Discounting and impatience with overlapping generations (Crossposted at CT)
During the discussion of discounting and the Stern Review, I got an email raising a point that I had already been worrying about. In discussing costs and benefits in 2100, I and others routinely refer to future generations, and in a sense that’s right, since the people involved in the discussion won’t be around then. But, children alive now have a reasonable chance of living to 2100 – quite a good chance if life expectancy keeps rising. Economists often deal with this kind of thing by modelling a series of overlapping generations, but I haven’t seen much discussion of this in relation to benefit-cost analysis, though no doubt it’s in the literature somewhere.
I finally got around to thinking about this, and in particular the following question. Suppose we accept an ethical framework in which everyone now alive matters equally. Suppose also that as individuals we have a consistently positive rate of time preference, preferring to have higher utility now at the expense of less in the future, that is, more when we are young and less when we are old (this isn’t obvious by the way, but I’m assuming it for the sake of argument) . What is the appropriate pure rate of time preference for society as a whole?
My preliminary answer, somewhat surprisingly to me, is “Zero”. I’ll set out the outline of the formal argument over the fold, but the simple summary has two parts. First, since generations overlap, if, at all times, we treat all people now alive as equal then we must treat all people now and in the future as equal. Given this equality, positive individual rates of time preference translate not into a social preference for the present over the future but into a social policy that consistently puts more weight on the welfare of people when they are young than when they are old.
For a formal argument, consider the special case of a stationary society with overlapping generations constant population, equal wealth, no technical progress and a steady state capital stock. In this case, positive time preference means that individuals will choose a declining level of consumption over their lifetime, but the continuous replacement of old people by young people exactly offsets this, so aggregate consumption is constant. Saving (social or individual) arises from the bequest motive of ensuring that newly-born members of society have the same average wealth as existing members. It seems clear that, in such a society, the interest rate, which, in the absence of market failures, is also the social rate of time preference must be zero.
The catch, if there is one, is that the model requires that individuals who prefer, in this setting, a declining consumption path for themselves, are nonetheless willing to arrange transfers of wealth so that their children can enjoy the same lifetime utility as themselves. But this is clearly entailed by the assumption that everyone now alive is treated equally.
Coming back to the assumption of positive individual time preference, there’s lots of evidence that people engage in behavior that implies positive time preference, consuming now when they could get significantly more by waiting. But, a lot of this behavior isn’t consistent with the model of a consumer rationally optimising over time. In all sorts of choices, people consume in haste and repent at leisure; that is, when they reach the lower future levels of consumption entailed by their earlier choices, they regret those choices. The analogy with social decisions that favor current generations (more precisely, those currently in a position to make social choices) over future generations is obvious.