Education choices, longevity and optimal policy in a Ben-Porath economy

We develop a 3-period overlapping generations (OLG) model where individuals borrow at the young age in order to finance their education. Education does not only increase future wages, but also raises the duration of life, which, in turn, can affect education, in line with Ben-Porath (1967). We examine the conditions under which the Ben-Porath effect prevails. Although the existence of a positive Ben-Porath effect requires, under exogenous longevity, a change in lifetime hours of work, we find, under endogenous longevity, that a positive Ben-Porath effect arises even when old-age labor is fixed. It is also shown that the Ben-Porath effect may not be robust to allowing for adjustments in production factor prices. On the policy side, we show that the social optimum can be decentralized provided the capital stock is set to the Modified Golden Rule level. Finally, we introduce intracohort heterogeneity in learning ability, and we show that, under asymmetric information, the second-best optimal non-linear tax scheme involves a downward distortion in the education of less able types, which reinforces the longevity gap in comparison with the first-best.