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?
We assume that other consumption goods have diminishing marginal utility, and we say that's why people save for their retirement. They save because they don't want to consume all their income when young and consume nothing when old. They prefer to smooth their consumption over time. But if we assume consumption of leisure has diminishing marginal utility too, people wouldn't retire, and wouldn't save. They would work part-time instead. They would prefer to smooth their consumption of leisure over time too.
OK, maybe our ability to work diminishes as we age. But maybe our ability to enjoy leisure diminishes as we age too? Which will diminish more quickly as I age: my ability to give an economics lecture; or my ability to paddle my canoe? It's not obvious.
Positive real interest rates are one reason why individuals would want to postpone consumption, including the consumption of leisure. If the intertemporal substitution of leisure is more elastic than for other consumption goods, that might explain why we would want to postpone consumption of leisure more than consumption of other goods, if real interest rates are positive.
But if real interest rates fall, that same theory would also predict that this would cause a bigger reduction in postponement of consumption of leisure than the reduction in the postponement of consumption of other goods.
As real interest rates approach zero, we would expect to see retirement disappear, and people working part-time for their whole lives instead. So that, in a simple OLG model, as the real interest rate approached zero, desired saving would also approach zero. But if desired saving approaches zero as real interest rates approach zero, then real interest rates cannot be permanently zero, as long as desired investment is strictly positive at zero real interest rates.
We wouldn't expect to see this full effect immediately, because the current generation might already have been working full-time and saving for retirement, anticipating positive real interest rates.
In an earlier post, I got a bit upset about OLG models of secular stagnation and dynamic inefficiency that forget to include land as a savings vehicle. But maybe this retirement question is as big a deal. Those same models assume that retirement is exogenous. They assume that people want to smooth the consumption of everything else, except leisure, and that's why they want to save. And if they want to save too much, we get negative real interest rates in a stationary economy. But if they made the same assumption about the consumption of leisure as they make about the consumption of other goods, this couldn't happen. People would stop retiring and stop saving as real interest rates approached zero. They would work part-time instead. Or take sabbaticals. So real interest rates couldn't go negative. Not permanently, anyway.
Worthwhile Canadian Initiative 
Bob: one of the good things about the Eggertsson Mehrata paper is that it did a 3 period OLG model. The young borrow, the middle-aged save to pay off debt and accumulate assets, and the old then consume their savings. But for the retirement question, we can simplify by combining the young and middle-aged. In other words, people are “young” until around 65, then “old” after 65. (Sounds good to me!)
We need to remember to count the saving done by the young through CPP and the employer’s pension plan too.
Would I be totally misreading your argument to say that “young” people go to work to escape the kids, and only retire when they can safely do so, and have fun without the kids getting in the way!
“Would I be totally misreading your argument to say that “young” people go to work to escape the kids, and only retire when they can safely do so, and have fun without the kids getting in the way!”
No, I think there’s a component of that. More seriously though, I think the argument, inelegantly made, is that hitchhiking through Europe with a 2 year old isn’t a lot of fun, while doing the same trek by cruise ship 30 years later is. We don’t devote time to leisure when we’re “young” because we have other, more important things to do.
Or may be do devote time to leisure when we’re young. It would be helpful to think about what we mean when we’re discussing “leisure” in the OLG model. Think about what happens if we define leisure simply as not engaging in paid work (capable of giving rise to savings) – which I think is how it must be envisioned in the simple OLG model. A good chunk of the population (traditionally, woman, although that’s slowly changing) devote a good part of their youth to “leisure” (so defined), namely raising children (whether they’re out of the work force entirely, or working part time, or with reduced hours/responsibilities). That’s not what anyone of us think of as being “leisure” in any meaningful sense of the word (I love my kids, but leisurely they ain’t), but that’s “leisure” for the purposes of the OLG model. Moreover, in that model, the working parent (traditionally male, but again that’s changing) may be working not to save for the future, but to fund the “leisure” of the non-working parent. Or perhaps, both parents are working so that they can afford to hire the substitute “leisure” of a third person (a daycare, a nanny, the lady down the street).