We analyze the impact of input tariffs on the export status and export performance of heterogeneous processing firms. Using a theoretical model with downstream firms exhibiting different levels of productivity, we show that lower input tariffs may increase the export sales of high-productivity firms at the expense of low-productivity firms and may decrease the probability of firms entering foreign markets. We compare the predictions of the theoretical model with firm-level data from the French agrifood sector by developing a two-stage estimation procedure that uses an equation for selection into export markets in the first stage and an export's equation in the second stage. The liberalization of agricultural trade appears to favor the reallocation of market share from low- to high-productivity agrifood firms. In addition, our results suggest that, whether lower input tariffs increase total export sales (and jobs), a large fraction of the least productive exporting firms may lose from an additional decrease in agricultural input tariffs.