Optimal redistributive pensions with temptation and costly self-control

We characterize an optimal redistributive pension scheme when individuals face temptation, but can exert costly self-control (as in Gul & Pesendorfer, 2001; 2004). Our results challenge the common wisdom that forced savings tend to reduce individuals' mental cost of self-control. In our model, individuals heterogenous in the intensity of their self-control problem and in productivity. A pension scheme simultaneously has three effects: it redistributes income across retirees, it forces young individuals to save and it affects their mental cost of exerting self-control, which is entailed by voluntary savings. In a scheme with a proportional income tax and benefits with a contributory component, taxation generally increases the mental cost of self-control. This effect partially offsets the forced-saving benefits of public pensions, and call for a more redistributive system. This result contrasts with a first best optimum, where the mental cost of self-control is driven to zero and consumption is smoothed across periods.