This paper explores the macroeconomic and welfare implications of the sharp rise in U.S. wage inequality . In the data, cross-sectional earnings variation increased substantially more than wage variation, due to a sharp rise in the wage-hours correlation. At the same time, inequality in hours worked and consumption remained roughly constant through time. Using data from the PSID, we decompose the rise in wage inequality into changes in the variance of permanent, persistent and transitory shocks. With the estimated changes in the wage process as the only primitive, we show that a standard calibrated OLG model with incomplete markets can successfully account for all these patterns in cross-sectional U.S. data. Through a set of counter-factual experiments, we assess the role of each component of the wage process for the evolution in the various dimensions of inequality. The model also allows us to investigate the welfare costs of the rise in inequality: we find that the unconditional expected welfare loss is equivalent to a 5 percent decline in lifetime income for the worst-affected cohorts, those entering the labor market in the mid 1980's. Ex post, these costs are widely dispersed across agents, due both to differences in permanent individual attributes and to differences in labor market histories. An extensive sensitivity analysis verifies the robustness of our results to alternative preferences and borrowing limits, and to the inclusion of female labor force participation. JEL Classification Codes: E21, D31.