Aggregation and the Gravity Equation

Abstract

One of the most successful empirical relationships in international trade is the gravity equation. A key decision for researchers in estimating this relationship is the level of aggregation, since the gravity equation is log linear, whereas aggregation involves summing the level rather than the log of trade. In this paper, we derive a Jensen's inequality correction term for nested constant elasticity of substitution preferences, such that a log-linear gravity equation holds exactly for each nest. We provide evidence that sectoral composition is quantitatively relevant for the aggregate effect of distance on international trade, particularly for more disaggregated definitions of sectors.