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.