Multi-sector versions of the international trade model of Eaton and Kortum (2002) usually restrict trade elasticities to be identical across sectors, with potentially distorting effects on the estimates of the model parameters. This paper allows for heterogeneous sectoral trade elasticities and quantifies them by estimating an equation for bilateral market shares, with tariffs and standard gravity variables used to model trade barriers. Results show that sectors differ signiftcantly in the size of trade elasticities. The paper proves that this heterogeneity matters at least in three different respects. First, it matters when inferring measures of relative productivity from trade and production data. Secondly, it matters when considering the trade-induced reallocations of production within and between sectors. When assessing their relative contribution to the productivity gains that each country obtains from opening to trade, gains turn out to be largely due to the reallocation within sectors, especially for richer countries. Finally, accounting for the heterogeneity in elasticities is crucial when running general equilibrium counterfactual studies, such as that performed in this paper, which assesses the effects on aggregate of sector-specific technology shocks.