We study how technological change affects between‐ and within‐education‐group inequality in the United States. We develop a model with heterogeneous workers and firms in which the demand for skills is characterized by firms' recruiting behavior. We use the model to quantify the relative contribution of two types of technological change that affect the relative demand for skilled labor: technological change in firm‐specific productivity and technological change in labor productivity. We find that technological change in labor productivity, in the form of higher returns to skill in production, is the main driver of the increase in between‐ and within‐group inequality. Technological change in firm productivity, in the form of higher firm productivity dispersion, plays a less important role in explaining rising inequality, except for the increase in within‐group inequality for workers without a college degree.