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Testing the binomial fixed effects logit model; with an application to female labor supply


  • Rainer Winkelmann
  • Lin Xu


Regression models for proportions are frequently encountered in applied work. The conditional expectation function is bounded between 0 and 1 and therefore must be non-linear, requiring nonstandard panel data extensions. One possible approach is the binomial panel logit model with fixed effects (Machado, 2004). We propose a new and simple implementation of the conditional maximum likelihood estimator for standard software. We investigate the properties of the estimator under misspecification and derive a new test for overdispersion. Estimator and test are applied in a study of contracted working volumes, measured as proportion of full-time work, for women in Switzerland.

Suggested Citation

  • Rainer Winkelmann & Lin Xu, 2019. "Testing the binomial fixed effects logit model; with an application to female labor supply," ECON - Working Papers 321, Department of Economics - University of Zurich, revised Oct 2019.
  • Handle: RePEc:zur:econwp:321

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    References listed on IDEAS

    1. Machado, Matilde P., 2004. "A consistent estimator for the binomial distribution in the presence of "incidental parameters": an application to patent data," Journal of Econometrics, Elsevier, vol. 119(1), pages 73-98, March.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
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    4. Gordon Kemp & João Santos Silva, 2016. "Partial effects in fixed-effects models," United Kingdom Stata Users' Group Meetings 2016 06, Stata Users Group.
    5. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, December.
    6. Abrevaya, Jason, 1997. "The equivalence of two estimators of the fixed-effects logit model," Economics Letters, Elsevier, vol. 55(1), pages 41-43, August.
    7. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
    8. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    9. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    10. Steinhauer, Andreas, 2018. "Working Moms, Childlessness, and Female Identity," CEPR Discussion Papers 12929, C.E.P.R. Discussion Papers.
    11. Andreas Steinhauer, 2018. "Working Moms, Childlessness, and Female Identity," Sciences Po publications 79, Sciences Po.
    12. Kunz, J.S.; & Staub, K.E.; & Winkelmann, R.;, 2018. "Predicting fixed effects in panel probit models," Health, Econometrics and Data Group (HEDG) Working Papers 18/23, HEDG, c/o Department of Economics, University of York.
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    More about this item


    Proportions data; unobserved heterogeneity; conditional maximum likelihood; overdispersion;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • J21 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Force and Employment, Size, and Structure

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