“Future generations” are already here

by John Quiggin on April 22, 2012

The Journal of Public Economic Theory has a special issue on Managing Climate Change, to which they are providing free access (hopefully, this link will work). I’m mentioning it partly because I have an article which I think is really important, even though the point it makes is a simple one, and partly because any initiative to make important information more freely available (even a limite special case like this one) deserves some applause.

My paper is a bit wonkish, but the basic point is simple, and, I think provides a knockdown argument against any form of utilitarianism that discounts future utility (including those misleadingly referred to as future generations.

The paper gives a mathematical demonstration, but the key idea, stated in the introduction is a simple one

Much of the debate on the question of whether a pure rate of time preference can be justified is concerned with determining the appropriate way to balance the interests of “current” and “future” generations. The central question, in this framing of the problem, is whether, and to what extent, members of the current generation have the right to allocate resources in their own favour, at the expense of unborn future generations.

The central point of this note is to observe that this way of posing the problem is invalid, because members of different generations are alive at the same time. Any policy that discounts future utility must discriminate not merely against generations yet unborn but against the current younger generation. Assuming that members of any given generation are concerned about their own lifetime utility, rather than myopically concerned with current utility alone, a social allocation rule that incorporates pure time preference gives higher weight to the lifetime utility of earlier born generations than to their later born contemporaries. Assuming a 3% pure rate of time preference, as above, and 25 years between generations, the lifetime welfare of those aged 50 or more is valued twice as highly as the welfare of their children, and four times as highly as the welfare of their grandchildren, all of whom may be alive at the same time. This is obviously inconsistent with any form of utilitarianism in which all those currently alive are valued equally.

Furthermore, by the nature of overlapping generations, there is no point at which a coherent distinction between current and future generations can be drawn. In the absence of some general catastrophe, many children alive today will still be alive in 2100, at which time people already alive will reasonably be able to anticipate the possibility of survival well into the 22nd century.

{ 131 comments }

1

Matt McIrvin 04.22.12 at 11:55 am

I’ve said elsewhere that I feel justified in more or less personally worrying about stuff happening out to 2100 on the grounds that my grandmother is still alive and well, and my daughter will be the same age she is now in 2099.

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Tim Worstall 04.22.12 at 12:18 pm

OK….beyond me in many ways but that will surprise no one.

Is it now possible to put it into a number I do understand? Say, the social cost of the emission of one tonne of CO2-e?

Stern’s end result was $80. How does your paper change that end result? What does the $ number become?

3

Watson Ladd 04.22.12 at 2:09 pm

There’s a mistake in the proof in the if case. We have to show that given the comparison function that it satisfies the three conditions. But the result is true and very interesting: count me as among those who would have expected the opposite result.

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conchis 04.22.12 at 2:10 pm

Tim
It doesn’t change Stern’s result. It’s a justification of Stern’s approach to discounting against those who argue he should have discounted more.

P.S. “…beyond me in many ways but that will surprise no one”. Colour me surprised. I really didn’t think the point was that complicated. Which bit of it is puzzling to you?

5

Enda H 04.22.12 at 2:25 pm

Hi John,

In the neoclassical model we have rho (time preference), n (population growth, assumed>0) and g (income growth, assumed>0). Am I right in thinking that there is no steady-state if rho > n+g, and that the trajectory diverges towards infinity for future generations?

6

Nick Barnes 04.22.12 at 4:07 pm

“2100, at which time people already alive will reasonably be able to anticipate the possibility of survival well into the 22nd century.”

Well, I should hope so, yes. Possibly you meant 23rd?

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Tim Worstall 04.22.12 at 4:48 pm

“P.S. “…beyond me in many ways but that will surprise no one”. Colour me surprised. I really didn’t think the point was that complicated. Which bit of it is puzzling to you?”

I simply go blurry when algebra is used. I find I understand things much more when they’re expressed in English than I do when anything beyond arithmetic in maths is. I know what integration is, summing a series, all sorts of concepts I get. But the method of notation just, as I say, goes all blurry.

I have actually studied these things, did (old style) A level maths which certainly included these concepts and notations. But they never sank in, never made sense as a language to me. Personally I think of it as being a little like being tone deaf (which I’m not, but not perfect pitch either). You can certainly teach someone all about music but if they’re tone deaf it’s just not really going to make any real sense to them. You can get them to grind through the exercises (playing scales or manipulating equations) and end up with, if you try hard enough, a reasonable simulacrum of somebody who understands the subject.

But they don’t not really. Performing dog stuff, not real understanding.

The statement “Stern’s discount rate is proper because utilitarianism demands that we treat all those alive at the same time as having equal value. There is no such thing as “a generation” because the number of those alive at any one time is a constant flow at either end, those appearing and those disappearing. Thus we must consider future humanity as not being succeeding generations but as a constant flow of current and future humanity. Thus we cannot discount using market interest rates as if there are those generations for this violates the utilitarianism and equal treatment principle.” QED, Stern is right with the 0.1 % thing about extinction (although he actually uses asteroid strike in my memory, not nuclear war but that’s probably my memory).

I think I’ve got John’s argument right there and apologies if I haven’t. But for me it’s entirely the way the argument is presented that allows me to understand it or not.

And I most certainly did not understand whether John’s result led to Stern being correct or in need of revision.

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JW Mason 04.22.12 at 5:48 pm

This is exactly right.

But here’s the problem. Market interest rates do behave very strongly as if they reflected an element of pure time preference. So if you believe what you wrote here, you need to abandon the idea that interest rates are a valid market signal for any kind of intertemporal allocation. Which will require throwing out quite a bit of existing economic theory, including pretty much everything we teach about growth.

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JW Mason 04.22.12 at 5:56 pm

(ok, “pretty much everything” is an overstatement. Consider it corrected to “a lot of what”.)

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Capt Mal 04.22.12 at 6:29 pm

Why do we discount the future? At least in good part this must be because life is uncertain. I could get hit by a bus tomorrow so why scrimp and save for a future that may never come. But whole societies face much less of this type of uncertainty about the future–the possibility of nuclear war or the earth being hit by a large asteroid, yes, but these risks are very low. The social rate of time discount should be far less than the individual rate of time discount.

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Tom Bach 04.22.12 at 6:32 pm

There is an interesting discussion of the American Founding Fathers, generations, and politics here
http://us-intellectual-history.blogspot.com/2012/04/jefferson-paine-and-question-of.html

12

Bruce Wilder 04.22.12 at 6:40 pm

Market interest rates can only apply to investments, from which a return can reasonably expect to be “captured” in the future. Even if a sunk-cost investment has an a priori expected benefit, which would satisfy a time-preference criteria — more good stuff in the future sufficient to justify foregoing some good stuff in the present — it doesn’t follow that, ex post, a claim on incomes associated with that sunk-cost investment can be made to pay off a market interest rate. It may be that market prices, after the sunk-cost investment has been made, simply do not afford a sufficient surplus to pay a market rate of interest. It could be a problem of insufficient market power and, of course, an acknowledgement that it is never rational to factor in sunk costs — which the investment has become, once made — into competitive pricing decisions.

Historically, we’ve tended to gloss over this paradox at the center of investment and returns, presuming without proving that finance can manage to approximately coordinate and manage progress. Finance got a lot of help from expansive “growth” — settling new continents, rapid population growth, etc., which had the effect of pushing up economic rents in an often acceptably benign fashion. Governments, which taxed real property and high incomes, could borrow to make infrastructure and public goods investments, and their borrowings were “risk-free”; private investments could be hedged and arbitraged in relation to that base of public debt, while taking advantage of the expanding infrastructure to achieve returns.

On the way up the mountain, to speak metaphorically, in the expanding industrial revolution, we understood, intuitively, that polluting the environment was a cost of making investments in expanding industrial capacity. Poor people making an investment in an industrial economy — never mind that the decision-makers were unimaginably rich people — would accept pollution, and high-accident rates, and low-pay and all the rest, but as incomes rose with increasing productivity, than demand would surface for cleaner air and water and safe workplaces — an increase in “luxury” purchases, as incomes rose on the back of the industrial machine. And, just so, London, eventually, lost its smog, and Cleveland reclaimed its flaming river. Isn’t that a story we used to tell?

Now, we are approaching the down-slope of the industrial revolution’s mountain. It ought to be an open question, whether there’s an important sense that incomes in the future will “naturally” trend higher. There’s good reason to think that some underlying components of economic prosperity and productivity will be eroding and diminishing, as we go forward. The ocean ecology may collapse. The congestion effects of increasing population and production are significant, pushing down the marginal productivity of “Land”.

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John Quiggin 04.22.12 at 6:57 pm

@JWM Actually, market rates are pretty much consistent with the position I’m arguing. The real rate of interest on government bonds has averaged 1-2 per cent (currently < 1 per cent) for the last 100 years. As Stern's numbers illustrate that can be explained entirely by the assumption that income grows at 2 per cent and that utility is logarithmic.

The real problem with market rates is the magnitude of the equity premium (6 percentage points when theory suggests < 0.5). To use your words, that's inconsistent with any idea that market rates of return to capital (both bonds and equity) are a valid guide to intertemporal allocation. At least one of the rates must be wrong, or else markets must work very differently from any known model.

I’ve argued at great length that it’s the equity rate that is wrong, and that the bond rate is the right one to use. Much of the confusion in the debate over discounting arises from the fact that many people aren’t even aware there is a contradiction here

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Ben 04.22.12 at 7:44 pm

“””
the basic point is simple, and, I think provides a knockdown argument against any form of utilitarianism that discounts future utility
“””

Is there any such form of utilitarianism? The usual argument is that resources expended for the benefit of future generations provides less utility because they will be better off due to economic growth (AKA technological improvement) and therefore derive less marginal benefit from the same resources than current generations. Often this is conflated with the choice of discount rate, which itself conflates a number of issues including opportunity cost. However I am not aware of anyone who has ever argued that the **utility** of future generations should be discounted, so if your point is to argue against that I think you are being somewhat pre-emptive.

“””
The central point of this note is to observe that this way of posing the problem is invalid, because members of different generations are alive at the same time. Any policy that discounts future utility must discriminate not merely against generations yet unborn but against the current younger generation
“””

That seems to be simply asserted. It certainly doesn’t follow from anything. Just on spec, I can thing of at least one reason why you might want to discount future utility which doesn’t imply that we should discriminate against today’s youth.

None of this is to defend any form of utilitarianism – The flaws of utilitarianism are bigger and more fundamental than anything you attack here. Only the mirageous attractions of utilitarianism can compete with its flaws.

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JW Mason 04.22.12 at 7:51 pm

John Q.,

OK, you’re right, I think that’s a better way of putting it than what I wrote.

The other issue though is the relationship of utility to income. You don’t get Stern’s low discount rate unless you assume the marginal utility of income does not decline too fast, which means that in Stern’s framework you can’t care both about distribution today, and about climate change in the future. Or at least, that’s what Partha Dasgupta argues, and it looks right to me. Have you responded to this argument somewhere?

Seems to me the only way we can sensibly analyze the costs of climate change is to give up the idea of a single homogeneous “output” and start from the premise of limited substitutibility between market and environmental goods, as argued here and here.

16

Ed 04.22.12 at 7:54 pm

“Now, we are approaching the down-slope of the industrial revolution’s mountain. It ought to be an open question, whether there’s an important sense that incomes in the future will “naturally” trend higher. There’s good reason to think that some underlying components of economic prosperity and productivity will be eroding and diminishing, as we go forward. The ocean ecology may collapse. The congestion effects of increasing population and production are significant, pushing down the marginal productivity of “Land”.”

Again, peak oil becomes a factor, and later on peak fossil fuels in general. This is why we are very much on “the down-slope of the industrial revolution’s mountain”. This means increasingly the trade-off will not be degrading the natural environment through extraction, to produce economic growth. It will be degrading the natural environment through extraction to keep the economy at the current level, for the current generation. This will become all the more true when to get at the remaining oil deposits techniques such as fracking and deep see drilling will have to be used.

Where future generations enter the picture is that they don’t benefit from these extraction techniques, because they are not producing economic growth. They are used simply to ensure that it will be future generations that fall off the resource cliff, not current generations. But the good news for the environment is that the fact that there are limits to how much fossil fuels can be extracted means that there is also a hard limit to the amount of environmental damage that can be done. The Earth will turn out to have an amazing capacity to heal itself, once industrialization has run its course.

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JW Mason 04.22.12 at 7:58 pm

I am not aware of anyone who has ever argued that the utility of future generations should be discounted

Actually, using a discount rate that incorporates a pure rate of time preference is completely standard. For instance, William Nordhaus in his very widely cited work on this stuff, uses a pure time discount (i.e. a discount on the utility of future generations) of 1.5 percent. So John Q. is definitely not arguing with a strawman here; within the eoconomics profession, the position he’s criticizing (correctly IMO) is the majority one.

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JW Mason 04.22.12 at 8:03 pm

the fact that there are limits to how much fossil fuels can be extracted means that there is also a hard limit to the amount of environmental damage that can be done.

I dunno. James Hansen has said that if we burn all available fossil fuels, we will certainly trigger a runaway greenhouse effect that boils the oceans.

Would Earth proceed to the Venus syndrome, a runaway greenhouse effect that would destroy all life on the planet, perhaps permanently? While that is difficult to say based on present information, I’ve come to conclude that if we burn all reserves of oil, gas, and coal, there is a substantial chance we will initiate the runaway greenhouse. If we also burn the tar sands and tar shale, I believe the Venus syndrome is a dead certainty.

Why are you confident that he’s wrong?

19

Watson Ladd 04.22.12 at 8:11 pm

@Ben: Quiggin isn’t against discounting, he just thinks the discount rate should be given by the rate of economic growth, as you pointed out. Or to put it another way, the discount you are talking about translates dollar costs into utility, whereas the paper argues that all utility should be considered equally.

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christian_h 04.22.12 at 8:20 pm

Also a “hard limit” is pretty useless – we don’t have to agree with Hansen to acknowledge that for the purposes of human survival it matters very much what that limit is!

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John Quiggin 04.22.12 at 9:11 pm

@Ben What Watson said

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John Quiggin 04.22.12 at 9:17 pm

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James B. Shearer 04.22.12 at 9:18 pm

… Assuming a 3% pure rate of time preference, as above, and 25 years between generations, the lifetime welfare of those aged 50 or more is valued twice as highly as the welfare of their children, and four times as highly as the welfare of their grandchildren, all of whom may be alive at the same time. …

I don’t understand this. Suppose people live 75 years. Then someone aged 50 has 25 years of remaining life while someone aged 25 has 50 years of remaining life. Because of discounting the value of these 50 years won’t be twice the value of 25 years but it will still be more (about 1.5 times the value). It won’t be half the value.

… This is obviously inconsistent with any form of utilitarianism in which all those currently alive are valued equally.

I don’t understand this either. Why would you value the life of someone about to die the same as someone who was just born?

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Watson Ladd 04.22.12 at 10:02 pm

@James B. Shearer: When JQ discusses lifetime values he doesn’t mean the remaining enjoyment in life, but all of it. Imagine we pull back enjoyment across our lifetimes to the moment we are born. Then the 50 year old, who was born 25 years earlier, counts much more then the 25 year old who was born later. It’s got nothing to do with lifespan remaining, and everything to do with when you were born.

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JW Mason 04.22.12 at 10:40 pm

JQ-

Thanks! Can you spell out this thought? “Stern uses a low discount rate but wants to use a high risk premium when considering uncertainty and income distribution. In my view, this is reasonable.”

It seems to me that eta is eta: If we are going to talk about utility as a function of income, it should be a consistent function whether we are comparing populations at different times, different individuals in the same population, or different states of the world for a given individual. No?

I prefer to say you need a second argument (at least) in the utility function, so that we can’t assess the costs of climate change simply in terms of lost GDP. Actually, I think you need to do this regardless of discount rates. Even at the high end of Stern’s cost estimates, we would still conclude that the representative person living in 2100 in a world with catastrophic climate change would be just as happy as a person living in 2075 in a world where the costs of climate change had been fully prevented. I think any analysis that leads there is missing the real urgency of global warming, even if it does conclude that mitigation efforts are worthwhile in the present. Better to think of market goods and environmental goods (and various other nonmarket goods) as close to perfect complements, it seems to me. But you must have had this argument before.

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John Quiggin 04.22.12 at 11:22 pm

A quick point is that even Stern’s high-end estimate is still a probability-weighted mean with a low probability of catastrophe. I think he gets a bit tangled in this, and doesn’t really deal well with the tail. The Weitzman and Nordhaus pieces in the JPET issue are relevant here, but I haven’t read them closely yet.

More on eta when I get a free moment to think carefully about it.

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Watson Ladd 04.22.12 at 11:26 pm

JW Mason: there are two different things going on. Time preference is expressed as follows: “one today, or two tomorrow”. Risk aversion is “one today, or a 50% chance of two and 50% of nothing”. They are usually connected: future possibilities tend to be more tenuous, but we can separate them out under some (seemingly mild, but actually strong) requirements of dynamic consistency. (Prefer today what you wanted yesterday)

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Tim Wilkinson 04.23.12 at 12:39 am

Am I right in thinking that the initially rather odd-looking “those alive at the same time” in utilitarianism demands that we treat all those alive at the same time as having equal value is ultimately explained by the need to bracket off any issues concerning average versus total utility and the effect of more or fewer people coming into existence? If not, I don’t see why it’s there.

In general use, I’d take talk of current vs future generations to be just an allusion to people who will be around at times far enough in the future that they can’t have been born yet (and those currently alive won’t still be alive). Even in the literature JQ is referring to – which I’m not familiar with (let me stop you there! – no I’ve started now), I wonder if very much actually rests on this, since this is only one further discretisation further than the treatment JQ offers, in the first instance, anyway.

This may be obvious, but I should have thought that pure time preference (discounting of future utility other than via probabilities?) is irrational for enduring beings, and discriminating in favour of more proximate timeslices of one’s enduring self represents a kind of weakness of will. The extreme case would be someone who lives entirely in the present, at the mercy of their current whims or appetites – such a maximally disintegrated person would I suppose be incapable of forming plans, let alone carrying them out, and would certainly be very odd.

On this view, it’s potentially a touch misleading to speak of ‘preference for consumption when young’, since the older time slices will not share that preference, only the younger ones. A preference for consumption when young would be expressed as a greater utility attaching to consumption-when-young, in such a way that the old codger slices would (presumably) be glad that they’d seized the opportunity – anyway they would not (justifiably – this gets a bit tangled) resent their selfish younger selves.

A pure time preference, as distinct from a genuine age component in the utility of consumption, is for consumption now, or failing that very soon, or failing that soon, etc. It’s indexed to a situated, subjective ‘now’, so it makes a great deal of sense that such ‘revealed preferences’ should not be carried over into attempts at objective and stable evaluation of social welfare (or indeed any other halfway sensible kind of aggregation of utilities).

However, proposition 2 looks like an interpretation of ‘pure’ time preference as an age component in the utility of consumption, and this still shouldn’t be carried over to social welfare since society doesnt have an equivalent of human age (or aging) that might be thought to justify it. (Though I also see that what I think is the same thing is referred to as ‘impatience’ which does sound like my idea of pure time pref.)

—-

re: the equity premium puzzle: the explanation should reflect some combination of individual preferences and market failure if the individual prefs. are something like impatience, this might be an emergent phenomenon rather than ‘inherent’ impatience – I can vaguely envisage a number of ways in which short-termism could come to infect investors’ behaviour by pathological processes of bounded competition based on simplistic indicators, or a kind of uber-bubble in stock yields in general. And one relevant form of ‘market failure’, the homogeneity and small number (oligopoly power -> surplus) of those rich enough to be investors would tend to exacerbate this. Actually this is inadequately thought out and not very useful.

I see too that the real bond rate should be somewhat higher than it it has been on average. Is this the US govt bond rate? And could a relevant ‘market failure’ be anything to do with the kind of exogenous variables that wear camouflage and carry guns, as recently discussed? Or anyway the more proximate phenomenon of dollar hegemony?

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James B. Shearer 04.23.12 at 12:48 am

24

@James B. Shearer: When JQ discusses lifetime values he doesn’t mean the remaining enjoyment in life, but all of it. Imagine we pull back enjoyment across our lifetimes to the moment we are born. Then the 50 year old, who was born 25 years earlier, counts much more then the 25 year old who was born later. It’s got nothing to do with lifespan remaining, and everything to do with when you were born.

But any decision made at some particular point in time will only depend on the remaining values and hence will value young people over old people. Correct?

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JW Mason 04.23.12 at 1:13 am

27-

Yes, I know. The point is that eta is a parameter in a function of the form V=w1*u(c1) + w2*u(c2) + … + wi*u(ci) where V is total utility, c1 … ci are consumption levels, and w1 … wi are weights. The function should be the same whether we consider the index i to be over time (in which case the weights would reflect pure time preference), over individuals, or over states of the world (in which case the weights would reflect probabilities). Logically the three are exactly equivalent. So I’d like to know John Q.’s argument for treating them differently (if that is what he’s saying — I may have misunderstood).

31

Omega Centauri 04.23.12 at 1:18 am

My point was similar to Ben’s. The excuse for discounting future harm (from for instance climate change, or resource depletion), was that the delta in the current economy would lead to a delta in the future economy as well. And the assumption was made that we could estimate these effects by the simple use of a discount rate. I think this is tantamount to the assumption of indefinite exponential growth, which is of course mathematically impossible. Climate change future damages are a difficult one to assess. The tail of the time decay curve of a ton of additional atmospheric CO2, is quite slow to decay, i.e. there will be significant impacts ten thousand years from now.

Tim.
I can sympathize with the math thing. For me the problem comes at the theorem-lemma-corollary level. I can get about one page into a math book before my eyes glaze over. Yet in other ways my math abilities are better than 99.9 percentile. I also cannot follow a legal argument; I suffer from the same glazing over of the eyes syndrome. I suspect most of us have one or more areas that just can’t engage our interest. When they block a seemingly successful career choice, it is a tragedy.

JW. Everything I hear from the good folks at RealClimate says the runaway Greenhouse is not possible with the present level of solar luminosity. I think Hansen is way out on a limb on that one. Now, a runaway to a PETM-like hothouse planet, may be entirely possible. But, that represents a medium-sized extinction event (far less than the magnitude of the human caused one already going on, in fact).

But, the issue of future costs to future civilization is an important one. We will have several hundred to a few thousand years of inconveniently fast sea level rise for one. And anyone planning to build anything near sea level will have to take that into account. So the cost of for instance seaport infrastructure will be necessarily higher than would otherwise be the case. And the S curve of technological advancement will have probably run it’s course long before these burdensome environmental conditions have died away.

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Watson Ladd 04.23.12 at 1:33 am

JBS: not necessarily. Let’s say we have a utility transfer from the old to the young. This doesn’t change the total utility, hence it isn’t preferred so the young aren’t preferred. If you increase the utility the young experience every moment of their life, then you are giving them more then the old, so it isn’t the same situation. Think about utility as bank accounts, and the sort of change you are probably thinking of as a shift in income.

Tim: not really. If foreigners were told “buy Treasuries or else” to drive the rates down, rational domestic investors wouldn’t take them, and would invest in the S&P 500 instead. The equity premium also exists in Europe iirc.

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Tim Wilkinson 04.23.12 at 1:58 am

James B Shearer: If we were talking about a ‘real’ utility advantage to consuming-when-young, or simply taking account of people’s own apparent preference for frontloading their own consumption, that could be factored into social welfare and if that were all there were to it, no problem would thereby arise. The question of what counts as real utility rather than an artefact of irrational behaviour from the standpoint of the enduring person is indeed tricky, but without going the full Samuelson we might decide that even in clear cases of young people choosing to shaft their older selves by being impatient, trying to protect their older self (who is not in a position to privilege themself over younger selves) may involve excessive interference in personal choices.

But if we are talking about true impatience – that is, a discounting of one’s future utility that is overall irrational/suboptimal as a life plan for the enduring person, and if such an approach is applied at the social calculation level, i.e. if policy makers are themselves ‘impatient’, then (at least) 2 problems arise: 1. there is no reason to introduce impatience at the level of social decision; it simply privileges earlier timeslices-of-all-people over later timeslices-of-all-people, for no reason, and in particular none related to liberty, autonomy etc.

2. Intrapersonal impatience-discounting ends at death, but if social welfare is itself calculated impatiently, the discounting extends indefinitely into the future. This doesn’t really show up much in JQ’s initial case of two overlapping generations, but if extended further it will be a really grim lookout for people further in the future who are predictably affected by current decisions.

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Steven E Landsburg 04.23.12 at 2:29 am

What are the implications of your argument for optimal savings rates and for the taxation of capital?

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Frank Ashe 04.23.12 at 2:49 am

IIRC in order to explain some people’s savings habits for retirement we have to assume they use a negative discount rate i.e. they value future utility of level X utils higher than they value X utils today. This may be an actuarial urban myth as I’ve heard this many times in conversation but have never sighted the ground zero (or seen it cited).

But it does tend to show how hard it is to generalise in this area. But JQ’s point is perfectly valid.

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Ed 04.23.12 at 3:06 am

JW Watson at #18: we won’t burn “all the reserves” of fossil fuels, only the ones that are economically profitable to extract and exploit. There are some reserves where it will take more energy and money to extract that could possibly be recouped from use of the fuel. Now TPTB could be insane and try to extract them anyway, but if TPTB are that insane and suicidal, there are tons of nuclear weapons available so I doubt we will get to that point.

I recognize that environmentalists keep trying to tax extracting and exploiting fossil fuels so that the price incorporates the externalities, eg environmental damage, and they keep getting defeated. I’m actually pretty optimistic about this, it should be enough to prevent their extraction and use being subsidized, otherwise the price will rise quite a bit on their own as the reserves are depleted, with the most economical reserves to extract being depleted first.

(I apologize for being off the main thread, but its an important question)

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John Quiggin 04.23.12 at 3:19 am

@JWM OK, now I’ve had time to reread my post, and I can clarify. When I say “Stern wants to use a low discount rate”, I’m referring to the 0.1 per cent he allows as a pure rate of time preference. At least in my interpretation, this covers “all bets are off” events, that render climate mitigation investments irrelevant. These events include the obvious ones, like a nuclear cataclysm, but also the possibility of a technological deus ex machina that solves the problem at essentially zero cost. (An allowance of this kind is consistent with the arguments in my JPET article).

Leaving that aside, my view is the same as yours – eta is eta, over time, under uncertainty and in evaluating income redistribution.

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awy 04.23.12 at 3:55 am

The discount rate itself seems like a philosophically suspect way of forcing a round modal peg into a square spectrum hole.

ok, the geometry might not work out but the picture is there.

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reason 04.23.12 at 8:04 am

Ed
Coal?

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Chris Bertram 04.23.12 at 8:08 am

_Assuming that members of any given generation are concerned about their own lifetime utility, rather than myopically concerned with current utility alone_

I agree with you about pure time preference and the need to take account of the interest of all _persons_ equally, so therefore with the post John. On the other hand, I can imagine someone with a different view of the metaphysics of personhood quibbling with the reasoning, if not with the conclusion. Suppose the location of value were not the person but some temporally-extended person slice. If that were that were so then a pure discount rate could take equal account of the interest of all person-slices at t, equal (though lower) account of all PSlices at t+1, etc. On that model, the co-existence of different generations at one time would not be available to you as an argument.

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windwheel 04.23.12 at 1:48 pm

Loved this paper!
I suppose one could argue that kids born today have parents and grand-parents and uncles and neighbours and so on who love them and whose Utility function adjusts so as to reflect their interest in the kids’ own genetic lineage.
Indeed, if we have perfect information and there is no polymorphism of prefences, we could just derive everything from Ancestral Adam. But, why stop there? According to Dawkin’s extended phenotype principle we should be maximizing the reproductive success of a bunch of genes, which control this aspect of our behaviour, no matter in what species it may be found! So Utilitarianism takes in in just two steps to the sort of tie-dyed trippy hippy Gaiaism some of us can still remember from the Seventies. (If you can remember the Seventies, you didn’t do enough cocaine in the Eighties).

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Tim Wilkinson 04.23.12 at 1:52 pm

a pure rate of time preference…covers “all bets are off” events, that render climate mitigation investments irrelevant

But isn’t that, conceptually at least, another branch of the (sketchy) tree of possibilities, with the utility to be weighted by some estimated probability in standard c-b fashion, rather than a rate of pure time-preference?

Maybe I’ve totally misunderstood, but a pure time-preference, which seems aptly labelled ‘impatience’, would (assuming all the usual apparatus) tend to produce a suboptimal life-plan for the enduring person, and is if anything even more clearly irrational from the impersonal perspective of social welfare.

CB – yes, but such a metaphysic (not that I’m supposing you to endorse one) would have some specific problems besides just intuitively seeming weird – it would reintroduce the issues of creating/destroying enduring persons, and indeed would collapse the two into one, I think. In particular, killing some (enduring) person who’s dragging down average utility would not clearly be any different from refraining from creating some (enduring) person for the same reason (if this were to be a reason). These problems are there in the background anyway, but since attempts to solve them are likely to involve peoples’ obvious interests in their life not being suddenly cut short(!), there would at least be some tension involved in applying a conception of persons which can’t really recognise such a concern as well-founded. But this is to get into much wider issues.

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JW Mason 04.23.12 at 3:59 pm

37-

OK, got it. And I see your point that Dasgupta’s argument that eta=1 implies impossibly high optimal savings rate, depends on an arguably exaggerated estimate of the risk-free return available on new investment. So is his criticism just wrong in general, do you think? Is logarithmic utility compatible with a reasonable level of concern with distribution, for some liberal-left value of “reasonable”?

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michael e sullivan 04.23.12 at 4:38 pm

Frank@35: that may be true of a few people, but i don’t think it’s accurate for people in general. Very few people save enough to expect full consumption replacement at a normal retirement age while investing in nearly riskless assets (even if you count social security expectations as riskless), and that’s essentially what a zero pure time preference rate would look like in savings behavior with eta ~ 1.

Now, because most people invest in assets that aren’t riskless, a fair proportion of people (well, middle class people) do, in fact, end up with more wealth than is necessary for full consumption replacement when they retire — but they are balanced by a similar proportion of people who saved similar amounts and had lower returns who did not.

A negative time preference would involve saving more than enough for full consumption replacement using riskless assets.

For someone who gets above zero at 30 (student debt paid off, steady income stream available) , expects to need to retire at 70 and live to 90, the savings amount consistent with a zero discount rate is around 25% of income. How many people actually save this much? Hardly any, and most of them are fairly well off even by rich world standards. The average is somewhere around 5% after stripping out the poor, which implies a discount rate of about 5.5%/year. Even standard best practices for financial planning for the middle class suggest something more like 15%, which would imply about a 2% discount rate.

I would suggest that most of the people saving more are not considering late future consumption as strongly as near future control of what they do with their time. Their marginal utility of consumption in the present is already quite low.

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mpowell 04.23.12 at 7:09 pm

@44: What is your justification for requiring that people with zero time preference to invest in riskless assets? That makes no sense at all to me. It is enough to for them to invest in assets that will give them an average result that allows them to replace their current consumption. Then you can add some risk aversion on top of that, but that is a fundamentally different dimension and has to do mostly with how a person’s utility varies with their consumption. Another problem with your 25% number is that young people can quite reasonably expect real income growth over time. There is risk there, as well, but really if you want to take that into account you would have to allow for downside risk as well. At least within wealthier economies, I think there is a larger set of people than you acknowledge with reasonable retirement plans.

There is another problem with your argument even aside from this, which is that if you look at older defined benefit pension plans plus employee contracts, they are frequently structured such to provide more or less constantly increasing consumption up until retirement and then constant consumption thereafter. Which implies that when people are able to make an actual choice about the issue without requiring significant exercise of willpower or good judgement over time, they prefer increasing consumption over time.

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John Quiggin 04.23.12 at 8:13 pm

@44 and 45 I think most retirement investment plans (individual and institutional) over the past 30 years or so have been based on over-optimistic assumptions about the risk-return trade-off. As Michael E Sullivan says, savings haven’t been enough to provide the desired income without taking on a lot more risk than people imagine they are facing.

@JWM As I mentioned, log utility would support quite radical income redistribution policies, far more so than are currently followed. Dasgupta didn’t (AFAIK) develop his argument in response to criticisms from me, DeLong and others, so I don’t know where he ended up

@Chris I agree that if people regard their future selves as being different people, then my argument fails. I spell this out in the passage quoted in the OP “Assuming that members of any given generation are concerned about their own lifetime utility, rather than myopically concerned with current utility alone,”. On the other hand, I show that it doesn’t matter that people are impatient, preferring consumption earlier rather than later. And what matters is what people actually think about their personhood, not what a metaphysician might say they should think.

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michael e sullivan 04.23.12 at 8:24 pm

I don’t require that anyone invest in riskless assets, but I think to judge a person’s time preference from their level of savings, it is the right level of return to look at.

Why? Because a risky asset, by definition, is one that is less likely to *actually* experience it’s expected return than a riskless asset. So by investing in risky assets, we can on average invest less than we otherwise might, but our 1-2 std dev floor might actually be *less* than the expected return on riskless assets. Most humans’ marginal utility of money declines with wealth/income. Humans are generally wired to experience losses as more than cancelling some equivalently large gain.

I don’t know, when I try to put the argument together logically, I’m not sure it adds up to an airtight case that using riskless return is correct, but it *feels* right for those reasons.

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mpowell 04.23.12 at 8:26 pm

@46: I don’t see how an argument that people have been misled about the risk/reward trade-off actually disproves a claim that people actually prefer their consumption to increase over time (or at least not decrease). And even if typical assumptions have been wrong, I don’t think that is a reason to believe the equity premium won’t exist going forward. It does not make sense to me to conclude that the rational way to do retirement planning is with risk free investments returns.

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mpowell 04.23.12 at 8:33 pm

@47: The typical model for a risky asset is one with a distribution in expected return, but with a higher average return than a riskless asset. An investor’s willingness to use risky assets will be related to their willigness to absorb risk in their retirement consumption levels. If I can engage in 50K/annum consumption today with the consequence that I get 40K/annum consumption in retirement with 50% probability and 60K/annum consumption with 50% probability, to first order that reflects zero time preference. If the utility of 0.5*40K/annum + 0.5*60K/annum is less than 50K/annum due to nonlinearity in my utility function (very likely), I may need to shift the balance to 48K/annum today to get 52K/annum in retirement on average to balance this. But I don’t need to completely eliminate risk in future consumption in order to reflect zero time preference.

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ragweed 04.23.12 at 8:43 pm

JWM @ 18 and OC at 31

The problem with Hansen’s runaway greenhouse is that, as far as I know, he has never really presented what it is based on, other than Hansen’s Considered Opinion. I wouldn’t completely discount it as an outside possibility, but before giving it too much credance, I would like to see a few numbers behind it. Hansen says he bases it on the fact that solar luminosity is 3% higher than during the PETM, and that he thinks the PETM was a lot closer to a runaway greenhouse than the prevailing wisdom thinks, but, again, I don’t know how solidly grounded in evidence that is. I would not discount it, but I also would put it in the more speculative end of potential climate change outcomes.

As for the good folks at Real Climate, I am not sure which are being specifically referred to, but I assume it is several posts by Ray Pierrehumbert and Chris Colose. I think the expertise involved there is pretty top-notch, but there are also different definitions of a runaway greenhouse. I think Ray and Chris are clear that they are talking about the kind of runaway greenhouse conditions that you find on Venus where oceans have boiled away completely, releasing all the geologically sequestered carbon in surface rocks and dissociating atmospheric H2O etc. Hansen seems to be referring to a different run-away greenhouse where feedbacks increase to the point that water-vapor becomes a forcing rather than a feedback, and clouds switch from being a negative feedback to a positive one. This could tip the earths climate into a state where surface temperatures are mostly outside of the range that could support life, but not necessarily have all the oceans boil away. Pierrehumbert argues that the latter scenario is also pretty unlikely, but acknowledges that there is a possibility of a runaway scenario where clouds stop being a negative feedback.

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John Quiggin 04.23.12 at 9:04 pm

I’m not asserting that everyone should invest solely in riskless assets. But if you are trying to analyze the adequacy of your strategy, a good starting point is to see how you would go if you did invest in riskless assets, and to remember that there are no free gains to be had. By definition, every increase in risk you take on increases the probability that you will end up with less than under the riskless investment plan. So, if that starting point was inadequate, you can’t secure an adequate income without saving more.

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michael e sullivan 04.23.12 at 10:15 pm

John@51: the problem, which I realized, as I was trying to spell things out in 46 is that according to the empirical data, there really are some free gains to be had, if you are anything but astoundingly risk averse.

There are two sides to the equity premium puzzle. One is why equity returns are so high relative to what you would expect (roughly GDP growth) and the other is why risk free returns are so low (nobody can get anywhere near GDP growth returns without taking on risk).

Of course, these things happen because of market pricing, but the fact is that equity simply can’t return > GDP growth forever as an asset class. Doing better means either that profits are increasing relative to the economy, or that equity ratios are increasing (people’s willingness to pay for a given level of profits/assets is increasing). Neither of those trends can go on forever, so presumably, no matter how cheap equity is right now, there will eventually come a time when equity returns will fall to GDP growth, and it is hard to predict when that time will be.

I believe that given this uncertainty and hard limit on long-long-run equity returns, a prudent investor will make savings plans based on real equity returns around the level of expected GDP growth, minus some modification for equity risk. That plan will have you looking at a number closer to the riskless return than to the standard historical equity return.

And I do agree with you John, that these are very puzzling questions. I do not understand why there is so much money in riskless assets today, nor even before the crisis. There really *shouldn’t* be a free lunch if even a very weak form of EMT holds, and yet it seems that equity investment really is one, unless the market knows something I don’t about the expected future path of GDP growth.

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michael e sullivan 04.23.12 at 10:23 pm

Sorry, John, I just reread my comment after posting, and I am a bit embarrassed my tone, after morphing into a more general discussion. I took a professorial tone, as an autodidact, when I am directly addressing you, an expert, and one of the people from whom I have learned much of what I know about these issues, due to the incredible generosity of your professional blogging and comment thread participation over the years. Please trust that I’m really not that pompous, except for when I apparently am.

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John Quiggin 04.24.12 at 3:54 am

Michael, if mildly pompous comments were the worst I had to deal with, I would be a much happier blogger. Seriously, thanks for taking the trouble to reconsider your comment and for your kind words. I’ll try for a substantive response soon.

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Emily 04.24.12 at 4:28 am

John, thanks for this post and link – interesting reading. Forgive my functional economic illiteracy but I’m currently undertaking a course which partially looks at climate change mitigation/adaptation responses, and economic arguments come into discussions quite a bit. However, (from a humanities background) I find a lot of the economic arguments used against mitigation somewhat baffling. The sums you use in your article are beyond me, but can I ask you to indicate what the principles/premises are behind them? And is it right for me to gather from the discussion here that economics as currently practiced is based on a specific sort of utilitarian philosophy?

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John Quiggin 04.24.12 at 7:18 am

@Emily Economics as currently practiced is mostly utilitarian (or at least consequentialist). What’s being debated here is a divide between two visions about how to treat the future, both of which are held by a lot of economists
(a – my view) Everyone, present and future, counts equally, but extra consumption gives less utility for those who are rich. If we expect people to be richer in the future, we should value extra consumption in the present more highly
(b – Nordhuas and others) People in the future count for less than people today, so unless they are going to be a lot poorer than we are today, we should value extra consumption for them less highly than extra consumption today

To give you an idea of magnitudes, with standard parameter values*, we can justify a transfer of consumption from our grandchildren to ourselves, even if we expect them to have an income level one-eighth of ours. Alternatively, if we expect incomes to remain unchanged, we can justify spending a dollar on ourselves even if it creates a mess that will cost them eight dollars to clean up.

I hope that makes some sense, even if you have to take the numbers on faith

* For those who want to do their own math, that’s a pure time preference of 3 per cent 35 years between generations and for the first part of the example, log utility.

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Tim Worstall 04.24.12 at 8:29 am

“To give you an idea of magnitudes, with standard parameter values*, we can justify a transfer of consumption from our grandchildren to ourselves, even if we expect them to have an income level one-eighth of ours. Alternatively, if we expect incomes to remain unchanged, we can justify spending a dollar on ourselves even if it creates a mess that will cost them eight dollars to clean up.”

And to ask the next question.

If we expect our grandchildren (OK, not quite, but 2100 from the starting point of 1990) to be 8 times richer than ourselves (somewhere around the A1 assumptions in the SRES) or 4 times richer (the lowest of the SRES assumptions, in B2) what does this mean for that spending a dollar on us and costs to them?

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John Quiggin 04.24.12 at 8:49 am

If you accept the standard parameters and a growth rate of 3 per cent, you get a real discount rate of 6 per cent. That means a dollar now is worth around $150 in 2100.

And, regardless of your growth rate projection, a life saved now is worth eight premature deaths in 2100.

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Chris Bertram 04.24.12 at 9:01 am

_I show that it doesn’t matter that people are impatient, preferring consumption earlier rather than later. And what matters is what people actually think about their personhood, not what a metaphysician might say they should think._

No that can’t be right. I agree with you that we should look at lifetime utility and that it doesn’t matter, morally speaking, when in a life the utility comes. But the opinion people commonly have about personhood is neither here nor there: why should we care what people actually think about the nature of personhood? We should care about what’s right.

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Emily 04.24.12 at 9:16 am

Thanks John@56.

I have a further question and if anyone has any recommended reading I would be grateful. I have read what seem to be reputable articles and reports recommending pricing mechanisms be more widely introduced to value growing negative externalities, but I have also read an article by Andrew Sentance of the Bank of England which suggests that doing so might effect a significant structural economic shift. Are current modeling methods able to project possibile outcomes and recommend ways to manage such a shift?

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John Quiggin 04.24.12 at 10:03 am

@Chris I’m unclear as to what it would mean for a view about personhood to be “right” or “wrong”. Do you mean that these are empirically testable propositions?

But, suppose that the belief people hold about their continuity as persons are wrong. As I show on the paper if they act on those beliefs, and maximize their (perceived) lifetime utility, and if policies discriminate against later-born persons (and their time-slice continuations), the result will be that the contemporaneous distribution of income will violate the utilitarian norm of valuing all utilities equally. (I know this is clumsy, but it’s hard to this stuff with words – the paper has mathematical and diagrammatical expositions that are much clearer for those comfortable with those styles).

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Chris Bertram 04.24.12 at 10:49 am

No, not empirically testable (though I suppose there could be relevant evidence from neuroscience) but rather best-supported by argument.

Incidentally, we should arguably reject “the utilitarian norm of valuing all utilities equally” in favour of prioritarianism: i.e. giving greater weight to the same utility gain if it goes to someone with less utility. If we made that shift then it would justify a stronger presentist bias.

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Tim Worstall 04.24.12 at 12:12 pm

“If you accept the standard parameters and a growth rate of 3 per cent, you get a real discount rate of 6 per cent. That means a dollar now is worth around $150 in 2100.”

That’s not quite what I mean. Using your parameters (0.1%?) plus that level of economic growth what does it mean?

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Matt 04.24.12 at 12:40 pm

why should we care what people actually think about the nature of personhood? We should care about what’s right.

It seems unlikely that the two are completely distinct, doesn’t it? I don’t know that you’re suggesting that they might be, and I don’t want to suggest that they are identical, but this does seem to be an area where what people think is at least partially (I might want to say very significantly, though I’m less sure of that) constitutive of what’s right.

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michael e sullivan 04.24.12 at 1:43 pm

Chris@62: If you are judging utility purely as some function of one or more of income, wealth and consumption, as economists are wont to do for simplification, then prioritarian concerns are equivalent to changing your utility function to make a steeper drop off in utility as people become wealthier or consume more. Using an eta of 2 is equivalent to a prioritarian log weight on utility plus an eta of 1.

(for reference, even though I think you already know this: eta of 1 is roughly log utility of money, eta of 2 is roughly log log utility of money).

Basically, you can build prioritarianism into your utility function. Of course there are other forms of utility than money, but they are much harder to quantify and put in a social welfare function. To the extent you are able to do so, they are amenable to similar treatment. To the extent you aren’t, you can’t really use expected utility theory anyway.

In principle I agree with you, and would like to see these analyses use eta somewhat greater than 1, perhaps in the 1.1-1.3 range.

Practically, if it were generally agreed in the corridors of power that economic and social policy decisions should be analyzed with an expected utility framework that included an eta of even 1, it would represent a *huge* win for progressive policy. In fact, combined with John’s proposal of a very low rate of pure time preference for long term planning, it would get us close to the end goal state of a social democracy welfare state as currently envisioned by people well to the left of today’s overton window in any rich country.

IIRC, That was the essence of John’s rebuttal back in 2006 (hard to believe it was that long ago) to those who claimed Stern’s eta was too low. In any other context, an eta of even 1 would result in *far* more progressive policy toward income redistribution and social welfare than we have even in europe, let alone the US. Yet none of the people arguing for a higher eta would have supported any such thing. You might think this makes their arguments for a higher eta specious and merely an ad hoc excuse to do less about climate change. I couldn’t possibly comment.

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John Quiggin 04.24.12 at 9:09 pm

@62 & 65 Prioritarian aka rank-dependent welfare/utility functions (which make up a large part my day job, or, at least, the work that got me my day job) aren’t the same as “more concave utility”, though they can be locally approximated that way. I give this approach a mild plug in footnote 4 of the paper, but, since the central point is valid either way, I stick to classical utilitarianism for the formal presentation.

Michael’s final para is spot-on (as is the one before). I’d exempt Dasgupta from this, since he does support a lot more redistribution, but this criticism applies to lots of Stern’s critics. Without the math it’s just Lomborgism, which in turn is a special case of whataboutery. Lomborg is always going on about how much better it would be to help the poor today than to spend money on climate change but when the Danish government (which was funding him at the time) cut its foreign aid budget he spoke not a word.

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Chris Bertram 04.25.12 at 11:03 am

John: completely agree on the Lomborgism point. However, I think this just illustrates the difficulties of bridging the gap between ideal-theory and real-world policy. If prioritarianism is the right specification of the consequentialist goal, then that is so even if, in the real world, opportunists can use such ideas to make things worse.

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Emily 04.25.12 at 12:16 pm

Some of the arguments here are a little above my economic understanding and education, but…

@59 Re: cultural/individual notions of personhood and economics:
“But the opinion people commonly have about personhood is neither here nor there: why should we care what people actually think about the nature of personhood? We should care about what’s right.”
Not having taken any social sciences undergrad courses, before this current course the only economic theory books I had read happened to be for Asian-Pacific history subjects, and in most cases were written by anthropologists concerned with structures and practices of social/material exchange among and between economic agents in small scale economies in S/E Asia, Melanesia and Polynesia (Marilyn Strathern and Marshall Sahlins spring to mind). In these instances, in small scale communities, agents’ individual/cultural conceptions of personhood and shared social-economic traditions were understood by the authors as being intimately bound together – with one effecting the other.

@65 ” Of course there are other forms of utility than money, but they are much harder to quantify and put in a social welfare function.” Not meaning to quibble, but from a theoretical perspective I would expect that a professional or academic economist would accept that the value (and utility) of money is not found in its numerical denomination (which is easily quantifiable, but the functional value of which is prone [without sovereign management] to variations – re: fluctuating exchange rates, inflation, price variations etc) but in it’s structural exchange and ownership function and in its cultural meaning. Is this not the case?
And if so, wouldn’t this mean that the value of £1 in the wallet or the bank account is evidently not any more intrinsically quantifiable than the value of an apple or a person or an abstract social relation or concept?

@66 I vaguely remembered Lomborg (if it’s the same bloke) from an appearance on Lateline last year, where he discouraged carbon pricing mechanisms (at the most supporting a carbon price of $7) in the near term, recommending action further down the track when technological developments may have become more effective and affordable (price-wise).
The other part of the exchange I remembered (copied below from the online transcript) seems suggestive to me that professional economists, in constructing cost benefit analyses concerning sovereign near-term mitigation measures, might possibly be commencing their analysis from an unstated position which implicity discounts the utility value of sovereign mitigation measures due to the risk of such measures potentially incurring certain qualitative negative externalities. Sorry for the clumsy terminology, I am not very familiar with the economic academic language.

“TONY JONES: Once again, the counter-argument would be that if countries like India, China and even the United States don’t inevitably adopt a price on carbon, countries that do will impose border tariffs on their goods when they’re sent in to – when they’re imported, and so inevitably, they will have a charge on their carbon in their manufacturing.

BJORN LOMBERG: Well, I mean, in some ways you just said yourself here the countries that will do so may be Australia, maybe the EU, they will exclude the rest of the world. Listen, it’s us that would be excluding ourselves from the rest of the world.

There’s a much bigger danger here, which I think pretty much everyone recognises, is that if we have a trade war, the losses for everyone could be hugely bigger, and that’s probably why this will never happen.”

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Greg 04.26.12 at 7:20 am

I don’t know if anyone’s still reading this thread, but I remember doing Nordhaus as an geography undergraduate and finding the whole approach of “discounting the future” somehow deeply unsatisfactory.

Still can’t put my finger on it.

Maybe it’s a feeling that discounting the future has it backwards, and what we actually do is inflate the present. Tomorrow has the same value as next month or next year, but if I don’t get through today they are all worthless. So in my head this is illustrated by a little artificial hump of value that moves along a flat timeline, so taking any given NOW as your start point, it would look like you were doing some kind of discounting. Conceptually this feels like a big difference, maybe mathematically it isn’t.

Maybe I just dislike naked utlitarianism.

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James Wimberley 04.26.12 at 11:00 am

Style tip to JQ: cut the parentheses. In blogland, they create an impression of indecisiveness rather than the intended judiciousness. I find my natural style uses them too much, as I’m also an on-the-other hand kind of guy, and need to weed them and the semicolons before posting. A genuine aside probably deserves a new paragraph instead.

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Joshua W. Burton 04.26.12 at 1:43 pm

In college bull sessions, we always used to shorthand this problem as “Robert Herrick’s sled” (gather ye Rosebud, har har). There’s equity risk premium, and there’s anticipated economic growth; factor those out (“candy before Hallowe’en”) and there is still a finite “candy now” liquidity preference, implying a generational utility slope. Imagine a hypothetical simplified world with zero population growth, zero economic growth, stable full employment, no inflation. You’d still have nonzero, albeit very low, safe return on money, and you’d still have the problem of how to divide up finite consumable resources. Does everyone alive get the same share, today? (This maximizes living-voter utility, but screws over the unborn.) Does everyone, alive or not, get the same share, today? (This diverges, unless we go extinct.) Or, does everyone get, today, the (NPV of) the same lifetime share? (This maximizes market utility, or exponentially-damped voter utility, and converges into futurity.)

If we deplete half of an irreplaceable resource every 50 years on the exponential plan, every generation will be able to tell the next that, at constant date, they were offered the same future value at the same age as everyone else as of that date. So no one can fairly say that her generation was shortchanged, except by the chance of birthdate and the time value of money set by her generation’s own lifestyle preference (the 50-year time constant, revealed as a 1.5% return on safe money). Since no one chooses her birthdate, this is the unique “fair” solution, but it does imply as a corollary that, at least with respect to irreplaceable
resources, “that age is best which is the first.”

It’s fashionable in some libertarian circles to pretend that there are no (important) irreplaceable resources. But suppose, just for the sake of argument, that we were living on a planet.

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Joshua W. Burton 04.26.12 at 1:54 pm

Of course, the existence of stubborn finite liquidity preference, in the absence of risk or anticipated growth, is a bit of a puzzle. My own tentative theory is that the safe return on capital in a static world is the “subjective mortality,” defined as the revealed-preference alienation of our future selves (either because they may not be alive to pick the fruit, or because dude, who cares?). In a world of prudent eidetic immortals, the risk- and growth-hedged interest rate would be zero on this view, and Herrick’s sled would come to rest.

And this brings us to the political punchline. Human civilization is not mortal, at least (we hope) on a scale comparable to 1.5% per annum. Therefore, civilization has preferences that differ quantitatively from those of its members. This is a very difficult statement to even frame coherently in a context of pure autonomous individual rights (libertarian’s head asplode); nonetheless, I believe it is true. Even if we, and all other generations, agree (as, by my analysis, we all should) that current labor is worth more to us than future labor, and hence that descendants are small, our lasting institutions, such as democratic government, should consider us all to be the same size. A day spent hiking in the redwoods in 2012 is worth more to me than one in 2112, but the Park Service shouldn’t care, at least insofar as we have a rational expectation that it will still be around a century hence.

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Joshua W. Burton 04.26.12 at 2:07 pm

All this stuff really does matter, by the way. When we decide how much to spend mitigating best-guess long future consequences of our actions (windmills today, versus levees tomorrow) we should recognize that the market picks the right discount rate for mortal humans, so it’s no wonder it isn’t much moved by the fate of our great-grandkids. If we calculate the future costs at a zero discount rate, however, we can approximate the goal of stewardship for which governments are instituted among men, deriving their just powers also from the prospective consent of the not-yet-governed. To “secure the blessings of liberty to ourselves and our posterity” is structurally incompatible with the wisdom of the market, and it’s up to us to choose. But our descendants get the consolation prize of writing our epitaphs, so we might want to choose with humility.

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Watson Ladd 04.26.12 at 5:15 pm

Joshua: It seems that the only thing to do is not burn the resource ever, but that’s a strange conclusion: there should be some way to spread the benefit fairly, and we would all be better off if we did so.

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Emily 04.26.12 at 6:18 pm

Watson, to work out the math to spend the resource fairly (should we ever haver have started spending it at all) implies a rational mass economic agents decision of start and end dates – care to lay out the sums for posterity’s sake with your names to them?

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Emily 04.26.12 at 6:48 pm

To be specific, by decision I mean thoughtful selection, declared nomination and implementation of.
Also, can you define what you mean by ‘benefit’; ‘we’ (in terms of actors, duration and any other specifics); fairly (do you mean without blemish? or in the common sense it’s used in Oz eg. “fair go, mate”, or in terms of equal distribution or…); and ‘better off’?

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piglet 04.26.12 at 8:33 pm

“It seems that the only thing to do is not burn the resource ever, but that’s a strange conclusion: there should be some way to spread the benefit fairly, and we would all be better off if we did so.”

Try this:

Natural Capital and Sustainable Development
Author(s): Robert Costanza and Herman E. Daly
Source: Conservation Biology, Vol. 6, No. 1 (Mar., 1992), pp. 37-46
Published by: Blackwell Publishing for Society for Conservation Biology
Stable URL: http://www.jstor.org/stable/2385849

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piglet 04.26.12 at 8:55 pm

This seems to be relevant and I think hasn’t been quoted yet:

Right for the Right Reasons – A final rejoinder on the Stern Review

Dietz, Simon and Stern, Nicholas and Anderson, Dennis and Taylor, Chris and Zenghelis, Dimitri (2007) Right for the right reasons: a final rejoinder on the Stern review. World economics, 8 (2). pp. 229-258. http://www.world-economics-journal.com/Contents/ArticleOverview.aspx?ID=292

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michael e sullivan 04.26.12 at 10:04 pm

Emily@68. I can’t really speak for professional and academic economists, but I suspect they would agree with you, as there is a theorem to the effect that individual utilities are not the same.

In practice, the very act of doing expected utility analysis of a social policy assumes for the sake of argument that you can represent most people well enough with some kind of standard utility function. It’s a lot like assuming a can opener, except that this is one of the cases where there’s some empirical evidence that people’s utility of money behaves similarly enough for these assumptions to be workable. Or rather, there a general agreement that certain kinds of common apparent utility of money functions are simply enough, and represent rational enough behavior to be worth using for social policy modeling.

In practice many people use hyperbolic and discontinuous discounting, but I think few academics consider those to be potential rational preferences, as opposed to wetware defects.

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Emily 04.26.12 at 10:36 pm

But Michael, would you (and other economists) not agree that people’s behaviour re: the utility of money is similar because there are laws enforced by the State ie. property title, monetary laws, corporation acts etc that actively coerce people within State territoryopt those in other territories subject to treaty agreements to adapt their innate socio-economic behavior in accordance with the laws of the State and the social hierarchy that they are productive of?

Whilst behaving within the legal framework is certainly rational in a self-preservatory sense (ie. you save your own neck) I don’t think it’s rational in the true sense of the word – which would be, surely, that if the legal framework was irrational, unjust and unmerciful you ought (through duty to your fellows) try to alter it rather than perpetuate it.

When the can washes ashore to the isolated island the people generally don’t assume a can opener – they assume a cargo cult (see pacific ethnography).

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Matt 04.26.12 at 10:42 pm

I would like to challenge (or rather invert) Lomborgism at another level.

Texas, notorious refuge of spendthrift green fanatics, has installed enough wind to provide more than 15% of total grid demand on the windiest days. Recent wind contracts in Texas have gone for $35-$45 per megawatt hour on a 25 year fixed price contract. Even if you add in the $22 per megawatt hour production tax credit for a total of up to $67 per MWh, that is well short of the minimum $86 per MWh that the US DOE estimates as levelized cost for new conventional coal plants.

Germany, home of the vast solar boondoggle that costs a fortune and doesn’t really produce any energy, has driven down the wholesale price of daytime electricity by about 1/3 in the last 4 years.

The reason China, Indonesia, India, Mexico, and Brazil are building out wind and solar is also no doubt because their populations are so rich and stupid that they can’t help but waste money on eco-follies.

Just how sure are we that burning more fossil fuels is the economic equivalent of eating ice cream and playing video games, and that renewable energy is the equivalent of eating plain rice and cleaning toilets? It looks to me that renewable energy can produce significant quantities of energy, at reasonable cost, and can scale up quickly. There will be challenges integrating intermittent renewables at higher penetration rates, but most of the world isn’t yet close; let’s at least get that 10-20% penetration most places before wringing our hands over the things renewables can’t (yet) do.

There’s another bonus from renewables: they create more jobs than equivalent fossil energy production. The extra cost of extra workers is considerably (sometimes completely) offset by the diminished rents going to mineral resource owners. If you include just the short-term economic damage of fossil fuels to health, neglecting the global warming effects completely, renewables come out ahead most places. The economic effects of renewable energy are more pie-reslicing than pie-shrinking. Now all becomes clear: government renewable energy loans are a scandal and externalized smokestack health burdens are Just the Way the Real World Works because, were it otherwise, the wrong people would get the pie.

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JW Mason 04.26.12 at 11:04 pm

Michael Sullivan writes;

there’s some empirical evidence that people’s utility of money behaves similarly enough for these assumptions to be workable.

and a couple sentences later he writes:

In practice many people use hyperbolic and discontinuous discounting, but I think few academics consider those to be potential rational preferences, as opposed to wetware defects.

I’m kind of tempted to leave those two sentences there to just look at each other, but this is so typical of academic economists that one has to spell the point out. Is the model problematic logically, but ok as an empirical generalization? Or is it empirically falsified, but important as a logical baseline? Can’t be both — except it can be, if you are an economist looking for whatever ad hoc argument will justify continuing doing what you’ve always done.

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Matt 04.26.12 at 11:25 pm

Follow-up on health costs: the 2011 Harvard report “Full cost accounting for the life cycle of coal” shows a minimum externalized cost of $175 billion per year in the United States from using coal. If you further lowball it by ignoring all climate impacts, because that might all be sunspots or Al Gore’s lies, you’re left with at least $154 billion of annual health costs externalized to the public from coal. But of course the big US energy scandal of 2011 was when a solar company cost the public $0.535 billion.

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Emily 04.26.12 at 11:55 pm

Matt, In my somewhat limited experience (urban planning student) when a report writes on pricing ‘externalities’ ( likely actual consequences for human beings, natural creation, and built things by continuing to follow the directives of a specific economic model, including in State planning control to facilitate the continuation of the model) – they approximate a monetary price value but the actual ability or not to deal with and recover from the consequences is somewhat like the MasterCard advert “Priceless”.

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Matt 04.27.12 at 12:34 am

Emily, it’s true that ‘externalities’ includes consequences that are not really commensurable or reparable with currency. That is another way that the high costs of fossil fuels are hidden. The point that I would like to make is that even sticking to externalized but quantifiable impacts, like medical bills and missed work, a coldly calculating Supreme Homo Economicus of the USA would be retiring coal at high speed. Conservatives aren’t any less sentimental than progressives when it comes to energy choices, it’s just that their sentiments favor more capital-intensive mineral extraction industry over more labor-intensive renewable energy industry.

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geo 04.27.12 at 1:40 am

JQ@58: a life saved now is worth eight premature deaths in 2100

Hope this isn’t OT (if so, please ignore), but I’m not sure I see this. Do you mean eight exactly, or “any number”? In either case, why? And doesn’t it also depend on the degree of certainty of the trade-off? Would a life saved now be worth preventing, with 100 percent certainty, eighty premature deaths in 2100? Or with 90 percent certainty, eight thousand premature deaths? Or with 75 percent certainty, eight hundred thousand?

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John Quiggin 04.27.12 at 5:24 am

@Geo I mean 8 which is approximately 1.03^70 so, the correct date is actually about 2080.

As you say, certainty matters. But, if you accept a 3 per cent pure rate of time preference in a utilitarian discounting framework, and you assume that the utility of not dying remains constant, then you are committed to the conclusion that one life saved now with certainty is worth eight lives with certainty saved in 70 years time, or 16 lives saved with probability 0.5 etc.

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Joshua W. Burton 04.27.12 at 1:06 pm

But, if you accept a 3 per cent pure rate of time preference in a utilitarian discounting framework, and you assume that the utility of not dying remains constant, then you are committed to the conclusion that one life saved now with certainty is worth eight lives with certainty saved in 70 years time, or 16 lives saved with probability 0.5 etc.

As of course you should be. After all, a 20 year old man today, without obvious coercion, will trade an hour of a 43 year old man’s present salary for a claim on two hours of his own salary at age 43. If lives are made of years are made of hours, and future hours are discounted in the present labor market, then the man who offers mostly future labor cannot claim an equal stake with a present peak earner of equal ability. He might “need” a share of untapped ANWR oil or old-growth forest or clean air just as much as I do, but unlike me he has to buy it on credit.

The exponential time-weighting also restores, rationalizes and quantifies an intuitive weighting (respect for elders) that seems to be normative in all human societies, probably exactly because (on this analysis) it is just. If there had been financial pages to look up the bond yield curve, we can imagine that Moses, Confucius and Plato would have hyperlinked them to the relevant passages in Torah, Analects, and Euthyphro.

Be it noted, per @73, that I consider this a Bad Thing on a finite planet, or even in a flat cosmos (in hyperbolic space, where dead Mormons allegedly go, it is salutary). One baseline duty of a civilization is to rise above this sterile representative agent view, and to Think Of The Children.

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geo 04.27.12 at 4:25 pm

JQ: Got it. I thought you were saying something else: i.e., that one mustn’t forego saving a life now, no matter what the likely (or certain) future benefit. In other words, I thought you were disagreeing with Orwell’s “comfortable English professor defending Russian totalitarianism,” who can’t bring himself to say “I believe in killing off your opponents when you can get good results by doing so,” even though, as I’m sure Orwell would agree on reflection, if the results are sufficiently good and sufficiently certain (which, as Dewey pointed out in reply to Trotsky’s Their Morals and Ours, they obviously weren’t in the case of the innumerable people whom Trotsky and his Bolshevik comrades and successors shot), then one can hardly justify not doing so.

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leederick 04.27.12 at 7:08 pm

“Everyone, present and future, counts equally, but extra consumption gives less utility for those who are rich. If we expect people to be richer in the future, we should value extra consumption in the present more highly… if you accept a 3 per cent pure rate of time preference in a utilitarian discounting framework, and you assume that the utility of not dying remains constant, then you are committed to the conclusion that one life saved now with certainty is worth eight lives with certainty saved in 70 years time”

I don’t really follow much of this. First off, it’s kinda hard for me to get my head around discounting lives saved on the basis that extra consumption gives less utility for those who are rich. I can understand that say an extra Porsche would grant less utility to someone who already has three, than to someone who doesn’t have any. But it’s hard for me to understand how not dying is worth less utility to millionaires than the rest of us. If anything, isn’t it worth more utility since they get to spend their extra years enjoying all their money?

Secondly, I’m not sure there’s any fundamental time element to this argument – it’s just posed in generational terms by using the assumption that due to economics growth people in the future are more likely to be rich, by talking about shifting consuption between the rich and the poor. Wouldn’t people who believed the value of lives depend upon money via utility believe in making the same tradeoffs now, so saving 8 lives of people earning $10k is worth saving one life of someone earning $80k. But I don’t see utilitarians arguing that.

I think I should also thank John for taking the time to try and explain these ideas to the rest of us.

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Joshua W. Burton 04.27.12 at 9:42 pm

Secondly, I’m not sure there’s any fundamental time element to this argument – it’s just posed in generational terms by using the assumption that due to economics growth people in the future are more likely to be rich, by talking about shifting consuption between the rich and the poor.

No, this is a separate effect — call it “candy before Hallowe’en”. If there will be a lot more candy next month, we overvalue candy today, even to the extent of borrowing it at a time-value-of-money premium. Insofar as our liquidity preference (LM in the IS/LM diagram) reflects a rational expectation of a rich future, interest rates are higher than they would otherwise be.

But even if it’s not October, there is still a “candy now” preference, which may or may not have to do with human mortality, impatience, forgetfulness, or other factors. Because older and younger generations, even when they are living at the same time, have lifespans that are differently situated relative to “now,” the market value of their life’s work, and hence arguably of their lives, is weighted by a time-value-of-money factor. A 43 year old earns the same $10/hour for the same work as a 20 year old, and can put it away for 23 years (even without assuming economic growth) and then pull out $20 and buy two hours of work from a 43 year old. Since they both see this deal and (in a revealed preference sense) accept it, the younger man agrees that his utils are only worth half what the older man’s are worth.

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John Quiggin 04.27.12 at 11:34 pm

@leederick If you are worried about differing utility of lives, the point can be restated as “Assuming similar utility when alive, and pure time preference, one life saved now is worth 8 in 70 years time”

@joshua As long as people’s preferences are coherent, my argument is consistent with a preference for early consumption. It’s a bit complicated for a comments thread, though, you’ll have to read the paper.

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John Quiggin 04.27.12 at 11:37 pm

@geo There’s a sharp passage in Orwell where he notes supporters of the Bolsheviks saying “you can’t make an omelette without breaking eggs”, then being asked “but where’s the omelette” and responding “Rome wasn’t built in a day”.

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geo 04.28.12 at 1:44 am

JQ: Very true: It’s a hard decision. Though I would hope we could agree on shooting Grover Norquist.

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John Quiggin 04.28.12 at 3:34 am

I believe drowning in a bathtub is the preferred method :-)

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Jake 04.28.12 at 5:23 am

I’m confused. Is “one life saved with certainty today is worth eight lives lost with certainty in 70 years” supposed to be self-evidently false and thus refute pure time preference? Situations that would cause 8 deaths with certainty in 70 years feel trolley-problem-esque; I’m having a really hard time come up with a plausible example.

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John Quiggin 04.28.12 at 5:29 am

The certainty bit is just there to allow a one-sentence statement of the result. Any real problem would involve uncertainty, but the 8:1 ratio would still be in their.

For a plausible example, think about how you would look at a decision on storing radioactive wastes. Some lives will be lost in the future, and what we do now will affect that. This isn’t a trolley problem designed to tweak intuition one way or the other, it’s an actual decision that has to be made.

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JW Mason 04.28.12 at 6:12 am

Insofar as our liquidity preference (LM in the IS/LM diagram) reflects a rational expectation of a rich future

Not for nothing, but the notion of liquidity preference was introduced specifically to reject the idea that the interest rate reflects any sort of intertemporal substitution. The choice in the ISLM framework is between money today and illiquid assets today; the future doesn’t come into it.

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dsquared 04.28.12 at 12:10 pm

@geo There’s a sharp passage in Orwell where he notes supporters of the Bolsheviks saying “you can’t make an omelette without breaking eggs”, then being asked “but where’s the omelette” and responding “Rome wasn’t built in a day”.

This is actually an improvement on Orwell’s quote, attributable to Kevin Donoghue in comments on Crooked Timber! The bit including “Rome wasn’t built in a day” is now nearly the standard Internet version, but Orwell originally said “And if one replies, “Yes, but where is the omelette?”, the answer is likely to be: “Oh well, you can’t expect everything to happen all in a moment.””

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Henry 04.28.12 at 1:16 pm

Randall Jarrell – “A War”

There set out slowly, for a Different World,
At four, on winter mornings, different legs …
You can’t break eggs without making an omelette
That’s what they tell the eggs

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Emily 04.28.12 at 5:21 pm

I have to say, in terms of adults writing fables about pigs and other animals, I always preferrerred Charlotte’s Web by E B White – another author nominaaly concerned about the use of plain language. Charlotte seemed more sacrificial and fruitful though.

“Cries of ‘Good-bye, good-bye, good-bye! came weakly to Wilbur’s ears. He couldn’t bear to watch anymore. In sorrow he sank to the ground and closed his eyes. This seemed like the end of the world, to be deserted by Charlotte’s children. Wilbur cried himself to sleep.

When he woke it was late afternoon. He looked at the egg sac. It was empty. He looked into the air. The balloonists were gone. Then he walked drearily to the doorway, Where Charlotte’s web used to be. He was standing there, thinking of her, when he heard a small voice.

‘Salutations!’ it said. ‘I’m up here.’
‘So am I,’ said another tiny voice.
‘So am I,’ said a third voice. ‘Three of us are staying. We like this place, and we like *you.*
Wilbur looked up. At the top of the doorway three small webs were being constructed. On each web, working busily, was one of Charlotte’s daughters.
‘Can I take this to mean, asked Wilbur, ‘that you have definitely decided to live here in the barn cellar, and that I am going to have *three* friends?’
‘You can indeed,’ said the spiders.”

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Joshua W. Burton 04.29.12 at 3:11 am

John Quiggin @92: It’s a bit complicated for a comments thread, though, you’ll have to read the paper.

I saved it for the sabbath, to do it justice — and I’m still puzzled. I’m still hoping that you’ve got a “knockdown argument” against Herrick’s sled, but it seems to me that you may be invoking a hidden fourth axiom that begs the essential question.

In section 2.1, you make in passing what to me is your key assertion, when you say that “However, since the lifetime utility of all generations is valued equally, the consumption of each generation is the same.” If we grant this, then I agree that all your conclusions follow, but it seems to me that I could just as easily build a model, consistent with Pareto optimality and generational independence and with your Axiom 3 of utilitarianism within periods, in which the lifetime utility of different generations is not valued equally. Further, I think that, possibly contra your note 4, the commonsense assumption implicitly made by most utilitarians is that the instantaneous utility per unit time of all living persons at any given time is valued equally, rather than the time-integrated lifetime utility. (There was a notorious medical ethics paper by Ezekiel Emanuel probing this assumption in extreme cases like organ transplants, and the suggestion that we would underweight the instantaneous utility of living persons who have “already had their share” ignited a partisan firestorm during the 2008 US elections. Politically at least, the idea that people right now all have equal worth has a compelling appeal, in the sense that it’s demonstrably hard to argue against in public.)

Under the contrary assumption of equal present utility flow, Herrick’s sled slides down your Figure 1 (which is identical to what we drew on a blackboard in Jefferson Lab thirty years ago) without a brake. The consumer in generation N wants (1/theta) times more of the consumption good in his first period, so we ought to allot that much to consumer N-1 in his second period, so consumer N-1 gets (1/theta) times more again in his first period, and so on back to Sutter Mill and the Spindletop gusher. Note that this weighting also solves the infinite-time boundary problem, because there was a first generation that had access to the consumption good, and far futurity is exponentially damped.

Have I missed something here? In particular, do you believe that equal lifetime utility value (as opposed to equal instantaneous utility flow value, or some other arbitrary intergenerational assumption) is (1) already implied by your axioms, (2) morally self-evident and not in need of defense, or (3) worth defending, but assumed for the sake of argument in this paper? I totally agree that with this additional assumption the Herrick gradient between generations is flat and the sled doesn’t move.

My own tentative view, after many many years of noodling this problem, is that the answer lies outside of the individual preferences of representative agents: I value my present utility over my future utility, but I’m indifferent as between your present and future. Or, to put it another way, public institutions which guard our durable interests should not underweight the future as much as we individuals, by revealed-preference market signals, evidently do. There is nothing intrinsically unjust to individuals about a system that values the lifetime utility of earlier generations more highly (in a Rawlsian sense, we don’t choose our birthdates), but our civilization has a collective interest that is maximized when we take a longer view.

JW Mason @98: Not for nothing, but the notion of liquidity preference was introduced specifically to reject the idea that the interest rate reflects any sort of intertemporal substitution.

I would say, rather, that liquidity preference is introduced to abstract away intertemporal preference. People in the present want a certain balance between liquid and illiquid assets, and if the underlying reason for their preference is (as it ultimately must be) rooted in their present vs. anticipated future consumption utility, we can nonetheless wave that away and consider liquidity preference, operationally, as a thing in itself. Common stock has present market value we can read off the ticker without reference to the future, but only because someone somewhere believes there is a future profit stream.

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Tim Wilkinson 04.29.12 at 12:56 pm

That sounds similar to a comment I’d shelved, so I’ll post that too fwiw:

consumption preferences do not change over the lifecycle, but, starting from an initial position of constant consumption, members of generation t prefer additional consumption in period t (when they are young) to additional consumption in period t+1(when they are old)…In life cycle terms, a consistent preference for consumption earlier rather than later means a preference for consumption when young over consumption when old.

This is modelled by two utility functions which accept as arguments consumption at the two different periods, and which can be combined to make a single invariant utility function for the whole person, accepting consumption-indexed-to-a-period as arg. The discount factor’ is said to relate the utility function for later consumption to that for earlier consumption – but surely to the extent that this is a structural feature of the combined utility function which is supposed to describe consistent prefs over consumption-packages-at-times, it’s not really a discount factor, is it? Instead time-indexation is being treated as a property, relevant to utility/preference/etc., of the consumption packages themselves.

When the simple model is generalised to smaller time periods, we add in more and more constituent utility functions for consumption-indexed-to-time, and the idea that this is based on a consistent/time-invariant preference for consumption-when-young becomes less plausible: the same (annual) discount factor has to be interpreted as a preference for ‘consumption-when-one-year-younger’, for example, which happens to conform to this ‘discount factor’.

If we’re positing this discount-factor, isn’t it more apt to abandon the assumption of a single invariant utility function and instead model the phenomenon as a preference for ‘consumption now’, with later consumption discounted more as it becomes more remote because further into the future? (Chance of death is presumably dealt with by probabilistic, rather than purely temporal, discounting in this kind of model.)

Call our representative member of gen. t ‘Gray’. Gray prefers consumption in t to consumption in t+1. The alternative way of modelling impatience would be by positing ‘Younger’ and ‘Elder’ as two long time-slices of Gray, the latter conceived as the ‘whole person’ enduring from birth to death. This can be taken just as a picturesque way of saying there are two not-necessarily-consistent utility functions, one underlying or encapsulating Gray’s behaviour in t, the other in t+1.

One reason for doing so is to accomodate the asymmetry of the situation: Younger prefers additional consumption for Younger over additional consumption for Elder – but Elder is not capable of manifesting a revealed preference about Younger’s consumption versus Elder’s, because it’s too late.

So (to pretend to be formal about it) Elder’s utility function yields undefined values for consumption-at-t, which means it can’t be identical to Younger’s. If constant preferences are to be modelled, then they will have to be for ‘consumption now’ (or ‘in this period’ in the simple case). Under this model, the motivation for deferring consumption occurs at a higher-order level – that of Gray, who is thus in an analogous position to that of policy makers or other social planners, trying to make Younger take proper account of Elder’s needs – i.e. not be impatient.

Because in fact and informally, Elder may well (‘unrevealedly’) prefer that younger had been less ‘impatient’. Impatience – if this term is not to be stipulatively defined – involves a deviation from prudence from the perspective of the enduring person: it makes Gray worse off overall. Since it benefits Younger, presumably then it does so at the expense of Elder. To the extent that the attempt to prevent Younger shafting Elder is successful, Gray exhibits one form of integrity, a kind of intrapersonal equity.

This doesn’t really contradict the conclusion of the article; rather it goes further in pointing out an intrapersonal analogue of the same phenomenon. Not only should rational, consistent lifecycle time-preference not be confused with utility discounting applicable at a social level (as the paper says, against whomever holds that it should), but if there is impatience (which should be modelled as discounting) it is an irrationality even at the individual level, so certainly should not be indulged in by policy-makers.

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Joshua W. Burton 04.29.12 at 1:43 pm

but if there is impatience (which should be modelled as discounting) it is an irrationality even at the individual level, so certainly should not be indulged in by policy-makers.

Partly, yes. But remember that Younger does not know with certainty that Elder will ever exist. Some of Younger’s impatience is actuarial, and for that reason entirely rational. It’s at least suggestive, too, that the orders of magnitude are right: a low 1.5% safe real interest rate implies a 67-year life expectancy for (adult) investors, in that 98.5 cents now is worth a 98.5% chance of living to enjoy a dollar next year. As I said @72, it might be reasonable to unify true actuarial mortality with impatience, imprudence, forgetfulness, self-alienation and so on to infer a “subjective mortality” that is actually being figured into market interest rates. Children have no idea they’re going to die, but they still want “candy now.” In the limit as I become foresighted, sharpwitted, and centered, my subjective mortality approaches my actuarial mortality; insofar as I live in the moment, it is higher.

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Joshua W. Burton 04.29.12 at 1:58 pm

And policy-makers, when their fiduciary duty is to institutions that are not “subjectively mortal” on a human timescale (the General Sherman tree lived 4000 years without us; it would be petty and resentful to impose our 67-year horizon on its future), should use neither irrational nor human-lifespan rational discounting, but at most some very slow discounting that reflects our collective aspirational indifference to their institution’s future. The park service should care about the sequoias in the 23rd century nearly as much as in the 21st, and similarly for clean air, fresh water, climate and so on. But on “hard” stewardship questions, involving tens of thousands of years instead of centuries, there is room to debate that even our institutions should accept their own imprudence or mortality. We dig up dinosaur bones, knowing that the cities in which their museums reside and the libraries in which their scholarly value is recorded will probably be destroyed long before the strata in which we could have left them intact. When we worry about nuclear waste storage beyond a hundred centuries, we should in humility consider that the probability that the human race will (1) still be around, and yet (2) never have reached a technological level where they can solve the problem far more easily than we can, is unknowable but probably pretty low.

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Joshua W. Burton 04.29.12 at 2:18 pm

In a nutshell, Herrick’s sled is the following argument. Old boomer and young Gen-X’er, meeting in the present, reach philosophical or political agreement that each has an equal claim on a day of present happiness. (John Q would say, “on lifetime happiness,” and this would stop the sled. But real utilitarians don’t think and vote that way.) Real safe interest rates show by revealed preference, and surveys confirm, that Gen-X’er values a day of present happiness more than a day of happiness in the 2040s, and that boomer once valued a day of happiness in the hazy 1960s more than a day of present happiness. It follows that boomer’s lifetime happiness is worth more than Gen-X’er’s, according to everybody, and that boomer was entitled to the lion’s share of the Ghawar oilfield. (“Hey, wait!” says Gen-X’er.)

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John Quiggin 04.29.12 at 7:24 pm

@Joshua – “Real safe interest rates show by revealed preference”
I pointed out back at #13 that this is wrong

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Emily 04.29.12 at 9:21 pm

“In a nutshell, Herrick’s sled is the following argument. Old boomer and young Gen-X’er, meeting in the present, reach philosophical or political agreement that each has an equal claim on a day of present happiness.”

I am on the cusp of gen x gen y depending on where statisticians take it upon themselves to draw the line and I have grown up with many girls now women who have borne children. I would simply refuse to make that agreement, it’s premises are illusionary and it’s logic faulty. Then what?

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Emily 04.29.12 at 9:25 pm

“In a nutshell, Herrick’s sled is the following argument. Old boomer and young Gen-X’er, meeting in the present, reach philosophical or political agreement that each has an equal claim on a day of present happiness.”

I am on the cusp of gen x gen y depending on where statisticians take it upon themselves to draw the line and I have grown up with many girls now women who have borne children.

If person A asked person B to enter into your agreement, and in good faith B refused, for the argument relies upon faulty premises – or illusionary – and it’s logic terrible. Then what?

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John Quiggin 04.29.12 at 9:33 pm

More generally, Joshua, a number of the points you make were addressed before you came in – time-slices, mortality risks and so on. I don’t mind you making them slightly differently, but my previous responses stand.

111

Emily 04.29.12 at 9:43 pm

Have none of you read Maus or Strathern. Marriage is the basis on a stable socio-economy.

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Joshua W. Burton 04.29.12 at 10:34 pm

I pointed out back at #13 that this is wrong

Sorry, I don’t see this: I agree completely with @13, and with most of the rest of what you write. Equity risk premium is mysteriously high, sure, and not the subject in question here. Safe interest rates are 1-2%, and we’ve had a growing economy for as long as we’ve been measuring them, so we don’t know what safe static economy interest rates would be. It’s a good guess, however, that they’d be less than 2% and more than 0%. If they are zero, then your intertemporal theta is 1, and there is no gradient to explain.

The difficult case (for me, and I have indeed read all your responses and the cited paper with some care — if I restate unnecessarily, it’s only to offer a fat target for instructive correction) is if you stipulate, as in section 2.1, that each generation prefers early consumption, for reasons not related to secular economic growth. You still get an intergenerational brake, because, lifetime utilities being equally valuable, the present young not only outweigh their future older selves, but also the present old. If, as a naive utilitarian might suppose — I don’t say should suppose, but the Emanuel affair inclines me that way — the present young and present old have equal present claims, then there is an unchecked intergenerational slope, and “that age is best which is the first” by natural right.

I’m not baiting you; I’d really truly like to be unconvinced of this, and I think that is the intent of your paper so I’m trying hard to draw you out. I think an answer (@102, para 4) from you to my question about the grounds for your “lifetime utility” assertion will help me a lot here. Why ought I to value my (living) son’s generation’s lifetime happiness equally with that of my own generation? My generation, after all, is offering present labor to earn their share, while his generation is offering only a discounted promise of future labor. And none of us chose when to be born.

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JW Mason 04.29.12 at 10:38 pm

People in the present want a certain balance between liquid and illiquid assets, and if the underlying reason for their preference is (as it ultimately must be) rooted in their present vs. anticipated future consumption utility

No, it’s not. Keynes devotes quite a few words to explicitly rejecting this view. The interest rate is not the premium you pay to consume now rather than later, the interest rate is the premium you pay to have your claims on a given quantity of future consumption in a form that can be exercised freely at any time vs one that can only be exercised on a certain date or in a certain state of the world. In Keynes’ vision, savings as such responds little or not at all to the interest rate; rather, the interest rate tells us how much people prefer a form of savings that allows them the freedom to respond to unexpected contingencies.

You don’t have to accept Keynes’ view, of course, but you should not misrepresent it, or pretend that the loanable-funds story of the interest rate is the only possible one.

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JW Mason 04.29.12 at 10:42 pm

Why ought I to value my (living) son’s generation’s lifetime happiness equally with that of my own generation? My generation, after all, is offering present labor to earn their share, while his generation is offering only a discounted promise of future labor.

Surely this is circular? Leaving aside the — utterly wrongheaded, IMO — assumption that people’s claim to happiness is solely based on their labor, you need to have already established that there is a positive social discount rate to conclude that future labor is less valuable than present labor.

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Joshua W. Burton 04.29.12 at 10:54 pm

Emily @109: If person A asked person B to enter into your agreement, and in good faith B refused, for the argument relies upon faulty premises – or illusionary – and it’s logic terrible. Then what?

Well, then there would be no individual agreement, of course, and we’d have to look to our political mechanisms for the collective agreement that was really what I meant. Note that the broad trend over the last century has been strongly in the direction I suggest — that is, toward equally valuing the happiness of the old with that of the young. Early 20c reformers would be astonished to learn that in the early 21c there are more American children living with food insecurity than American senior citizens.

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Joshua W. Burton 04.29.12 at 11:13 pm

JW Mason @114: Surely this is circular? Leaving aside the—utterly wrongheaded, IMO—assumption that people’s claim to happiness is solely based on their labor, you need to have already established that there is a positive social discount rate to conclude that future labor is less valuable than present labor.

I agree! If the whole story of real interest rates is some combination of option value (you @113, after Keynes) and anticipated economic growth (“candy before Hallowe’en,” as opposed to “candy now” simpliciter), then there is nothing to explain; the intergenerational sledding hill is flat. But Prof. Quiggin appears to be claiming that even if there is a utility gradient between time slices inside each generation, the equality of lifetime utility (postulated, unless he proved it from his axioms and I missed it) creates a reverse gradient between generations and brings the sled to rest. In other words, if everybody prefers to enjoy utility while young, the present old should help the present young, to the same extent that the future old should help themselves, the present young.

This seems to me to violate intuitive justice, observed political behavior, and common sense, forcing me to justify intergenerational stewardship more awkwardly, as a collective trust that transcends the commonsense interest of individuals. And, while I certainly believe in a wider social justice than just desserts “based solely on . . . labor,” it remains the case that many forms of enjoyment presuppose labor, by somebody, and that at any given time the older living generation has done a lot more of it. “What has posterity ever done for us?”

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Joshua W. Burton 04.29.12 at 11:33 pm

Consider, too, that a zero social discount, at least as between time slices within a single cohort, would be somewhat surprising for the actuarial reason. If I’d just as happily eat my candy at 70 instead of 50, why not wait until I’m 110?

Per John Q @13, we don’t know that the safe zero-growth interest rate is inconsistent with zero. But as there are several lines of plausibility argument that it might be positive, I’d like to have a theory of intergenerational justice that works in the case of nonzero discount — and he claims in the paper to have one. Hence, my persistence.

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Tim Wilkinson 04.30.12 at 1:39 am

J.W.B: The paper explicitly endorses actuarial social discounting, but on the basis of the prospects for survival of society (or other ‘all bets are off’ eventualities), which is obviously not to be derived from some aggregation of projected individual survival rates. (I’ve questioned whether this should be treated as a discount factor separate from other (subjective-) probabilistic discounting, but nothing else in the paper depends on doing so anyway, and in any case that is not your objection).

The paper then addressenon-irrational individual time-discounting as an own-age-based feature of individuals’ preference profiles. I’ve (no doubt ignorantly, or at least ineptly) questioned whether this is aptly treated as ‘discounting’ and thus encapsulated in a single discount factor.

But with actuarial (and more generally probabilistic) discounting and own-age-preference both accounted for, what further kind of individual discounting do you think JQ should be accommodating at a social level?

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Consumatopia 04.30.12 at 1:39 am

This whole argument puzzles me. To me, selfishness is harder to overcome than short-sightedness: on the ladder of enlightenment, first I realize that my future utility matters as much as my present utility, then I realize that other people’s utility matters as much as my utility. There’s no principled reason why I would care about all people alive today equally, but not all people who will be alive eventually equally. Unselfish shortsightedness is incoherent.

There might be selfish, prudential reasons why should worry more about people alive today, but those would also point me towards caring more about what certain subsets of powerful people think than everyone equally. And that certainly matches “observed political behavior”, as Burton puts it–we care about the present more than the future in the same way that we care about American voters more than African children. Because we’re jerks.

To put it another way, I never feel bad when I see someone lacking a cigarette. Suppose a smoker knows that smoking causes cancer. They choose present pleasure over future health. But perhaps when they are old, they will regret that decision and wish they had chosen future health. Unselfish shortsightedness assumes the young smoker was correct–that if I see people valuing utility now over utility in the future, that means utility is inherently worth less in the future. But often that perspective is reversed-people may regret taking pleasures in the past that cause them diminished pleasure in the present. When people are evaluating their pasts, do they apply the same time preferences that they applied when they made forward looking decisions? Not typically, in my experience. Therefore using the preferences “revealed” by forward looking decisions to justify inter-generational distributions is nonsense–there is no reason to think the future will look upon our decisions the same way we do, and while we didn’t decide when we were born, we do decide when they are born.

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Joshua W. Burton 04.30.12 at 2:44 am

Tim Wilkinson @118: But with actuarial (and more generally probabilistic) discounting and own-age-preference both accounted for, what further kind of individual discounting do you think JQ should be accommodating at a social level?

None; that and (instantaneous) equal worth between living generations gets me where I don’t really want to go. As @30, 37, eta is eta.

If both generation T and T+1 have own-age preference discounting, and if this discounting or any substantial part of it reflects a pure individual time preference shared by all players, then equal value for T’s and T+1′s present utility flow implies Nordhaus-like discounting of future generations’ lifetime utility, which JQ rejects (without obviously contesting any of the inputs) @56. My son’s future $100 is worth present $50 (to him), which is worth present $50 to me (by flow utilitarianism) which is worth past $25 to young me, and so on down to the bottom of the sledding hill. Replace flow utilitarianism with lifespan-integrated utilitarianism and the backslope at step 2 stops the sled, but we also get lifespan-integrated healthcare choices, and Zeke Emanuel lost that one to Gov. Palin in a very public fight that brought “death panels” into American political discourse. (Not that the point was coherently or honestly argued, of course, but from the way the soundbites played, it is clear that most Americans implicitly reject integrated utilitarianism in favor of something like flow utilitarianism, when presented with a naked chance to weight grandma against a younger person.)

As you say, actuarial discounting of societal risks should probably be weighted as a matter of policy by (long, slow) institutional mortality, rather than by individual revealed preference. I get to this stance by reifying our institutions as things in themselves, with preferences that can’t be derived from individual mortal agents. I came into this hoping that Prof. Quiggin could get there directly from his representative agents, without assuming lifetime egalitarianism up front.

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Joshua W. Burton 04.30.12 at 3:12 am

Consumapedia @119: Unselfish shortsightedness is incoherent.

Very astute psychological analysis here. But, again, the shortsightedness of own-age preference is not purely irrational; there is a real, actuarial reason for the young smoker to outvote the (possibly already killed by a bus) old cancer sufferer, util for util. In a whole society of mortals, this actuarial slope stretches into an exponential between generations, if we allow unselfish handoff at present instantaneous utility value. Not just because we’re jerks, but because the math is jerking us.

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JW Mason 04.30.12 at 3:34 am

If both generation T and T+1 have own-age preference discounting, and if this discounting or any substantial part of it reflects a pure individual time preference shared by all players, then equal value for T’s and T+1’s present utility flow implies Nordhaus-like discounting of future generations’ lifetime utility

I don’t see why this is so. The social discount rate is not just an aggregation of the individual discount rates.

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Joshua W. Burton 04.30.12 at 4:02 am

I don’t see why this is so. The social discount rate is not just an aggregation of the individual discount rates.

Isn’t it? Provided, that is, that we equate utility endowment (as utils/time) between any two living individuals at any instant, the whole world acts like a lot of individuals patched together like one of those lives-of-notables timeline charts you see in high school classrooms. Now, I’m not sure whether you mean by the social discount rate “what we all will tend to do with our own money” or “what responsible institutions should do with entrusted money.” I absolutely agree that the latter should look nothing like the piecewise manifold of individual imprudence. But, ideally, I’d like a reason why that doesn’t assume the consequent. Otherwise, I’m left with a view like this: the National Park Service and the NOAA should take the long view, and indeed the public sector as a whole should do all it can to bail back the tide of individual shortsightedness; but, for individuals investing privately, the tide is a rational optimization. I don’t like that very much.

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JW Mason 04.30.12 at 4:23 am

Isn’t it?

No, it isn’t.

, I’m not sure whether you mean by the social discount rate “what we all will tend to do with our own money” or “what responsible institutions should do with entrusted money.”

The second, obviously.

, I’m left with a view like this: the National Park Service and the NOAA should take the long view, and indeed the public sector as a whole should do all it can to bail back the tide of individual shortsightedness; but, for individuals investing privately, the tide is a rational optimization. I don’t like that very much.

Why not? Seems perfectly reasonable to me.

You value a dollar received by you, Joshua, in 30 years less than a dollar received today, because you may not be around to collect it. But society is not allocating goods for you personally. It is allocating goods for people in general, who certainly will be around in 30 years.

When we are acting as individuals, it is rational to take our individual mortality into account. When we are acting collectively, it is rational to take our collective immortality into account. The point seems so obvious that it seems we must be arguing about something else, but I’m not sure what.

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Joshua W. Burton 04.30.12 at 4:49 am

OK, that leaves me back where I started this thread. I want a low enough SDR to save redwoods (perhaps not low enough to save dinosaur bones), no matter how we get there.

My whole reason for engaging was the hope that JQ had a novel argument showing that (as he says in his abstract) “the only ordering consistent with utilitarianism for all people currently alive at any given point in time is one based on weighting all people equally.” This would have the advantage of setting the SDR to zero on grounds of interpersonal justice, rather than collective prudence, and might make the long view an easier sell in some contexts. Unfortunately, “utilitarianism for all people currently alive” here seems to mean lifetime utilitarianism, not instantaneous flow utilitarianism, and I don’t think many people believe that (I, for one, don’t) so the paper doesn’t knock anything down for me. I’d be open to a strong argument for lifetime utilitarianism (and hence, by JQ’s tight reasoning, for the paper’s conclusion), but I don’t find one here.

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Joshua W. Burton 04.30.12 at 5:10 am

When we are acting as individuals, it is rational to take our individual mortality into account. When we are acting collectively, it is rational to take our collective immortality into account.

To take a concrete example, I already believe that we pollute collectively (externalities belong to society), so carbon taxes should reflect a zero SDR. But primary resource extraction tends to involve private property, or public property privately leased. If I could convince myself that it is interpersonally fair to weight future lives equally to present ones (already stipulating that it is collectively prudent to do so), I would exhort oil drillers to apply a zero SDR to their pretax private activity, and would consider it a point of personal virtue to apply that rate to my own consumption of irreplaceables. As it is, I am (contra section 2.1 of JQ’s paper) undeterred from believing that fairness to my descendants requires only that I leave them the exponentially diminished share I would leave myself at their future date — while allowing that public policy will see it otherwise. In a mixed economy, this does make a difference.

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John Quiggin 04.30.12 at 5:57 am

I guess we are down to untestable psychological/philosophical claims here. I regard the comments in this thread under my name as associated with a continuing identity and motivated by a range of forward-looking concerns, at least some of which involve my personal lifetime utility. You and (in a different way, I think) Chris, disagree, but I can’t really make sense of an instantaneous/timeslice view.

As far as I can see, the only evidence we both agree to be relevant comes from market interest rates, and they strongly support my view.

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Chris Bertram 04.30.12 at 6:54 am

No, I didn’t disagree John, I was just canvassing the options.

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Tim Wilkinson 04.30.12 at 10:40 am

JQ: if one alternative isn’t ‘testable’, then neither is the other, I’d have thought. But tests for how far people have diachronic integrity are not obviously going to be any less conclusive than tests of any other proposition involving theory of mind, human motivation etc.

In any case, there are a variety of interpretative and methodological assumptions already operating in the background. Market-revealed rational prefs is one, consistent prefs over time (minimal diachronic rationality) another. These are both substantive theses about human behaviour, at least they are as soon as formal analysis comes to be applied to reality. And the former tends to support the idea that aggregate social welfare is to be determined by summing up the way individuals behave (even if we actually think they are being shortsighted), which is where JWB’s objection comes in (or rather refuses to go away) I think. Though ‘the way individuals behave’ actually stands for a theory of motivation/utility consistent with the way humans behave and some rationality postulate.

JWB: If both generation T and T+1 have own-age preference discounting, and if this discounting or any substantial part of it reflects a pure individual time preference

The idea would be that it doesn’t. I meant ‘own-age preference’ to be something like ‘everything is more fun the younger you are’, and to be reflected in a discount-like rate emerging from lifetime utility rankings. And I took this (e.g. @ 103) to be what the paper describes. (I don’t know how this relates to some eta; I don’t think I even really grasp what curve eta is the slope of anyway, and no idea why there would be a single value for it always and everywhere.)

So far as pure (irrational from a whole-person viewpoint) time pref is concerned, my own response (keeping the issue as narrow as possible, Chesterton style) would be that even if my son’s future $100 is worth present $50 (to him), that doesn’t tell us that his present $50 will be worth future $100. Maybe that would be the test for genuine youth-preference: if both Younger and Elder agree that $50 was twice as good for Gray in period t as in period t+1.

If instead we suppose Gray (ignoring changes in character) to have a ‘now’ preference, we might expect backward as well as forward discounting. Just as Younger takes from Elder, Elder would take from Younger if only it were possible to do so. And given that we are supposing some single discount rate, presumably that should apply both to prospective and retrospective discounting.

If so then (um,) either they are treated as irrational ‘contradictions’ and perhaps therefore to be disregarded, or they must in some way be reconciled, which I think means a lifetime perspective must be adopted. We then have a new dimension, time of evaluation: utilities are for consumption at t+n, as evaluated at t+m. In collapsing this 2d matrix back down to a a 1d one, presumably we average out the values over all times of evaluation, and given some handy assumptions, pure time discounting cancels itself out overall. Or something. Possibly.

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John Quiggin 04.30.12 at 8:16 pm

@Tim “Maybe that would be the test for genuine youth-preference: if both Younger and Elder agree that $50 was twice as good for Gray in period t as in period t+1.”

That’s pretty much the case I examine in the paper and show to be consistent with zero pure time preference. If people have strongly time-inconsistent preferences, such as hyperbolic discounting, my argument doesn’t work, but neither do any of the standard models, as you say.

My take on hyperbolic discounting is, roughly, that it’s significant and has real effects, but is counterbalanced by a set of heuristics and social institutions that stop it from driving big decisions. Mental accounts are one – people do hyperbolic discounting with their ready cash while still paying into a pension fund.

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John Quiggin 05.01.12 at 4:19 am

@Chris #127 Agreed. I expressed myself a bit clumsily there.

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