Income risks are not accurately captured by standard AR processes that are common in the literature. This paper proposes a simple stochastic process which matches several moments in the data including the cross-sectional distribution of income and the distribution income risk, and can be easily used in models with uninsurable income risk. Incorporating this process into an off-the-shelf OLG model leads to a rise in wealth concentration narrowing the gap between traditional models and the data. However, the right tail of the wealth distribution remains significantly thinner than the data.