In this paper we use the enhanced consumption data in the Panel Survey of Income Dynamics (PSID) from 2005-2017 to explore the transmission of income shocks to consumption. We build on the nonlinear quantile framework introduced in Arellano, Blundell and Bonhomme (2017). Our focus is on the estimation of consumption responses to persistent nonlinear income shocks in the presence of unobserved heterogeneity. To reliably estimate heterogeneous responses in our unbalanced panel, we develop Sequential Monte Carlo computational methods. We find substantial heterogeneity in consumption responses, and uncover latent types of households with different lifecycle consumption behavior. Ordering types according to their average log-consumption, we find that low-consumption types respond more strongly to income shocks at the beginning of the life cycle and when their assets are low, as standard life-cycle theory would predict. In contrast, high-consumption types respond less on average, and in a way that changes little with age or assets. We examine various mechanisms that might explain this heterogeneity.