Earnings dynamics are much richer than typically assumed in macro models with heterogeneous agents. This holds for individual-pre-tax and household-post-tax earnings and across administrative and survey data. We estimate two alternative processes for household after-tax earnings and study their implications using a standard life-cycle model. Both processes feature a persistent and a transitory component, but although the first one is the canonical linear process with stationary shocks, the second one has substantially richer earnings dynamics, allowing for age-dependence of moments, non-normality, and nonlinearity in previous earnings and age. Allowing for richer earnings dynamics implies a substantially better fit of the evolution of cross-sectional consumption inequality over the life cycle and of the individual-level degree of consumption insurance against persistent earnings shocks. The richer earnings process implies lower welfare costs of earnings risk.