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Multiple Fixed Effects in Binary Response Panel Data Models

  • Karyne B. Charbonneau
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    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.

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    File URL: http://www.bankofcanada.ca/wp-content/uploads/2014/05/wp2014-17.pdf
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    Paper provided by Bank of Canada in its series Working Papers with number 14-17.

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    Length: 37 pages
    Date of creation: 2014
    Date of revision:
    Handle: RePEc:bca:bocawp:14-17
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    1. 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.
    2. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07.
    3. 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.
    4. Matthieu Crozet & Pamina Koenig, 2008. "Structural Gravity Equations with Intensive and Extensive Margins," Working Papers 2008-30, CEPII research center.
    5. Postel-Vinay, Fabien & Robin, Jean-Marc, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," CEPR Discussion Papers 3548, C.E.P.R. Discussion Papers.
    6. Keith Head & Thierry Mayer, 2013. "Gravity Equations: Workhorse, Toolkit, and Cookbook," Sciences Po publications 2013-02, Sciences Po.
    7. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, 03.
    8. 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 909-38, July.
    9. James E. Anderson & Eric van Wincoop, 2001. "Gravity with Gravitas: A Solution to the Border Puzzle," NBER Working Papers 8079, National Bureau of Economic Research, Inc.
    10. Iván Fernández-Val & Martin Weidner, 2013. "Individual and time effects in nonlinear panel models with large N,T," CeMMAP working papers CWP60/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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