In this paper we highlight the importance of the PSID in understanding income dynamics and consumption insurance. We explore the nonlinear nature of income shocks and describe a new quantile-based panel data framework for income dynamics. In this approach the persistence of past income shocks is allowed to vary according to the size and sign of the current shock. The model provides a good match with data and we confirm the results on population register data from Norway. Using the enhanced consumption and asset data in the PSID, nonlinear persistence is shown to have key implications for consumption insurance.