Trade elasticity is a crucial parameter in evaluating the welfare impacts of changes in trade frictions. The value of this parameter varies widely across product categories, however, which is especially important for developing countries' evaluation of the welfare gains from trade. We estimate, and make publicly-available, trade elasticities at the product level (the 6-digit level of the Harmonized System, comprising over 5,000 product categories) by exploiting the variation in bilateral applied tariffs for each product category for the universe of available country pairs over the 2001 to 2016 period. We address potential endogeneity issues, as well as heteroskedasticity and selection bias due to zero trade flows. Homogenous elasticities lead to the underestimation of the welfare impact of trade, in particular for developing economies, and all the more so for those with high import penetration in less-elastic sectors.