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Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

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  • Thierry Magnac

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Abstract

This paper extends the conditional logit approach used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two-period two-state model, necessary and sufficient conditions on the joint distribution function of the individual-and-period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. Under these conditions, root-n consistent conditional likelihood estimators exist. Moreover, it is shown by extending Chamberlain (1992) that root-n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds. Imposing sufficiency is shown to reduce the dimensionality of the bivariate distribution function of the individual-and-period specific shocks. This setting is much less restrictive than the conditional logit approach (Rasch, Andersen, Chamberlain). In applied work, it amounts to quasi-difference the binary variables as if they were continuous variables and to transform a panel data model into a cross-section model. Semiparametric approaches can then be readily applied.

Suggested Citation

  • Thierry Magnac, 2003. "Panel Binary Variables and Sufficiency: Generalizing Conditional Logit," Research Unit Working Papers 0308, Laboratoire d'Economie Appliquee, INRA.
  • Handle: RePEc:lea:leawpi:0308
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    Cited by:

    1. Al-Sadoon, Majid M. & Li, Tong & Pesaran, M. Hashem, 2012. "An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects," IZA Discussion Papers 7054, Institute for the Study of Labor (IZA).
    2. Février, Philippe & Wilner, Lionel, 2016. "Do consumers correctly expect price reductions? Testing dynamic behavior," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 25-40.
    3. 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.
    4. Lechner, Michael & Lollivier, Stefan & Magnac, Thierry, 2005. "Parametric Binary Choice Models," IDEI Working Papers 398, Institut d'Économie Industrielle (IDEI), Toulouse.
    5. Ghanem, Dalia, 2017. "Testing identifying assumptions in nonseparable panel data models," Journal of Econometrics, Elsevier, vol. 197(2), pages 202-217.
    6. 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.
    7. Wladimir Raymond & Pierre Mohnen & Franz Palm & Sybrand Schim van der Loeff, 2007. "The Behavior of the Maximum Likelihood Estimator of Dynamic Panel Data Sample Selection Models," CESifo Working Paper Series 1992, CESifo Group Munich.
    8. Timothy Halliday, 2007. "Testing for State Dependence with Time-Variant Transition Probabilities," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 685-703.
    9. Albrecht, James & van den Berg, Gerard J & Vroman, Susan, 2004. "The knowledge lift: The Swedish adult education program that aimed to eliminate low worker skill levels," Working Paper Series 2004:17, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    10. Mogens Fosgerau, 2014. "Nonparametric approaches to describing heterogeneity," Chapters,in: Handbook of Choice Modelling, chapter 11, pages 257-267 Edward Elgar Publishing.
    11. Timothy Halliday, 2006. "Identifying State Dependence in Non-Stationary Processes," Working Papers 200601, University of Hawaii at Manoa, Department of Economics.
    12. Malikov, Emir & Restrepo-Tobon, Diego A & Kumbhakar, Subal C., 2016. "Heterogeneous Credit Union Production Technologies with Endogenous Switching and Correlated Effects," MPRA Paper 71593, University Library of Munich, Germany.
    13. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
    14. 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.
    15. Hyytinen, Ari & Pajarinen, Mika, 2008. "Opacity of young businesses: Evidence from rating disagreements," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1234-1241, July.
    16. Francesco Bartolucci† & Valentina Nigro, 2007. "A dynamic model for binary panel data with unobserved heterogeneity admitting a Vn-consistent conditional estimator," CEIS Research Paper 97, Tor Vergata University, CEIS.

    More about this item

    Keywords

    Binary models; panel data; conditional logit; sufficiency;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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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