We build into a Ricardian model sectoral linkages, trade in intermediate goods, and sectoral heterogeneity in production to quantify the trade and welfare effects from tariff changes. We also propose a new method to estimate sectoral trade elasticities consistent with any trade model that delivers a multiplicative gravity equation. We apply our model and use our estimated elasticities to identify the impact of NAFTA's tariff reductions. We find that Mexico's welfare increases by 1.31%, U.S.'s welfare increases by 0.08%, and Canada's welfare declines by 0.06%. We find that intra-bloc trade increases by 118% for Mexico, 11% for Canada, and 41% for the U.S. We show that welfare effects from tariff reductions are reduced when the structure of production does not take into account intermediate goods or input-output linkages. Our results highlight the importance of sectoral heterogeneity, intermediate goods, and sectoral linkages for the quantification of the welfare gains from tariffs reductions.