Working Paper 03-1
by J.M.C. Santos Silva and Silvana Tenreyro

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).

This paper was revised in March 2003.

JEL classification codes: C21, F10, F11, F12, F15

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

PDF version of paper