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Gravity or Dummies? The Limits of Identification in Gravity Estimations

  • Cecília Hornok

Trade economists often estimate gravity equations of international trade with fixed effects. Anderson and van Wincoop (2003, American Economic Review 93, 170–192) have shown the importance of controlling for multilateral trade resistances when estimating a gravity equation. This can be done by including exporter-time and importer-time fixed effects in a panel or exporter and importer fixed effects in a cross section estimation. I argue that this approach limits the identifiability of policy parameters that capture the effect of certain ”club memberships” (EU, NAFTA, euro area, WTO, etc.) on trade flows. I show that, in the baseline case, only one effect can be identified, which precludes, for example, the estimation of separate effects on the exporter and the importer side. The magnitude, and even the sign, of the estimated club effect are very sensitive to the precise identification assumptions, which are often left unspecified in empirical studies. The underlying problem is that club membership provides some, but very little bilateral variation. When heterogeneous club effects are to be identified, the membership dummies can become perfectly collinear with the fixed effects. Empirical researchers may not be aware of the lack of identification, because standard estimation techniques often permit them to run perfectly collinear regressions. I illustrate the findings with estimating the effect of EU enlargement in 2004 on the trade flows of new and old members. Finally, I discuss potential solutions.

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Paper provided by Department of Economics, Central European University in its series CEU Working Papers with number 2012_11.

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Date of creation: 20 May 2012
Date of revision: 20 May 2012
Handle: RePEc:ceu:econwp:2012_11
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  1. McCallum, John, 1995. "National Borders Matter: Canada-U.S. Regional Trade Patterns," American Economic Review, American Economic Association, vol. 85(3), pages 615-23, June.
  2. Pierre-Philippe Combes & Miren Lafourcade & Thierry Mayer, 2005. "The Trade Creating Effects of Business and Social Networks: Evidence from France," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00268768, HAL.
  3. Baltagi, Badi H. & Egger, Peter & Pfaffermayr, Michael, 2003. "A generalized design for bilateral trade flow models," Economics Letters, Elsevier, vol. 80(3), pages 391-397, September.
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  8. Hornok, Cecília, 2011. "Need for Speed: Is Faster Trade in the EU Trade-creating?," CEPR Discussion Papers 8451, C.E.P.R. Discussion Papers.
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  10. Jacks, David S. & Meissner, Christopher M. & Novy, Dennis, 2011. "Trade booms, trade busts, and trade costs," Journal of International Economics, Elsevier, vol. 83(2), pages 185-201, March.
  11. Peter Egger & Michael Pfaffermayr, 2003. "The proper panel econometric specification of the gravity equation: A three-way model with bilateral interaction effects," Empirical Economics, Springer, vol. 28(3), pages 571-580, July.
  12. Flam, Harry & Nordström, Håkan, 2006. "Euro Effects on the Intensive and Extensive Margins of Trade," Seminar Papers 750, Stockholm University, Institute for International Economic Studies.
  13. I-Hui Cheng & Howard J. Wall, 2004. "Controlling for heterogeneity in gravity models of trade and integration," Working Papers 1999-010, Federal Reserve Bank of St. Louis.
  14. Baier, Scott L. & Bergstrand, Jeffrey H., 2009. "Bonus vetus OLS: A simple method for approximating international trade-cost effects using the gravity equation," Journal of International Economics, Elsevier, vol. 77(1), pages 77-85, February.
  15. Davis, Peter, 2002. "Estimating multi-way error components models with unbalanced data structures," Journal of Econometrics, Elsevier, vol. 106(1), pages 67-95, January.
  16. Cecília Hornok, 2010. "Trade-Enhancing EU Enlargement and the Resurgence of East-East Trade," Focus on European Economic Integration, Oesterreichische Nationalbank (Austrian Central Bank), issue 3, pages 79-94.
  17. Richard Baldwin & Daria Taglioni, 2006. "Gravity for Dummies and Dummies for Gravity Equations," NBER Working Papers 12516, National Bureau of Economic Research, Inc.
  18. Luca De Benedictis & Roberta De Santis & Claudio Vicarelli, 2005. "Hub-and-Spoke or else? Free trade agreements in the 'enlarged' European Union," European Journal of Comparative Economics, Cattaneo University (LIUC), vol. 2(2), pages 245-260, December.
  19. Baldwin, Richard E. & Skudelny, Frauke & Taglioni, Daria, 2005. "Trade effects of the euro: evidence from sectoral data," Working Paper Series 0446, European Central Bank.
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