Discounting and impatience with overlapping generations

by John Q on January 8, 2007

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.

{ 28 comments }

1

Z 01.08.07 at 10:04 am

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.

Is that necessarily so? It is not entirely obvious to me that if I consider myself ethically commited to equality between myself and person A, and if person A considers herself commited to equality between herself and person B, then I must consider myself commited to equality with person B. This is already not entirely clear to me among people living in the same time period (in formal terms, is it obvious that social equality should be transitive?) but becomes highly problematic to me when different time-frames are considered.

Suppose, as it is indeed the case for myself, that some individual (or society as a whole) strive to treat all people equally but with the catch that this individual (or society) has a vivid conscience of his moral limitations and thus recognise that his choices might in retrospect look ill-advised. Isn’t there then a moral case for some time-preference (not necessarily to the present, I hasten to add) simply because the moral choice of this individual reflects only his present moral calculus and not that of future generations?

Future generations might after all think that some dimension of justice that we dismiss are absolutely crucial. Or they might decide that some we cherish dearly were in fact intermediate stages that they do not need to uphold anymore.

To your formal case of “a stationary society with overlapping generations constant population, equal wealth, no technical progress and a steady state capital stock”, I thus think it is necessary to add the hypothesis of a constant moral sentiment to reach your conclusion of a zero time preference. This hypothesis being exceedingly questionnable in my opinion, I look at your conclusions with some prudence.

2

aaron_m 01.08.07 at 10:19 am

Measuring individuals’ rate of time preferences and comparing how they value past decisions when they have a positive rate vs. a zero or negative rate can tell us something about how people ought to value their own consumption/wealth over time if they want to maximise their own satisfaction.

But this kind of information tells us next to nothing about how individuals ought to value other’s consumption/wealth in the future on moral grounds.

3

Michael Greinecker 01.08.07 at 10:40 am

What if parents have the possibility to give a consumption good to their children that is perishable so it cannot be transfered to the gneration T+2?

And then there is still the impossibility result of Diamond/Shinotsuka. Maybe you avoid it by your restrictions on utility steams, but I have my doubts.

4

Matthew Kuzma 01.08.07 at 10:54 am

I feel as though something is lost somewhere along the lines of your analysis by not dealing with the effects of time specifically enough.

As time progresses forward, society sees periods time (albeit on average less than a second long) during which nobody is born, and moments in which one person is born. Given your assumptions, what happens in each of those cases? What happens to a society with your assumptions during a period of time involving no births or deaths? What happens to a society with your assumptions when someone is born, or when someone dies?

I guess what I’m saying is that, because there are periods of time that pass during which there are no births and no deaths, the statement that everyone alive now is equal is not equivalent to the statement that everyone alive now and everyone who will ever live are all equal.

5

John Quiggin 01.08.07 at 11:12 am

Aaron – my point exactly.

Michael, I’m not trying to solve all the problems in the field here, just making a simple point. But, as in Stern, allowing a constant small possibility either that the human race will become extinct or that conditions will change so radically as to make our current choices irrelevant (eg The Singularity) seems to fix the impossibility problem.

6

aaron_m 01.08.07 at 11:39 am

Aaron – my point exactly

Then I am lost, what does this mean?

“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.”

Are you trying to make a normative point? Trying to guess what your point is I have come up with two possibilities

A) You are claiming that 1) because the individual’s time preference for their own wealth is morally irrelevant to what they are owed and what they owe to others we 2) have a moral duty to be concerned with future generations in some way. But the negative argument against 1) does not entail a positive argument for 2) and tells us nothing about what these obligations should be.

B) The other moral argument I gather from your text is that we have a duty to do what we can to make sure that future generations enjoy as much welfare as we enjoyed over our life times. This is certainly a popular moral stance but I do not understand how the analogy to individual’s time preference adds anything to our understanding of this moral claim. The only thing that does any normative work in your comment is your normative premise ‘all living people are owed equal consumption’ combined with the parameters of your example, namely a “stationary society with overlapping generations constant population, equal wealth, no technical progress and a steady state capital stock.” But what are the implications for intergenerational justice and wealth transfers, and does the analogy to individuals’ time preference tell us anything?

7

radek 01.08.07 at 12:22 pm

I’ve been bugged about this too, ever since it came up in all the previous discussions. From thinking/playing around with it I think the devil’s in the details in how you set it all up. So let’s take the standard social-planner welfare maximizing Ramsey excercise. First, overlapping generations or not, there are some things/parameters even a social planner must respect – for example the shape of individual’s utility function or in other words eta. With overlapping generations it gets more complicated because the social planner must now also respect the fact that individuals discount their own consumption and at any moment in time there are different individuals at different points in their lifecycle. At the same time, let’s assume that the “proper” weights to be given to each generation are all equal, in other words a inter-generational discount rate of zero. (Standard Ramsey excercise deals with a lot of messy details by assuming them away – assuming that a generation is born, lives for one period and is then replaced by the next generation)
If the social planner is choosing how much consumption to give to each generation born at time i then for reasons you mention in your post the proper social discount rate still should be zero though there is a preferance for the younger. In other words this is still a an ethical argument not an economic one and the fact that generations overlap doesn’t matter.
However when I set it up as the social planner choosing consumption per capita for all people alive at time t (and here the issue of how exactly the intertemporal transfer is achieved seems important, not to mention issues about stationarity of population and the economy as a whole) I get that the proper social discount rate is something like (individual’s rate of time preferance)*(age at which your kids are born/life span). So say individual’s rate of time preferance*(1/3) or something like that. But I am far far from sure that this is the proper way to set it up. This is messy.

As far as individual’s time preferance. I think to say that individual discounting is “irrational” implies a very strong notion of rationality one that goes beyond standard assumptions. All you really need is time consistancy, but even that gets violated often in practice.

8

John Emerson 01.08.07 at 1:26 pm

I basically doubt the premise of this and the other threads. In particular, I don’t think that this should be regarded as a transaction between this generation of individuals and a series of later generations of individuals. It’s really a relationship between the present generation and the future human race as a whole (every future generation). We have the possibility of doing permanent damage.

Environmental protection might be regarded as the kind of deferred gratification involved when an old man invests money he’ll never see the profits from instead of blowing it all on high living. Sacrifices of the latter type seem to be praised by most economists, whereas sacrifices for environmental protection. Getting to government-mandated sacrifices is a more difficult step, I suppose.

Economists tend to underestimate the risk and magnitude of environmental change while overestimating the costs of environmental preservation. They also tend to work in a short timeframe of decades or at most afew centuries, whereas environmental events often require looking at much millenia.

I have a much longer argument at my URL.

9

Michael Greinecker 01.08.07 at 1:58 pm

“But, as in Stern, allowing a constant small possibility either that the human race will become extinct or that conditions will change so radically as to make our current choices irrelevant (eg The Singularity) seems to fix the impossibility problem.”

It depends on what you would call “fix”. Any positive discount rate implies that there are future generations whose weight is smaller than any fraction of the weight given to current consumption. It is what Chichilnisky has called a “dictatorship of the present”.

And there are ways to evaluate utility streams that suffer less from that problem.

10

abb1 01.08.07 at 2:29 pm

What John E said. Relationship between this generation and the whole species. A matter of natural selection; evolution (or devolution, if you wish). You can find a longer argument here.

11

John Emerson 01.08.07 at 3:00 pm

“…whereas sacrifices for environmental protection aren’t”

“many millenia”.

12

Charlie Whitaker 01.08.07 at 3:03 pm

John, how do you feel about arguments such as Parfit’s:

… children conceived more than a month earlier or later would in fact be different children. Since the choice between … two policies would affect the timing of later conceptions, some of the people who are later born would owe their existence to our choice of one of the two policies. If we had chosen the other policy, these particular people would never have existed …

The gist of his argument seems to be that the population that eventually results from a policy is wholly different from the population that results from another policy. It’s therefore problematic to claim that future generations been harmed by a policy. In fact, that policy may have given them life.

13

Ken Houghton 01.08.07 at 4:04 pm

John Q – Now I’m confused. You now seem to be making the same argument with regard to future generations as John E.

What brought you around?

14

John Quiggin 01.08.07 at 8:42 pm

Charlie, this point doesn’t seem to be relevant to my concerns. Our obligation to other people is contingent on their actually existing – note that the overlapping generations point makes the idea of separate current and future populations untenbale.

Ken, I don’t think I ever had any substantive disagreement with John E. It’s just that he keeps claiming (as in #8 above) that economists can’t get questions like this right.

15

John Emerson 01.08.07 at 9:35 pm

John, if you agree to actually agree with me about everything all the time, I’ll let you continue to be an economist if that’s your kink.

16

Tom T. 01.08.07 at 10:55 pm

Well, we know that there will be an extinction-level event out there. According to well-settled science, the Sun will eventually expand to a size that will engulf the Earth’s orbit. It’s billions of years away, but modern science is as sure as it ever gets that it will happen. Isn’t your analysis saying that we owe it to future generations to spend some amount of money studying how to build space arks and Dyson spheres?

I’m not trying to be snarky; I’m just trying to use an extreme example as an illustration. Overlapping or not, there’s some point far enough in the future that even you don’t care about it yet, isn’t there?

17

Apollo 01.08.07 at 11:06 pm

“there’s some point far enough in the future that even you don’t care about it yet, isn’t there?”

Yes, but the year 2100, when people who we know and care about today may still be alive, is close enough to worry about.

18

John Emerson 01.08.07 at 11:46 pm

16: Given that we have billions of years to work with, I’d say we’re making pretty reasonable progress on the space ark. From an environemental POV the next million years is the approximate time frame.

Oddly, some of the transhumanist types I run into combine several seemingly-contradictory attitudes: 1.) there’s no real environmental problem, technological progress will take care of it; 2.) the world is hopelessly fucked up by politics, and there’s really no home; 3.) bulding homes in space to escape to really shouldn’t be that hard.

What I find odd is tech optimism combined with utter political fatalism, which is usually also combined with global warming denial and an intense hatred of environmentalists. This mix comes from smart, hyper-rational people, but it sometimes seems like a Rorschach test of personal obsessions.

19

radek 01.09.07 at 2:50 am

I played around some more. A lot seems to hinge on constant population – or as John Q says the continuous replacement of old people by young people exactly offsets this. What I wrote above was based on a setup where this isn’t the case and that’s why I get individual time preferance*some kind of ratio = social time preferance. With constant population it’s pretty much discount rate of zero. More specifically, it’s social discount rate of zero as long as you weight all generations or time periods equally. If you start off with a positive (social) rate of time preferance then the fact that individuals discount their own utility matters, but only for the welfare of the first generations, after that it’s still c(t+1)=B*c(t) where B is the weight which means that individual discounting has no impact on social discounting.

End of story on this one for me is that if you think the ethically proper discount rate is zero the fact that individuals have positive time preferance over their lives doesn’t play. Even if you think that we, as the present generation, have the right to discount future generation’s welfare, it (mostly) still doesn’t change anything. At most you’re still gonna get the same rate of time preferance you started out with. So while I may disagree about what the proper social discount rate is, this particular line of argument is a dead end. I spend a day thinking about it just to come to the conclusion that it doesn’t matter. Sometimes we come to know more when we learn of what we don’t know.

Of course social welfare comparisons when you have a (potentially) infinite number of agents are a mess and so something’s gotta give. You always run into the Diamond paradox Michael referred to above. But those setups are general enough so that you’re always between the Scylla and Harybdis. The Scylla eats you by not letting you say anything definite without making lots of crazy assumptions. The Harybdis eases you in with seeming plausibility and then makes you choke up crazy conclusions.

The only value in the analysis is to realize that “Hey! If I swim faster I will move closer to the other side where…the other monster is waiting…wait…swimming faster or slower has no impact on the final outcome. How did I get here in the first place again?”

And I have to say that re-reading some papers from the 1950’s and 1960’s Econometrica (which I did on this joyous occasion) is a very humbling experience. Even folks I have no agreement with like Lange, Tinbergen and Ronescu … let’s just say I’d hate to disagree with them and have them find out about it. Perhaps the present generation needs to suck more surplus out of the previous ones before we start worrying about how to screw over the next 7.

On the other hand Odysseus did make a choice and, though costly, he made it through. Take your chances with Scylla friends.

20

aaron_m 01.09.07 at 3:55 am

I call BS

“Our obligation to other people is contingent on their actually existing – note that the overlapping generations point makes the idea of separate current and future populations untenbale.”

If we are only concerned with the future consumption (as economist suggest) of people that are alive today then we have a clear moral duty NOT TO DO ANYTHING ABOUT CLIMATE CHANGE. The time lag between current efforts and future benefits (measured in benefits to consumption compared with the do nothing scenario) is too far off. Those making policy today best secure the future consumption of people alive today by not taking costly measures to address climate change.

Yet we can see the obvious implications of this choice structure. This means that we are valuing the future consumption of people alive today as opposed to the future consumption of people that are not alive now but will be alive in the future. Already here we are making a moral choice, and this choice is not dissolved by the fact of overlapping generations. We can see this easily when we consider the fact that each generation will, if they are only concerned with the future consumption of people alive at that time, make the same choice not to do anything about climate change. They may wish that past decision makers had chosen to address climate change but the best strategy for securing the future consumption of people alive at any given time will be to continue to do nothing. This is because any efforts they make will at best only give marginal improvements on climate (i.e. marginal improvements on the effects of climate change on consumption), and as a result avoiding the costs of mitigation will give much more in terms of consumption to the young of any given generation.

Again we are well aware on this feature of the climate change problem, and when we implement a policy based on the principle that “obligation to other people is contingent on their actually existing” we make a clear moral choice that the predictable pollution of the atmosphere and the effects on people over the long term is not morally important. So the fact of overlapping generations in no way allows us to avoid questions about what we owe to people in the middle to distant future.

(For an example of a study on the impacts on consumption levels from mitigating climate that simply compares consumption levels at various points in time between the mitigation and do nothing scenarios (i.e. a study that avoids controversial claims about how to weigh welfare between generations and the appropriate discount rate) see, Y. Okan Kavuncu and Shawn D. Knabb, “Stabilizing Greenhouse Gas Emissions: Assessing the Intergenerational Costs and Benefits of the Kyoto Protocol,” Energy Economics 27, no. 3 (2005).)

21

anon 01.09.07 at 8:07 am

Surely if we value all future generations equally we should spend not a single penny on social policy today that might be redirected towards economic growth, as the effect of that money in the future will be so much greater, yet of equal value to spending it on the citizens of today?

22

abb1 01.09.07 at 8:16 am

If this is indeed a matter of natural selection and species survival, then it’s hardly a matter of economics. It’s in the field of biology and evolutionary psychology. As long as individuals are predisposed to consume as much as possible and procreate as much as possible, nothing is going to help.

Considering diminishing birth rates in the developed world, it seems that there is some kind of a mechanism on the procreation side, but the drive to consume in the dominant strain seems virtually unrestricted, which is indeed the cause of its dominance.

Environment-minded balanced civilizations (like North-American indians) get wiped out and disappear, the splendid blonde beast prospers.

23

Matt McIrvin 01.09.07 at 9:09 am

What I find odd is tech optimism combined with utter political fatalism, which is usually also combined with global warming denial and an intense hatred of environmentalists. This mix comes from smart, hyper-rational people, but it sometimes seems like a Rorschach test of personal obsessions.

I’m not sure it’s so much personal obsessions as subcultural ones; this sounds like a collection of biases specifically associated with a certain type of science-fiction fandom. Forty or fifty years ago, it’d have been General Semantics, the Dean Drive and the Hieronymus Machine.

Speaking of science fiction, though, I’d be more willing to go along with John’s proposal if I didn’t worry that it might obligate me to completely disregard the welfare of people today, or for that matter the whole human species in 2100, in favor of the putative welfare of ten quadrillion people living in the year 29,465,783, because there are potentially so many more of them. Maybe the fact that I don’t have the foggiest idea how to help them helps ethics from devolving into complete madness. But I can’t help thinking that I’d be pretty miserable going around with the knowledge that the only reason I ought to give a damn about my daughter is that I don’t know enough to fulfill my far truer moral obligation to generations millions of years in the future who may or may not exist regardless.

Maybe this is just another manifestation of fundamental biological limits on utilitiarianism. But it does seem to me sometimes that we need some consequentialist analog of the regularization/renormalization that keeps divergent integrals from blowing up results in particle physics.

24

Charlie Whitaker 01.09.07 at 12:42 pm

I don’t myself like Parfit’s thinking much but can’t easily say why. However, am I right to think that when you say:

… 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.

this could be rephrased as:

… since generations overlap, if, at all times, we treat all people now alive as equal this will have the attendant effect of treating unborn future generations as equal

25

John Quiggin 01.09.07 at 5:29 pm

“Maybe this is just another manifestation of fundamental biological limits on utilitiarianism.”

I’ve always thought utilitarianism (and any policy based on treating everyone equally) makes sense as a basis for public policy, and not as a plausible theory of individual ethics. If I read the early utilitarians correctly, they took the same view.

Charlie, you’re spot-on.

26

Michael Greinecker 01.10.07 at 7:42 am

I think what Tom T wrote is kinda relevant. If we know that humanity will be extinct with certainty by a certain time, a 0 discount rate becomes actually feasible.

On the Parfit point: I think he is correct, but than we simply are forced to make comparisons between potentially existing persons. We get into the question of what people we want to exist. Peter Hammond argues that interpersonal comparisons of well-being are basically preferences for diferent kinds of people, so this may not be that troubling in a utilitarian framework.

27

Tom T. 01.10.07 at 8:54 pm

Michael G, couldn’t the opposite also be true? If I believe that the extinction event is coming next week (posit an asteroid headed this way), then I’m going to adopt a very high discount rate. :-)

28

Michael Greinecker 01.11.07 at 10:14 am

Of course. But there is a impossiblity theorem that basically say that one cannot order infinite utility streams in a way that treats all generations equaly. Extinction should IMO be a change in utility and be in the order. But if we know that only, say, n generatins will exist at most, the problem disappears.

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