On the Persistence of Income Shocks over the Life Cycle: Evidence, Theory, and Implications, Second Version
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 an age 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 find that shocks to earnings are only moderately persistent (around 0:75) for young workers. Persistence rises with age up to unity until midway in life. The variance of persistent shocks exhibits a U-shaped profile over the life cycle (with a minimum of 0:01 and a maximum of 0:05). These results suggest that the standard specification in the literature (with constant persistence and variances) cannot capture the earnings dynamics of young workers. We also argue that a calibrated job turnover model can account for these non-flat profiles. The key idea is that workers sort into better jobs and settle down as they age; in turn, magnitudes of wage growth rates decline, thereby decreasing variance of shocks. Furthermore the decline in job mobility results in higher persistence. Finally, we investigate the implications of age profles for consumption-savings behavior. The welfare cost of idiosyncratic risk implied by the age-dependent income process is 34 percent lower compared with its age-invariant counterpart. This difference is mostly due to a higher degree of consumption insurance for young workers, for whom persistence is moderate. These results suggest that age profles of persistence and variances should be taken into account when calibrating life-cycle models.