Retirement is weird, when you think about it. We consume small amounts of leisure for most of our lives, then suddenly stop working completely and consume a big bunch of leisure for the rest of our lives. We smooth our consumption of all other goods, but we don't smooth our consumption of leisure. Instead we binge on leisure at the end of our lives. (I have blogged about this puzzle before.)
Overlapping generations models assume that people work and save when young, and retire and dissave when old. Young people save for their retirement. Which makes sense, because it fits the facts. But the facts don't make sense. Why don't people work part-time when young, and work part-time when old, and save nothing for retirement, because they don't retire?