We analyze the sources of changes in the distribution of hourly wages in the United States using CPS data for the survey years 1976 to 2016. We account for the selection bias from the employment decision by modeling the distribution of annual hours of work and estimating a nonseparable model of wages which uses a control function to account for selection. This allows the inclusion of all individuals working positive hours and thus provides a fuller description of the wage distribution. We decompose changes in the distribution of wages into composition, structural and selection eﬀects. Composition eﬀects have increased wages at all quantiles but the patterns of change are generally determined by the structural eﬀects. Evidence of changes in the selection eﬀects only appear at the lower quantiles of the female wage distribution. These various components combine to produce a substantial increase in wage inequality.