Correct estimates of import demand elasticities are essential for measuring the gains from trade and predicting the impact of trade policies. We show that esti- mates of import demand elasticities hinge critically on whether they are derived using trade quantities or trade values, and this dierence is due to properties of the estimators. Using partial identication methods, we show theoretically that the upper bound on the set of plausible estimates is lower when using traded quantities, compared to the standard approach using trade values. Our proposed method using traded quantities leads to smaller point estimates of the import demand elasticities for many goods and imply larger gains from trade compared to estimates based on trade values.