On the persistence of income shocks over the life cycle: Evidence, theory, and implications

Abstract

How does the persistence of earnings change over the life cycle? Do workers at different ages face the same variance of idiosyncratic earnings 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 we estimate it using Panel Study of Income Dynamics 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 through 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 age-invariant persistence and variance) cannot capture the earnings dynamics of young workers. We also argue that a calibrated job turnover model can account for these nonflat 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 the variance of shocks. Furthermore, the decline in job mobility results in higher persistence. Finally, we investigate the implications of age profiles for consumption–savings behavior. The welfare cost of idiosyncratic risk implied by the age-dependent income process is up to 1.6 percent of lifetime consumption 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 profiles of persistence and variances should be taken into account when calibrating life-cycle models.