendix

Appendix

This appendix reports the additional results concerning the Monte Carlo simulation experiment described in Sect. 9.7 (Tables 9.5, 9.6, 9.7, 9.8, 9.9, 9.10, 9.11 and 9.12).

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Valentini, F., Pigini, C., Bartolucci, F. (2023). Advances in Maximum Likelihood Estimation of Fixed-Effects Binary Panel Data Models. In: Kateri, M., Moustaki, I. (eds) Trends and Challenges in Categorical Data Analysis. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-031-31186-4_9

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