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Multiple Fixed Effects in Binary Response Panel Data Models

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  • Karyne B. Charbonneau

Abstract

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

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    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. C. Kirabo Jackson, 2013. "Match Quality, Worker Productivity, and Worker Mobility: Direct Evidence from Teachers," The Review of Economics and Statistics, MIT Press, vol. 95(4), pages 1096-1116, October.
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    4. Thierry Mayer & Marc J. Melitz & Gianmarco I. P. Ottaviano, 2021. "Market Size, Competition, and the Product Mix of Exporters," World Scientific Book Chapters, in: Firms and Workers in a Globalized World Larger Markets, Tougher Competition, chapter 5, pages 109-150, World Scientific Publishing Co. Pte. Ltd..
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    11. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 441-487.
    12. 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.
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    14. 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.
    15. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-1721, September.
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    19. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
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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. Koen Jochmans, 2018. "Semiparametric Analysis of Network Formation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 705-713, October.
    3. Iván Fernández-Val & Martin Weidner, 2018. "Fixed Effects Estimation of Large-TPanel Data Models," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 109-138, August.
    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. Lazarov, Vladimir & Hinterschweiger, Marc, 2018. "Determinants of distress in the UK owner-occupier and buy-to-let mortgage markets," Bank of England working papers 760, Bank of England.
    6. André, Pierre & Dupraz, Yannick, 2023. "Education and polygamy: Evidence from Cameroon," Journal of Development Economics, Elsevier, vol. 162(C).
    7. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    8. Boneva, Lena & Linton, Oliver, 2017. "A discrete choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance," Bank of England working papers 640, Bank of England.
    9. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    10. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers 52/15, Institute for Fiscal Studies.
    11. Bryan S. Graham, 2015. "Methods of Identification in Social Networks," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 465-485, August.
    12. Bauer, Gregory H., 2017. "International house price cycles, monetary policy and credit," Journal of International Money and Finance, Elsevier, vol. 74(C), pages 88-114.
    13. repec:hal:spmain:info:hdl:2441/dpido2upv86tqc7td18fd2mna is not listed on IDEAS
    14. Bryan S. Graham, 2015. "An econometric model of link formation with degree heterogeneity," CeMMAP working papers 43/15, Institute for Fiscal Studies.
    15. Lena Boneva (Körber) & Oliver Linton, 2017. "A discrete choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance," CeMMAP working papers 02/17, Institute for Fiscal Studies.
    16. Jörg Claussen & Christian Essling & Christian Peukert, 2018. "Demand variation, strategic flexibility and market entry: Evidence from the U.S. airline industry," Strategic Management Journal, Wiley Blackwell, vol. 39(11), pages 2877-2898, November.
    17. Valentin Verdier, 2020. "Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 1-16, March.
    18. Leung, Michael P., 2019. "A weak law for moments of pairwise stable networks," Journal of Econometrics, Elsevier, vol. 210(2), pages 310-326.
    19. repec:hal:wpspec:info:hdl:2441/dpido2upv86tqc7td18fd2mna is not listed on IDEAS

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    More about this item

    Keywords

    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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