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.

14 thoughts on “Discounting and impatience with overlapping generations (Crossposted at CT)

  1. If you add some likely population growth to that, and hence suggest that people should be saving more for future generations than they consume (to make the division between populations equal), I somehow don’t think that your function is going to be realistically achievable.

  2. The fact that consumption per person is growing over time suggests that it is not only realistically achievable but being achieved in general. In this light, failure to do anything about global warming appears as a market failure caused by free-rider problems and similar.

  3. I’m not a professional economist, but it seems that your model is overspecified. Given the productivity of capital goods, why should a zero rate of time preference be consistent with a steady-state economy? It seems to me that an evenly rotating economy with zero time preference would have a growing capital stock, since the average period of production would become indefinitely long.

  4. A digression if I may. The entire issue of investment has to assume a finite time for the benfits of that spending to accrue. For example if you spend the money to build a house, the house could be assumed to last 40-50 years. OTOH investment in reducing greenhouse gas concentrations could have a benefit which lasts hundreds of years (see Real Climate post on how long an increase in atmospheric CO2 would last). How is this accounted for?

  5. You’re on 40 grand a year struggling along with the mortgage, the current utilities bills and the kids, whilst you become increasingly aware of this GW thingy the experts are all on about. Now you are concerned about the kids future and their kids future and some expert on 200 grand a year reckons we all need to reduce our GG emissions by 60% of 1990 levels in order for the kiddies not to have to suffer the nasties of GW. That’s gunna leave you and your kids on $16K a year while the expert has to make the sacrifice to $80k a year for the sake of his kids’ futures. That’s of course making the fairly logical assumption that fossil fuel use and welfare are closely correlated. It could be a whole lot worse if human welfare/consumption is exponentially dependant upon fossil fuel use of course, but let’s not get too despondent about necessary sacrifices. Stay focussed on the kiddies. Now you ask yourself will this sacrifice by you and the kids now, all be worth it? Well apparently not, since it will all be swallowed up by Indian and Chinese kids with no nett effect on the GW nasties anyway. Obviously a clear case of market failure with all this time preference stuff and one hell of a tough choice for the layman.

  6. JQ 27 Dec 06:If like Stern, you choose a value near zero (just enough to account for the possibility that there will be no one around in the future, or at least no one in a position to care about our current choices on global warming), you reach the conclusion that immediate action to fix global warming is justified. If, like most of Stern’s critics you choose a rate of pure time preference like 3 per cent, implying that the welfare of people 90 years (roughly three generations) in the future counts for about one-sixteenth as much as the welfare of people alive today, you conclude that we should leave the problem to future generations.

    ToS:“I see that JQ now accepts that Stern did indeed use a near zero discount rate �

    JQ: Erroneous as ever, Tam. Learn to distinguish between discount rate and time preference before rejoining the argument.

    JQ (Jan 9, 2007)”What is the appropriate pure rate of time preference for society as a whole?

    My preliminary answer, somewhat surprisingly to me, is “Zeroâ€?.”

    So Richard Tol is right about JQ and UQ. What is the time preference rate for if not for discounting?

  7. JQ again,9 Jan 07: “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”.

    A non sequitur and a false description of time preference. Alfred Marshall I think it was who said that interest is a reward for abstinence. I got out of compulsory pension deductions from my income whenever I could, guessing that I could out perform the pension, which I did. I saved to raise my income/utility when I became old, which I have done successfully, like many of us.

  8. Assuming that people are equal is not the same as assuming that people have equal wealth. You seem to have constructed a socialist utopia to justify the socialist policies you prefer.

    Why not start with the assumption that people come into this world with zero wealth and leave with zero wealth and ascend and decend the wealth ladder evenly over their lifetime with the peak somewhere in the middle. That would still be unrealistic but not as absurd as the assumption you currently build from.

  9. Tam, please write 100 times “The social rate of time preference is not the discount rate”.

    Terje, someone who entered the world with zero wealth (including zero human capital) and received no help from the existing generation (most obviously their parents) would die immediately. The fact that we are now highly productive is due to the capital stock (including ideas) inherited from the past. The model is just a simplified (and stock-standard) way of describing these facts.

  10. I’m a bit confused now, John. You’re talking about just the pure rate of time preference (delta) now, aren’t you, not the total discount rate. And of course they’re one and the same in a stationary state. And you’ve been saying all along you agree with Stern that this should be close to zero. That is, future generations have equal weight. If that’s the case, it doesn’t make any difference whether generations overlap or come in discrete waves.

    Perhaps what’s new in this post is the issue of weighting the uility of the young over the old. Then the age conposition of the society would matter. But it’s obvious that once a steady state is reached, the age composition will be constant, so the zero discount rate follows straghtforwardly. What’s the tricky bit I’m missing?

  11. Just to clarify: I wrote my comment before reading your reply to ‘Tam’ at #9, and that’s not what I’m confused by.

  12. I’m as confused as Farrell. (For once.)

    (At Christmas lunch, my sister-in-law hostess remarked on Climate Change: “I’ll be dead in 100 years, what do I care? More turkey darling [her small son]?”).

  13. James, maybe you’re just quicker than me. I thought there would be a problem in having a social time preference rate of zero, when individuals have positive time preference. It turns out not to be a problem, but that wasn’t obvious to me when I started.

  14. “What is the time preference rate for if not for discounting?”

    Of course it’s for discounting, but it isn’t the whole of discounting.

    Discounting includes both time preference and opportunity cost.

    A time preference of zero does not imply a discount rate of zero, except in a society where the risk free return on investment is zero.

    So if you postulate a society with economic stasis (opportunity cost of zero), then JQ’s views imply a discount rate of zero. In the actual world, they imply a discount rate in the 2-5% range, depending on your assumptions about investment and technological change.

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