Gravity-Defying Trade

FRB of Boston Working Paper No. 03-1

29 Pages Posted: 13 Jan 2005

See all articles by J. M.C. Santos Silva

J. M.C. Santos Silva

University of Surrey

Silvana Tenreyro

London School of Economics (LSE)

Date Written: March 26, 2003


Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: estimating economic relationships in logarithms can lead to significant biases in the presence of heteroskedasticity. This paper explains why this problem arises and proposes an appropriate estimator. Our criticism to conventional practices and the solution we propose extends to a broad range of economic applications where the equation under study is log-linearized. We develop the argument using one particular illustration, the gravity equation for trade, and use the proposed technique to provide novel estimates of this equation. Three results stand out. First, contrary to general belief, income elasticities are significantly smaller than 1. Second, standard estimators greatly exaggerate the roles of distance and colonial links. Finally, bilateral trade between countries that have signed a free-trade agreement is 30 percent larger than that between other countries, a magnitude remarkably di?erent from that predicted by conventional methods (above 100 percent).

Keywords: gravity equation, free-trade agreements, heteroskedasticity, Poisson regression

JEL Classification: C21, F10, F11, F12, F15

Suggested Citation

Santos Silva, João M.C and Tenreyro, Silvana, Gravity-Defying Trade (March 26, 2003). FRB of Boston Working Paper No. 03-1, Available at SSRN: or

João M.C Santos Silva (Contact Author)

University of Surrey ( email )

Surrey GU2 7XH
United Kingdom

Silvana Tenreyro

London School of Economics (LSE) ( email )

Houghton Street
London WC2A 2AE
United Kingdom

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