On the Persistence of Income Shocks Over the Life Cycle: Evidence and Implications, Second Version

Abstract

How does the persistence of earnings change over the life cycle? Do workers at different ages face the same variance of idiosyncratic shocks? 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 that the statistical model is identified and estimate it using PSID data. We strongly reject the hypothesis of a at 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. 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. 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. We conclude that the welfare cost of idiosyncratic risk will be overstated if one does not account for the age profiles in the persistence and variance of shocks.