A quantitative model brings together theories linking international trade to quality, technology, and demand for skills. Standard effects of trade on importers and exporters are magnified through domestic input linkages. We estimate the model with data from Colombian manufacturing firms before the 1991 trade liberalization. A counterfactual trade liberalization is broadly consistent with post-liberalization data. It increases skill intensity from 12 to 16 percent, while decreasing sales. Imported inputs, estimated to be of higher quality, and domestic input linkages are quantitatively important. Economies of scale, export expansion, and reallocation of production are small and cannot explain post-liberalization data. (JEL F14, F16, J24, L60, O14, O19, O33)