We quantify the contribution of firm-level technological change to skill demand and aggregate inequality in the presence of imperfect competition in the labor market. We show that skill-biased technological change increases both the firm-level skill ratio and the skill premium, while other shocks (e.g. firm-specific output demand shocks) cannot explain the increase in both outcomes. We exploit administrative data and a large survey measuring a broad class of firm-level technological changes from Hungary and Norway. We estimate that the aggregate college premium increases by 3.4% in Norway and by 4.9% in Hungary as a result of the skill bias in technological change.