This paper proposes a novel specification for residual earnings that allows for a lifetime profile in the persistence and variance of labor income shocks. We show theoretically that the statistical model is identified and estimate it using data from the PSID. We strongly reject the hypothesis of a flat life-cycle profile for persistence and variance of persistent shocks, but not for the variance of transitory shocks. Shocks to earnings are only moderately persistent (around 0.75) for young individuals. Persistence rises with age up to unity until midway in life and decreases to around 0.95 toward the end of the life cycle. On the other hand, the variance of persistent shocks exhibits a U-shaped profile over the life cycle (with a minimum of 0.01 and a maximum of 0.045). Our estimate of persistence, for most of the working life, is substantially lower than typical estimates in the literature. We investigate the implications of these profiles for consumption-savings behavior with a standard life-cycle model. Under natural borrowing limits, the welfare cost of idiosyncratic risk implied by the age dependent income process is 32% lower compared to an AR(1) process without age profiles. This is mostly due to a higher degree of consumption insurance for young workers, for whom persistence is moderate. The results hold qualitatively for an economy with no borrowing, although the difference between specifications is smaller (23%). We conclude that the welfare cost of idiosyncratic risk is overstated.