The wage premium for high-skilled workers in the United States, measured as the ratio of the 90th-to-10th percentiles from the wage distribution, increased by 20 percent from the 1970s to the late 1980s. A large literature has emerged to explain this phenomenon. A leading explanation is that skill-biased technological change (SBTC) increased the demand for skilled labor relative to unskilled labor. In a calibrated vintage capital model with heterogenous labor, this paper examines whether SBTC is likely to have been a major factor in driving up the wage premium. Our results suggest that the contribution of SBTC is very small, accounting for about 1/20th of the observed increase. By contrast, a gradual and very modest shift in the distribution of human capital across workers can easily account for the large observed increase in wage inequality.