A striking feature of U.S. data on income and consumption is that inequality increases with age. This paper asks if individual-specific earnings risk can provide a coherent explanation. We find that it can. We construct an overlapping generations general equilibrium model in which households face uninsurable earnings shocks over the course of their lifetimes. Earnings inequality is exogenous and is calibrated to match data from the U.S. Panel Study on Income Dynamics. Consumption inequality is endogenous and matches well data from the U.S. Consumer Expenditure Survey. The total risk households face is decomposed into that realized before entering the labor market and that realized throughout the working years. In welfare terms, the latter is found to be more important than the former.