Contrary to the predictions of a factor-proportions model, trade liberalization episodes in developing countries were followed by sharp increases in the skill-premium in a very short period. These increases are puzzling because the factor-proportions model describes cross-sectional data very well if it is reinterpreted to account for differences in factor intensities across quality levels within sectors. Specifically, a model of heterogeneous firms where high-quality goods are more skill intensive than low-quality goods explains well-documented facts about unit prices in the data on firms and bilateral trade. The standard channels of reallocation, export expansion and access to foreign inputs cannot quantitatively or qualitatively account for the rise in skill premium and changes in skill intensity. We then allow for the entry of high-quality alternatives during a trade liberalization to decrease the relative demand for low-quality goods. This effect, reminiscent of the Bertrand model, has long been used in theory to explain firm-level investments in productivity spurred by tightened competition. Here, this investment takes the form of quality-upgrading. Since higher-quality goods are more skill-intensive, the demand for skill increases. We use a panel data on manufacturing plants in Colombia to estimate the model and evaluate its predictions regarding a counterfactual decrease in tariffs.