Quantitative results from a large class of structural gravity models of international trade depend critically on a single parameter governing the elasticity of trade with respect to trade frictions. We provide a new method to estimate this elasticity and illustrate the merits of our approach relative to the estimation strategy of Eaton and Kortum (2002). We employ this method on data for 123 developed and developing countries for the year 2004 using new disaggregate price and trade flow data. Our benchmark estimate for all countries is approximately 4.5, nearly 50 percent lower than the alternative estimation strategy would suggest. This difference implies a doubling of the measured welfare costs of autarky across a large class of widely used trade models.