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Multiple Fixed Effects in Binary Response Panel Data Models


  • Karyne B. Charbonneau


This paper considers the adaptability of estimation methods for binary response panel data models to multiple fixed effects. It is motivated by the gravity equation used in international trade, where important papers such as Helpman, Melitz and Rubinstein (2008) use binary response models with fixed effects for both importing and exporting countries. Econometric theory has mostly focused on the estimation of single fixed effects models. This paper investigates whether existing methods can be modified to eliminate multiple fixed effects for two specific models in which the incidental parameter problem has already been solved in the presence of a single fixed effect. We find that it is possible to generalize the conditional maximum likelihood approach of Rasch (1960, 1961) to include two fixed effects for the logit. Surprisingly, despite many similarities with the logit, Manski’s (1987) maximum score estimator for binary response models cannot be adapted to the presence of two fixed effects. Monte Carlo simulations show that the conditional logit estimator presented in this paper is less biased than other logit estimators without sacrificing on precision. This superiority is emphasized in small samples. An application to trade data using the logit estimator further highlights the importance of properly accounting for two fixed effects.

Suggested Citation

  • Karyne B. Charbonneau, 2014. "Multiple Fixed Effects in Binary Response Panel Data Models," Staff Working Papers 14-17, Bank of Canada.
  • Handle: RePEc:bca:bocawp:14-17

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    References listed on IDEAS

    1. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    2. Head, Keith & Mayer, Thierry, 2014. "Gravity Equations: Workhorse,Toolkit, and Cookbook," Handbook of International Economics, Elsevier.
    3. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    4. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    5. Matthieu Crozet & Pamina Koenig, 2010. "Structural gravity equations with intensive and extensive margins," Canadian Journal of Economics, Canadian Economics Association, vol. 43(1), pages 41-62, February.
    6. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    7. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    8. Daniel Aaronson & Lisa Barrow & William Sander, 2007. "Teachers and Student Achievement in the Chicago Public High Schools," Journal of Labor Economics, University of Chicago Press, vol. 25, pages 95-135.
    9. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
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    Cited by:

    1. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    2. Bryan S. Graham, 2015. "Methods of Identification in Social Networks," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 465-485, August.
    3. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers CWP52/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Bryan S. Graham, 2014. "An econometric model of link formation with degree heterogeneity," NBER Working Papers 20341, National Bureau of Economic Research, Inc.
    5. repec:eee:jimfin:v:74:y:2017:i:c:p:88-114 is not listed on IDEAS
    6. Bryan S. Graham, 2017. "An econometric model of network formation with degree heterogeneity," CeMMAP working papers CWP08/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item


    Econometric and statistical methods;

    JEL classification:

    • 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
    • F14 - International Economics - - Trade - - - Empirical Studies of Trade

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