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The Log of Gravity

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Author Info
Joao Santos Silva
Silvana Tenreyro

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Abstract

Although economists have long been aware of Jensen's inequality, many econometric applicationshave neglected an important implication of it: the standard practice of interpreting the parameters oflog-linearized models estimated by ordinary least squares as elasticities can be highly misleading inthe presence of heteroskedasticity. This paper explains why this problem arises and proposes anappropriate estimator. Our criticism to conventional practices and the solution we propose extends toa broad range of economic applications where the equation under study is log-linearized. We developthe argument using one particular illustration, the gravity equation for trade, and apply the proposedtechnique to provide new estimates of this equation. We find significant differences betweenestimates obtained with the proposed estimator and those obtained with the traditional method. Thesediscrepancies persist even when the gravity equation takes into account multilateral resistance termsor fixed effects

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Paper provided by Centre for Economic Performance, LSE in its series CEP Discussion Papers with number dp0701.

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Date of creation: Jul 2005
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Handle: RePEc:cep:cepdps:dp0701

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Related research
Keywords: Elasticities Gravity equation Heteroskedasticity Jensens inequality Poisson regression Preferential-trade agreements

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
F10 - International Economics - - Trade - - - General
F11 - International Economics - - Trade - - - Neoclassical Models of Trade
F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies
F15 - International Economics - - Trade - - - Economic Integration

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Eaton Jonathan & Tamura Akiko, 1994. "Bilateralism and Regionalism in Japanese and U.S. Trade and Direct Foreign Investment Patterns," Journal of the Japanese and International Economies, Elsevier, vol. 8(4), pages 478-510, December. [Downloadable!] (restricted)
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  2. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-91, July. [Downloadable!] (restricted)
  3. Delgado, M.A. & Kniesner, T.J., 1992. "Semiparametric Versus Parametric Count-Data Models-- Econometric Considerations and Estimates of Hedonic- Equilibrium Model of Worker Absenteeism," Papers 92-018, Indiana - Center for Econometric Model Research.
  4. Davis, Donald R., 1995. "Intra-industry trade: A Heckscher-Ohlin-Ricardo approach," Journal of International Economics, Elsevier, vol. 39(3-4), pages 201-226, November. [Downloadable!] (restricted)
  5. Jeffrey Frankel & Andrew Rose, 2002. "An Estimate Of The Effect Of Common Currencies On Trade And Income," The Quarterly Journal of Economics, MIT Press, vol. 117(2), pages 437-466, May. [Downloadable!] (restricted)
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  6. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-20, May. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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  9. Robert C. Feenstra & James R. Markusen & Andrew K. Rose, 2001. "Using the gravity equation to differentiate among alternative theories of trade," Canadian Journal of Economics, Canadian Economics Association, vol. 34(2), pages 430-447, May. [Downloadable!] (restricted)
  10. Wooldridge, Jeffrey M., 1999. "Distribution-free estimation of some nonlinear panel data models," Journal of Econometrics, Elsevier, vol. 90(1), pages 77-97, May. [Downloadable!] (restricted)
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  11. Bergstrand, Jeffrey H, 1985. "The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence," The Review of Economics and Statistics, MIT Press, vol. 67(3), pages 474-81, August. [Downloadable!] (restricted)
  12. Silvana Tenreyro & Robert J. Barro, 2002. "Economic effects of currency unions," Working Papers 02-4, Federal Reserve Bank of Boston. [Downloadable!]
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  13. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September. [Downloadable!] (restricted)
  14. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May. [Downloadable!] (restricted)
  15. Leslie E. Papke & Jeffrey M. Wooldridge, 1993. "Econometric Methods for Fractional Response Variables with an Application to 401(k) Plan Participation Rates," NBER Technical Working Papers 0147, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  16. Rose, Andrew K, 1999. "One Money, One Market: Estimating the Effect of Common Currencies on Trade," CEPR Discussion Papers 2329, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  17. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July. [Downloadable!] (restricted)
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  18. Jon Haveman & David Hummels, 2004. "Alternative hypotheses and the volume of trade: the gravity equation and the extent of specialization," Canadian Journal of Economics, Canadian Economics Association, vol. 37(1), pages 199-218, February. [Downloadable!] (restricted)
  19. Windmeijer, F A G & Silva, J M C Santos, 1997. "Endogeneity in Count Data Models: An Application to Demand for Health Care," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 281-94, May-June. [Downloadable!]
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  20. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-16, March. [Downloadable!] (restricted)
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