“Future generations” are already here

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?

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?

“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?

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.

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.

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”.

“””
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.

“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.

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?

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!

@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.

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.)

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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?

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).

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.

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

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)

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.

_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.

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.

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.

@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.

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.

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.

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.

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?

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.

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.

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.”

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.

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.

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.

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’?

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

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).

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.

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”.

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?

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.

“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.

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

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.

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.

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

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.

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.

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.)

“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?

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.

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.

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?”

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?

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.

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.

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.

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.

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

@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.