We develop Bayesian inference for an unconditional quantile regression model. Our approach provides better estimates in the upper tail of the wage distribution as well as valid small sample confidence intervals for the Oaxaca–Blinder decomposition. We analyze the recent changes in the US wage structure using data from the CPS Outgoing Rotation Group from 1992 to 2009. We find that the largest part of the recent changes is explained mainly by differences in returns to education while the decline in the unionization rate has a small impact, and that earnings inequality is rising more at the top end of the wage distribution.