This paper investigates how international trade impacts the gender wage gap at different points of the skill distribution, by integrating statistical discrimination and job assignment into a model of trade. Workers differ by their skills and their job commitment. Firms decide whether they invest in technology upgrading and which workers they hire. The inability to observe workers’ job commitment induces employers to discriminate against women who have on average lower commitment. When skills and technology upgrading are complements, technological change is skill-biased. When, in addition, job commitment and technology upgrading are complements, technological change is gender-biased. The widening of the gender wage gap occurs all along the skill distribution if skills and job commitment are complement as well. The paper shows that the gender wage gap widens among skilled workers and decreases among unskilled workers as a result of trade integration. The theory can explain the increase in both within-group and between-group wage inequality following the adoption of new technologies, here induced by trade liberalization.