The Log of Gravity

Federal Reserve Bank of Boston Working Paper No. 03-01

41 Pages Posted: 7 Apr 2003

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

J. M.C. Santos Silva

University of Surrey

Silvana Tenreyro

London School of Economics (LSE)

Multiple version iconThere are 2 versions of this paper

Date Written: December 29, 2004


Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: the standard practice of interpreting the parameters of log-linearized models estimated by ordinary least squares as elasticities can be highly misleading 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 apply the proposed technique to provide new estimates of this equation. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method. These discrepancies persist even when the gravity equation takes into account multilateral resistance terms or fixed effects.

Keywords: Elasticities, Gravity equation, Heteroskedasticity, Jensen's inequality, Poisson regression, Preferential-trade agreements

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

Suggested Citation

Santos Silva, João M.C and Tenreyro, Silvana, The Log of Gravity (December 29, 2004). Federal Reserve Bank of Boston Working Paper No. 03-01, Available at SSRN: or

João M.C Santos Silva

University of Surrey ( email )

Surrey GU2 7XH
United Kingdom

Silvana Tenreyro (Contact Author)

London School of Economics (LSE) ( email )

Houghton Street
London WC2A 2AE
United Kingdom