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Sensitivity analysis

December 27th, 2006

One of the points on which economists generally agree on is that sensitivity analysis is a good thing. Broadly speaking, this means varying the (putatively) crucial parameters of a model and seeing what happens. If the results change a lot, the parameter justifies a closer look.

In the case of the Stern Review of the economics of global warming, sensitivity analysis quickly revelas that the crucial parameter is the pure rate of time preference. This is the extent to which we choose to discount future costs and benefits simply because they are in the future and (if they are far enough in the future) happening to different people and not ourselves. If like Stern, you choose a value near zero (just enough to account for the possibility that there will be no one around in the future, or at least no one in a position to care about our current choices on global warming), you reach the conclusion that immediate action to fix global warming is justified. If, like most of Stern’s critics you choose a rate of pure time preference like 3 per cent, implying that the welfare of people 90 years (roughly three generations) in the future counts for about one-sixteenth as much as the welfare of people alive today, you conclude that we should leave the problem to future generations.

So, responses to a Stern Review provide another kind of sensitivity analysis. If you don’t care (much) about future generations, you shouldn’t do anything (much) about global warming.

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  1. December 28th, 2006 at 10:09 | #1

    And, as I have argued before, the behaviour of people in investing in the upbringing of children and in their bequest behaviour suggests that they have low rates of time preference. In many cases you see people with negative rates of time preference – for example migrant (or other) families who work multiple jobs tryiing to give their kids more advantage than they had. Given mortality risks these rates of time prteference might be significantly negative. Social planning models for greenhouse issues, biodiversity conservation (and generally in conserving the environment for future generations) should have low social discount rates.

    I don’t think Frank P. Ramsay was right – social discounting at a positive rate does not necessarily imply myopia because we face a positive probability of death or of collective extinction. But the way we act in relation to our children (and in some cases our grandchildren) suggests that, as a matter of fact, social rates of time preference are often low.

  2. Paul G. Brown
    December 28th, 2006 at 11:25 | #2

    And so the Stern review reduces our dilemna to an ethical question.

    How much ‘ought’ we owe our children? How much ‘ought’ we owe our species?

    If your answer is ‘Not much’, then climate change really is a non-issue.

  3. December 28th, 2006 at 12:32 | #3

    Paul, I don’t think it is an ethical issue. If you respect individual preferences its an issue of fact. How much do we value future consumptions?

  4. still working it out
    December 28th, 2006 at 12:32 | #4

    Unless of course the critics don’t care one way or the other about time preference but are simply opportunistically attacking Stern’s most debatable point. The history of global warming criticisms suggests this is the more likely explaination.

  5. Paul G. Brown
    December 28th, 2006 at 13:53 | #5

    Harry –

    I’ve only got a minor quibble with you concerning the issues of fact. I just think we ought to carry the ball down-field a bit further.

    It seems to me that current climate policy decisions hinges rest on an an ethical dilemna because it’s not ‘our’ consumption we’re talking about here, or even the consumption of the next generation (our kids). None of my family will be around for long enough to have our consumption much reduced. So we are talking about the utility of a bunch of ‘strangers’ (‘hypothetical people’ is the term I’ve heard used in this context before) whom we will never meet.

    I agree with your observation that ‘social rates of time preference are [have been] low’, but note that our evidence only spans a single generation. Indeed, what the science of global climate change does, for the first time in history (big statement there), is to tie our behavior to outcomes 90 years ahead. Stern tries to quantify that entanglement.

    So – how are we to value the utility or prioritize the rights of these hypothetical people? This, it seems to me, is fundamentally an ethical question. (It’s also a ethical decision to defer your own consumption to support your kid’s education – and people who squander the money Grandma put aside for Pat’s college education are judged as unethical).

    My own moral instinct is to adopt a low rate of time preference in this case. But that’s just a personal preference, and I’d like to flesh out the justification a bit more. Also, from a political point of view (que Al Gore) moral arguments for doing something about climate change now carry more rhetorical weight than Stern’s numbers.

  6. December 28th, 2006 at 17:29 | #6

    Paul, I think the ideas of entropy and irreversible use of a depletable world (rather than Stern) raise the intergenerational issues. We have to make consumption decisions now which will partly determine consumption in the future.

    I think we want our kids (and the kids of our kids) to live in a world that is at least as good as ours. This suggests to me that we have low rates of vtime preference.

  7. December 28th, 2006 at 19:00 | #7

    Um… shouldn’t that be Ramsey, not Ramsay? I’m not sure myself, but that’s what I recall off the top of my head. The Ramsey Taxation fellow, anyway.

    I think the waters are further muddied by the way that beta can grow at different – often greater – rates than the discount factor. This would lead to the idea that actions now can’t always be projected very far ahead before the noise of unintended consequences swamps the intende ones. With that, you would also tend to reject too long term planning.

  8. Akshay
    December 29th, 2006 at 00:30 | #8

    Didn’t you just explain that the value of eta is relevant as well? It measures
    the force of the argument that we shouldn’t “transfer” money to richer, future
    generations. If eta = 3, this might also justify waiting for a generation
    before tackling global warming. Stern obviously does not care about this
    argument much; he sets eta = 1.

    Dasgupta therefore attacks Stern for caring little about inequality, but Dasgupta
    himself would “happily support” a climate policy paid for by OECD countries. This
    suggests Stern might be correct in separating the issues of intragenerational and
    intergenerational inequality.

    Question: What happens if I try to visualise the “adaptation” policy as a fund
    which compensates our future victims? Stern claims that this fund would have to
    have a ROI greater than that of riskless bonds to be cheaper than mitigation,
    is that correct? Translating from “ethical” discount rates to “market” rates
    has me confused somewhat.

    Clearly, attitudes towards non-quantifiable risk matter a great deal as well,
    though that would indeed take us outside of EU theory.

  9. George
    December 29th, 2006 at 04:30 | #9

    Why should we care about future generations at all? What have they ever done for us?

  10. garhane
    December 29th, 2006 at 09:32 | #10

    I live on the west coast of Canada, fellas, and I can tell you it might be a good idea tostop fussing about unethical comments on ethics. We should start doing a lot of things about “it” right now like this guy Stern says because “it” is happening right now big time. I mean the trees are falling in the gales, the rains are really something, the snow is piling up after, this follows seasons of fire in some of the forest and the spruce bud worm elsewhere. And, oh yes, I am told the Polar Bear has had it and really big chunks are splitting off from the Northern ice. What exactly are you waiting for, a message from Moses?

  11. Tam o’Shanter
    December 29th, 2006 at 11:01 | #11

    I see that JQ now accepts that Stern did indeed use a near zero discount rate but his further comments are both non sequiturs based on a fundamental misunderstanding of cost benefit analysis (shared by Stern, as already pointed out here by Tol Maddison and the links to Nordhaus).

    1. JQ: “If, like most of Stern’s critics you choose a rate of pure time preference like 3 per cent, implying that the welfare of people 90 years (roughly three generations) in the future counts for about one-sixteenth as much as the welfare of people alive today, you conclude that we should leave the problem to future generations.” This is a false conclusion. Our generation usually has an investment horizon of 30 years, which is the main reason why known PROVEN reserves of oil gold and other depletable resources are usually just 30 years worth of current consumption. But generations roll over seamlessly. Next year’s coal project in China will also be based on a 30 year horizon, and the one in 2008, to 2070 and onwards. If this 2006 generation accepted projects with a less than 3% real yield, next year’s would be out of pocket relative to the cost of funds, which is actually 3% real. Stern with his World Bank background has long since forgotten if he ever knew the importance of the cost of funds as a determinant of the discount rate. For Brown to have proposed borrowing at the real Treasury Bill rate to undertake sea defence work now for avoidance of a flood risk that even Stern and the IPCC admit will not emerge before 2100 would be the height of fiscal irresponsibility, which may well be why Stern found it expedient to leave the Treasury the day after Brown’s budget statement totally ignored his Review (other than adding the price of a glass of cheap wine to air fares).

    2. JQ: “So, responses to a Stern Review provide another kind of sensitivity analysis. If you don’t care (much) about future generations, you shouldn’t do anything (much) about global warming.” That is a false and therefore defamatory statement if it is directed at Tol and Nordhaus. Given that the worst net negative effect of climate change if any is far from imminent, and that the costs of mitigation are far higher than the costs of adaptation to any such net negative net impacts, it seems ethically defensible to see to it that the global economy is better equipped to undertake such adaptation as and when necessary than if we were all to invest now in proposals that do not meet the current test of fiscal viability because they are only worthwhile if the cost of funds is zero as per Stern and JQ. BTW, George Monbiot’s new book Heat (an excellent and very well argued read) shows clearly why mitigation is so unrealistic: aviation alone will on present trends emit enough new CO2 by 2030 to offset all feasible reductions by all other sectors, which is what leads dear George to insist that all aviation must be terminated forthwith.That is what zero rate discounting leads to!

  12. Roger Jones
    December 29th, 2006 at 11:25 | #12

    The question of discount rates is an interesting one and I agree that sensitivity analysis is required to explore the numbers (e.g. by Gary Yohe, article at http://journals.sfu.ca/int_assess/index.php/iaj/article/view/247), as well as discussion about how ethical concerns inform risk perception and rate of time preference. Such discussion needs to account for welfare today and also over time.

    We have done some analysis with the Energy Futures Forum that uses the UK Treasury Greenbook discounting rate and risk-weighting climate outcomes in a similar manner to how it was applied by Stern. Interestingly enough, our analysis suggests that even with a so-called “short run” (to 2100 rather than 2180 – 2200+) action is warranted. This is with about 3% discounting (The Green book starts at 3.5 and declines to 2.5 over time). One of the reasons why is because the reference case is very high emission/damage. We think the high emission assumption is justified because of recent data from India and China that contributes to a pathway in excess of that estimate by the International Energy Agency and at the very high end of the IPCC SRES scenarios.

    The report is very long, but can be found here: http://www.csiro.au/files/files/pb9u.pdf

    Also documented is a similarly high reference emissions case here: http://www.cfses.com/documents/climate/11_Sheehan_Jones_et_al_Climate_Change_.pdf

    One of the things we did in the EFF work was to ask, if we assess the minimum damage curve required to pay for mitigation costs to 2050 through avoided damages by 2100, how would that damage curve compare with estimates from the literature? The outcome is that it compares favourably. On that example, action would be justified in most of the possible outcomes we looked at.

    Further exploration not included in the report suggests that using a very low rate of discounting the decision is a no-brainer and that action begins to look costly towards rates of 4% to 5%. This would pan out differently with a low-growth economy – that has not been analysed yet.

    The other thing we did was to assess some biophysical measures separately because of the difficulty in valuing those. How do we value the ecological aspects of the Great Barrier Reef, for instance? There is an economic return tied to tourism, fishing and coastal protection that can be valued in monetray terms but there is also an entire ecosystem with its component species and an existence value that we may attach to the reef as a whole. I would argue that any discounting attached to coral reef ecosystems, is different to that of a climate-sensitive production system that is substitutable (e.g. regional agriculture). And the rate of time preferance we would attach to cash would be different again.

    In terms of how most people view things, they will not view them as infinitely substituable with a single discount rate. Many of the values of different systems subject to climate damages are incommensurate. This is one reason why it might be useful to assess risk separately across a range of economic, social and biophysical measures, but within a single framework, say using the likelihood of exceeding a given level of mean global warming.

    To me, applying high discount rates to long-run issues makes little sense. Will slightly more cash rich people in the future thank us for their marginal economic gains, if that future is without marine a range of lifeforms that produce carbonate shells (this is like contemplating the land without trees), iconic species, many other species, more droughts and more floods and a legacy of constantly rising sea levels over many centuries? They may consider cash for ecosystems and environmental security etc to be a poor bargain. Nor is there any guarantee that if we continue the way we are those in the future will actually be wealthier, because of the uncertainties surrounding the estimation of economic damages due to climate change. Will the application of adaptation and mitigation measures prevent people from developing their future social and economic interests, as argued by some? A rich literature now describes adaptation tied to development in least developed countries and through using methods such as those described in the UNDP Adaptation Policy Framework – This literature deliberately ties development and equity to solving the problem of climate change rather than having it in conflict with development aims.

    As mention by Akshay, adaptation funds will be required because of the un-evenness of its impacts and affect on the poor. At present we don’t know what the limits to adaptation are for different regions and sectors and, as outlined in Quiggin and Horowitz (Quiggin, J. and J. Horowitz, 2003: Costs of adjustment to climate change Australian Journal of Agricultural and Resource Economics, 47, 429-446.) costs of adaptation could be very high with high rates of climate change. Some adaptation will require a commercial rate of return (as will many market-based mitigation measures) and others will only need to return lower economic rates because of the other non-commercial gains we may value.

    Stern has very visibly opened a can of worms that only a few have cared to investigate up to now. It does seem that much of criticism is aimed at closing it up again.

    My preference is to 1. Use a risk management framework within thich we can apply subjective probabilities about future outcomes in order to explore different ways in which risk may be framed and 2. To analyse a range of risks separately by pulling the various issues apart and examine how our views of those component parts affect our view of the whole.

    Thanks to Pr Q for his role in keeping the discussion bubbling along.

  13. jquiggin
    December 29th, 2006 at 13:18 | #13

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

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

  14. Ken Miles
    December 29th, 2006 at 14:28 | #14

    Not being an economist, I’ve probably got this totally wrong, but surely a report into the economics of global warming should use a discount rate of zero (or else, a spread) and leave the rest upto policy makers.

  15. derrida derider
    December 29th, 2006 at 15:46 | #15

    Arguments about discounting are very prone to get very confused between “is” and “ought” – as Harry points out. In an area I know something about – pensions policy – this is a major cause of flawed policy. It looks like this is also quite likely to happen in areas I don’t know much about, such as global warming.

    I sometimes wonder whether we wouldn’t be better to put this more explicitly and formally in generational terms, rather than in constant or hyperbolic discount rate terms. I care greatly about the world my children will live in – after all, I love and care for them as individuals. I think I care a bit about the world their children grow up in – I’ll probably know and love them, and in any case their welfare will affect my children’s welfare. I care little about my great grandchildren’s adulthood, and not at all about their childrens’ (if only because I have no control at all over the world my children and grandchildren will make for them). Maybe we ought to be modelling all this as OLG models, as is done in growth economics and pension economics.

  16. Tam o’Shanter
    December 29th, 2006 at 15:52 | #16

    Roger Jones: I checked your link to Sheehan Jones et al, and see that there is no discussion of emissions of the aviation industry. George Monbiot’s book refers to “…calculations by the Tyndall Centre for Climate Change Research [that]aviation’s emissions alone would exceed the [UK]government’s target [of a 60% cut] for the country’s entire output of greenhouse gases in 2050 by around 134%(12). The government has an effective means of dealing with this. It excludes international aircraft emissions from the target”. Monbiot’s revised estimate this month is that “aviation will account for between 91% and 258% of all the greenhouse gases the United Kingdom will be permitted, under the [proposed] new law, to produce in 2050”. What will Australia’s situation and response be?


    JQ: call it what you will, Stern used a factor of 0.1 to compare far distant costs of climate change with near time costs of 1% of GDP. He did not use a factor of 3% for the very reason you give, that it substantially reduces values 100 years off.

  17. Paul G. Brown
    December 29th, 2006 at 16:37 | #17

    So Tam – you agree with JQ, then, and support Stern’s basic modelling approach.

    The Stern review quantifies your judgement. Because you don’t care (much) about ‘values 100 years off’, you conclude that ‘[we] shouldn’t do anything (much) about global warming’?

    Entirely rational. But is it moral?

  18. melanie
    December 29th, 2006 at 17:14 | #18

    JQ, Have you read the new CSIRO report that says the current drought is unrelated to climate change? (heard about on ABC recently?)

    Tam, If I understand the concepts correctly (far from certain), then the difference between pure time preference and discount rate is important. Poor people in China and India will go on increasing their emissions as fast as possible because, whatever their pure time preference, their discount rate is very high.

  19. Tam o’Shanter
    December 29th, 2006 at 17:51 | #19

    Paul: please read my first post on this thread, and better still Nordhaus’ commentary on Stern (17 Nov 2006) from which this quote comes: “The Review proposes using a
    social discount rate* that is essentially zero. Combined with other assumptions,
    this magnifies enormously impacts in the distant future and rationalizes deep
    cuts in emissions, and indeed in all consumption, today. If we were to
    substitute more conventional discount rates used in other global-warming
    analyses, by governments, by consumers, or by businesses, the Review’s
    dramatic results would disappear…” Nordhaus does not dismiss AGW, or the need to do something about it, but he is critical of Stern’s alarmist approach and the danger it could lead to inefficient solutions.

    * BTW here are Nordhaus’ definitions: “Discounting involves a concept called the pure rate of social time preference – I will call this “the social discount rateâ€? for short…. A zero social discount rate means that future
    generations into the indefinite future are treated equally with present
    generations; a positive social discount rate means that the welfares of future generations are reduced or ‘discounted’ compared to nearer generations”.

    Stern’s Review in effect treats a damage valued at say $100 in 2100 as equal to $100 now, whereas I believe (along with Tol and Nordhaus) that it makes no sense to invest $100 now to secure $100 in 2100 when I could invest it and get $105 in a year’s time. Constantly reinvesting to 2105 my heirs will then have $12,524, and will be well able to cope with the damage of AGW of $100 in that year. As Nordhaus notes, this kind of perverse discounting implies that we (you and me included) should give up 15% of world consumption today (the non-trivial amount of c.$7 trillion)to avoid a possible new loss from AGW of 0.01% of world income in 2200. Nordhaus also shows how Stern’s discounting has the effect of raising the optimal price of carbon now from $17 in 2005 to $159 – no wonder Brown was not sorry to see Stern depart.

  20. KY Choong
    December 29th, 2006 at 19:30 | #20

    As I understand it, critics of the Stern Review believe future costs and benefits should be discounted at a rate that the market currently requires for long term investments (“market rate”), and that this market rate is higher than the rate used by the Stern Review. If the economics of climate change is sensitive to the discount rate, it follows that, according to those critics, it is not worth investing in measures to control climate change. Is this correct? Or do the critics like Nordhaus accept that it is appropriate to invest in climate change measures even if the economics is not made out – e.g., on “ethical” grounds?

    Assuming the answer is that a positive economic case (based on market rates) is a necessary condition for investing in climate change measures, does this criteria apply not just to the current generation but to each future generation?

    Assuming that each generation is entitled to apply this criteria, what is the likelihood that each succeeding generation will decide that investing in climate change measures is not worthwhile? Is there a real prospect that human society could be headed for extinction? As I understand it, the technological structure of climate change is such that while the costs of investing in climate change measures is borne upfront by the current generation, the benefits of climate change measures will not be felt until far out into the future.

    Perhaps extinction is somewhat melodramatic. Our beloved descendants (or rather our “unbeloved” descendants) will simply have to find a way to live in the next Ice Age, which may arrive sooner rather than later. Wow, what an exciting prospect (depending on your point of view)!

  21. Richard Tol
    December 29th, 2006 at 20:31 | #21


    There are many things wrong with the Stern Review. His choice of discount rate is only one. As a person, Stern is of course allowed to use whatever discount rate he wants. As a civil servant and a government advisor, he does not have this freedom.

    I don’t know why people keep this exclusive focus on the discount rate in Stern.

    No worries: Homo sapiens will go extinct because of climate change, and greenhouse gas emissions will not cause a new ice age.

  22. SJ
    December 29th, 2006 at 21:55 | #22

    Melanie Says:

    JQ, Have you read the new CSIRO report that says the current drought is unrelated to climate change? (heard about on ABC recently?)

    You should raise this somewhere else, but in any case, there was no such report.

    Rain won’t end our problems: climate expert

    AUSTRALIANS should not stop being concerned about climate change when the drought eventually breaks, a retired climate scientist has warned.

    Barrie Hunt, the former head of the CSIRO’s climate modelling program, said there seemed to be widespread confusion about the causes of the drought sapping south-eastern Australia, with some people convinced it was entirely due to global warming.

    Using climate models to try to replicate how weather might change over 10,000 years, Mr Hunt has concluded that the drought is part of a naturally occurring cycle of dry and wet periods in Australia.

    But he said there were also clear signs that climate change was making the drought worse, with a run of record hot weather in recent years contributing to drier ground and record low run-off of rain.

    “The temperature signals we’re getting are very clear, distinct greenhouse signals,” he said. “The warming over the past 10 years, you can’t explain that. There isn’t any great variability from year to year; it’s going up and up and up. If it was natural variability you would be having years of below-average temperature.”

  23. melanie
    December 30th, 2006 at 11:19 | #23

    SJ, thanks for the clarification. Not the way the ABC news reported it!

  24. Tam o’Shanter
    December 30th, 2006 at 14:48 | #24

    Richard Tol is right, the various threads here dealing with Stern have been too narrowly focused. Stern’s claim to show that business as usual would result in falls in global GDP of “up to 20% p.a. now and forever” was endorsed all too unthinkingly by those who should have known better, including Martin Wolf of the FT who gave Stern (a friend of his) ringing endorsements in the FT and The Australian last month. Ironically the same Martin Wolf equally enthusiastically endorses (in the FT 20 Dec 06 and The Oz next day) the World Bank’s view (in its “Global Economic Prospects: managing the next wave of globalization”, http://www.worldbank.org)that the size of the world economy will double by 2030 under a business as usual scenario, with nary a mention of policies to implement Stern. Wolf adds that “neither environmental limits nor disease seems (sic) likely to halt the global economy over the next quarter of a century”. Good to see Martin come to his senses and resile from Nick’s fatuous 5-20% annual reductions in the world economy “now and forever” under BAU.

  25. December 30th, 2006 at 14:55 | #25

    Pr Q says:

    So, responses to a Stern Review provide another kind of sensitivity analysis. If you don’t care (much) about future generations, you shouldn’t do anything (much) about global warming.

    The implication is that childless people will be more sanguine about climate change. Ditto for persons with a proven short-term time horizon such as fatties, druggies and compulsive punters.

    I suspect this is true but does anyone have any poll research on this?

  26. Jill Rush
    December 31st, 2006 at 09:45 | #26

    The instinct to survive cannot be overlooked. There are those who are sanguine about climate change as they believe that their economic prosperity will be passed to their own future generations who will be able to advantage themselves accordingly ie buy property in better environments, buy security and the like. These people are likely to be many of the major decision makers unworried by massive fallouts to other gene pools. The early response to Hurricane Katrina can be seen as an example of this kind of behaviour.

    Short term survival is far more compelling than the long term survival of the species. The drought has focussed people’s minds on global warming which no warnings have ever done previously in Australia. Affects on the Arctic Ice may have a similar impact in America and Europe. Unfortunately as a species we have a history of solving one problem through the creation of another eg the use of nuclear power and its long life radioactivity where future generations are left a very big bill for our electric light today.

    As a species of nature we are compelled to propogate. Nature shows us that this can lead to extinction and/or adaptation of remnant populations when a crisis occurs. Humans have the unique ability to look to the future to minimise such catastrophes. However like our animal cousins and forebears we may not be inclined to do so despite any number of Stern warnings. Some of us will care and try to avert disaster – the question is will those who care be able to affect the result when there are so many who are unable to look beyond the next election or profit report as this impacts on short rather than long term survival?

  27. Richard Tol
    January 2nd, 2007 at 07:39 | #27

    Jill: No worries. Homo sapiens will not go extinct because of climate change.

    Besides, short term survival is essential for long term survival.

  28. Stephen L
    January 2nd, 2007 at 13:32 | #28

    Jack, I’d be very surprised if you are right that childless people are less concerned about climate change, although drug users and compulsive gamblers probably are.

    I’m not aware of any analysis of concerns about global warming correlated with having children, but I have seen data (admittedly rather out of date) that in the US Gays and Lesbians have far higher levels of concern about all environmental issues than straights. Since the proportion of gays and lesbians with children is lower than the straight population this would tend to argue against your hypothesis.

    Speaking personally I have no children, and don’t expect to have any. If anything this makes me more concerned about the fate of children who will be particularly affected by climate change – I donate a lot more to support children in poverty in the developing world than I would be able to do if I had to support my own.

  29. Tam o’Shanter
    January 2nd, 2007 at 19:26 | #29

    Reverting to sensitivity analysis, Stern’s Review states

    that “if we don’t act, the overall costs and risks of climate change will be equivalent to losing at least 5% of global GDP each year, now and forever. If a wider range of risks and impacts is taken into account, the estimates of damage could rise to 20% of GDP or more [now and forever].… Our actions now and over the coming decades could create risks … on a scale similar to those associated with the great wars and the economic depression of the first half of the 20th century.â€?’ (My emphasis and interpolation).

    Even if we take Stern’s first offer of 5%, as it is per annum as he states
    explicitly, then world GDP would be 10% of its current value by 2050; at Stern’s 20%, world GDP would be one per cent of the 2006 level in 2026.

    Stern appears at one point to be speaking in terms of consumption per capita, but if consumption is 80-100% of income/GDP, 100% for the poorest, my point stands.
    I hope JQ will be prepared to comment on this sensitivity analysis. Mt own view is that Stern and Robert Mugabe should set up a consultancy for advising on how to reduce all of us, not just the wretched Zimbabweans, to penury, and soon.

  30. January 2nd, 2007 at 22:12 | #30

    JQ’s assessment is incorrect. Discounting does not imply that we care about our children less than us (although we might). One reason for discounting is that if we had the money now we could invest it and have more in the future. Therefore, even if we cared more about the future (our own or our childrens) then we would still have a time preference.

    Further, the “care-about-the-future” analysis is in effect “intertemporal-utility-maximising” which, if consistently used, would lead to absurd conclusions that nobody would support. For example, we should all stop spending on ourselves and instead invest in capital and R&D… and the next generation should do the same… and the next generation should do the same. That would (if done properly by the necessary planning committee — unlikely) maximise total intertemporal utility. But the reality is that we have always used utility maximising for current humans.

    Luckily, this already includes consideration of future generations because people already care about their decendents, so future utility sets are already implicit in current utility sets. Quiggers & friends might wish that we cared even more (won’t anybody think of the children) but our time preference is determined by reality not by the opinions of Q&co.

    If you did want to insist on some appropriate intergenerations equity tests, surely a better test (and one without absurd conclusions) is that we try to leave the world with at least the same level of welfare as we found in it. Luckily, we will achieve this even if we do nothing about AGW… and this is admitted by the Stern Review. So with intergenerational equity considerations dealt with, we can continue to do proper economic analysis with proper discount rates and stop giving air to the economic denialists such as Stern & Quiggin. 😉

  31. January 2nd, 2007 at 22:27 | #31

    Ken — the use of discount rates isn’t an ethical issue. The time value of money is caused by two things, one can be measured and is objective in it’s size (the rate of return on investment) the other is subjective (how much you prefer doing things now). But even with the subjective element, it’s not appropriate to just let each person put in their own level of time preference.

    In doing public policy analysis you have to consider everybody’s time preference (not just your own)… and the reality is that people do have a time preference. By not including that and replacing it with your time preference you would be ignoring the reality of what people want and replacing it with what you want. That is not the appropriate way to analyse the effects of public policy.

    If you think people have the wrong time preference that’s fine. So do I. I think people value the future too much and often forget to live for the day. Too much working, not enough holidays. More to life than money. Carpe Diem and all that. But that’s my moral position and it would be wrong to add that to the economic analysis. I have to use what the time preference actually is.

  32. January 3rd, 2007 at 09:43 | #32

    I should have written “intergenerational utility maximising” instead of “intertemporal utility maximising”.

    Though experiment: How much should a caring parent leave to their children when they die?

    Under “intergenerational utility maximising” you would be obliged to work and save everything your whole life to pass on the maximum amount of money to future generations and enjoy none of it now. Quiggin is trying to imply that if you don’t do this — then you don’t care (much) about future generations.

  33. Tam o’Shanter
    January 3rd, 2007 at 22:48 | #33

    John H: great stuff! generations overlap; I have just done a quick and far from definitive analysis of the number of Test cricketers from WG Grace to SK Warne who played with somebody who played with one of them. The sequence I have is Grace-Jackson-Rhodes-Larwood-Bradman-Hutton-Benaud-Simpson-Greg Chappell-Border-Warne. Just eleven over 128 years or so. Stern and JQ simply fail to grasp the way generations transition seamlessly.

  34. January 3rd, 2007 at 23:39 | #34


    I have not read Stern but I think you have misinterpreted the quote that you have provided.

    “if we don’t act, the overall costs and risks of climate change will be equivalent to losing at least 5% of global GDP each year, now and forever.”

    I think you are reading this as saying that GDP will decline by 5% in the first year, and then decline a further 5% in the second year etc, etc.

    In fact I think the correct way to read this passage is that GDP will decline by 5% in the first year and then subsequent years will remain 5% below where it would otherwise have been (forever more). In other words that decline in output is not counter acted by any form of subsequent recovery.

    In short I think you are wrong in your assertion that:-

    “Stern and Robert Mugabe should set up a consultancy for advising on how to reduce all of us, not just the wretched Zimbabweans, to penury, and soon”.

    Perhaps it is a case of hyperbole based on a misunderstanding. 🙂


  35. January 4th, 2007 at 09:42 | #35

    Terje & Tam — I didn’t read Tam’s original comments but Terje has the correct interpretation of the data.

    Of course, the reality is that we will not lose 5% of anything now… but rather 0% now and about 3% in 100 years. But if you use the wrong discount rate and a few other tricks you can pretend that the costs will be much higher. Naughty naughty.

  36. Tam o’Shanter
    January 4th, 2007 at 11:22 | #36

    Terje and John H: here’s a letter published in the Financial Times this week which makes similar points:
    “Sir, The Stern Review’s claim to show that business as usual (i.e. in the absence of stringent policies to reverse climate change) would result in large and continuous falls in global GDP was endorsed all too unthinkingly by those who should know better, including the FT’s Martin Wolf when he gave the Stern Review ringing endorsements in November. Ironically the same Martin Wolf equally enthusiastically endorses (December 20) the World Bank’s view (in its Global Economic Prospects: managing the next wave of globalization) that the size of the world economy will double by 2030 under a business as usual scenario, with no mention of policies to implement Stern. Wolf adds that “neither environmental limits nor disease seems (sic) likely to halt the global economy over the next quarter of a centuryâ€?. Moreover the Review’s estimate “that if we don’t act, the overall costs and risks of climate change will be equivalent to losing at least 5% of global GDP each year, now and foreverâ€? shows an alarming ignorance of the arithmetic of simple interest, because if we lose 5% of national income every year, within 20 years our GDP will be about zero. Is that what Stern (and Wolf) really believe?”

    It has been suggested Stern probably meant to say that the present value today of recurring annual huge losses in the distant future at his discount rate of 0.1 would be 5-20% of GDP in 2006, 2007, and for ever. At best that is still disingenuous because Stern meant us to feel we would experience a present loss of well being equal to 5-20% of our incomes if the whole world does not now implement his proposals. But it is worse. For if World GDP was cUS$30,000 billion in 2006, 5% of that “now” is $1,500 billion. If that is the PV of climate change damage in 2100 using his social discount rate, it implies climate change cost of just $1,648 billion in 2100. That is a mere 0.5% of world GDP in that year of $305,600 billion (using a growth rate projection of 2.5% which is rather lower than the World Bank’s). Discount rates are two-edged, and Stern played fast and loose with them in order make political points as Richard Tol has noted.

  37. January 4th, 2007 at 12:09 | #37

    “Is that what Stern (and Wolf) really believe?”

    The answer is no. Sterns word choice was clearly poor, however we all do that sometimes.

  38. Tam o’Shanter
    January 4th, 2007 at 13:31 | #38

    Terje: Stern’s word choice was worse than poor, it was dishonest, involving lying with statistics to transfer damages of 0.5% of GDP in 2100 to “now” with its much smaller GDP so as to get 5-20%.

  39. jquiggin
    January 4th, 2007 at 14:19 | #39

    Stern’s word choice was spot-on; the interpretation given by the letter-writer is absurd, and therefore well worthy of being quoted by Tam. No one serious (and honest) would suggest that “5 per cent, now and for ever” means “5 per cent this year, 10 per cent next year,15 per cent the year after and so on.”

    The fact that this kind of thing is the best the do-nothing lobby can come up with speaks volumes. It’s on a par with the astrology the Lavoisier Institute relies on as an alternative to climate science.

  40. Tam o’Shanter
    January 4th, 2007 at 15:31 | #40

    JQ: Nobody did ‘suggest that “5 per cent, now and for everâ€? means “5 per cent this year, 10 per cent next year,15 per cent the year after and so on.â€?’ Kindly do your guests the favour of not putting words in their mouths. Stern’s statement of 5% losses p.a. now and forever implied in fact a compounding decline at 5% a year and was careless; the gloss of stating that all he meant to say was that a loss of 0.5% of world income in 100 years time would amount to 5% of today’s income would be fine if he had said that. He did not.

  41. jquiggin
    January 4th, 2007 at 16:35 | #41

    You can’t even get your misinterpretations straight, Tam

    “Moreover the Review’s estimate “that if we don’t act, the overall costs and risks of climate change will be equivalent to losing at least 5% of global GDP each year, now and foreverâ€? shows an alarming ignorance of the arithmetic of simple interest, because if we lose 5% of national income every year, within 20 years our GDP will be about zero. Is that what Stern (and Wolf) really believe?â€?” (emphasis added)

    The only way 5 per cent reductions will get to zero in 20 years is if they are done with simple interest, as stated in the letter. Your compound interest claim manages to misinterpret both Stern and the idiot who wrote this letter.

    To be absolutely clear, any competent economist would read “5 per cent, now and forever” as meaning (the welfare equivalent of) a permanent shift to a growth path 5 per cent below the baseline case. The fact that you don’t read it that way is evidence that the converse also holds.

  42. Tam o’Shanter
    January 4th, 2007 at 18:15 | #42

    But that is not what Stern said nor what he meant. I have it on excellent authority that he did mean the present value of loss arising in 100 years and onwards. Your “a permanent shift to a growth path 5 per cent below the baseline case” appears nowhere in the Report for there is at present no documented cost of climate change already amounting to 5% of current world GDP. On the contrary both the World Bank (according to Wolf) and the FT itself (on 30th) predict world GDP growth at around 3% and I assume you do not mean to say the baseline case is 8%.

  43. Richard Tol
    January 4th, 2007 at 21:34 | #43

    John, Tam, Terje:

    The 5% per year is an annuity. According to Stern, damage starts low and rapidly escalates. Others disagree: People are poorer and warming is more rapid before 2030 than after, according to all scenarios.

    The 5% of GDP per year is meant as the income-equivalent welfare loss. It is NOT the reduction in economic growth. Intriguingly, Stern has the correct interpretation in his model, but the incorrect interpretation in the chapter on development.

    I pity the students at the London School of Economics.

  44. Roger Jones
    January 5th, 2007 at 09:28 | #44


    could you please define the context of what “all scenarios” mean?

  45. January 5th, 2007 at 12:24 | #45

    John Quiggin,

    You seemed to have focused on Tams weak argument and avoided comment on Mr Humphreys seemingly stronger arguments. Mr Humphrey seems to be making sence and if what he says is actually flawed I for one would appreciate if you could expose any errors in his logic.


  46. Tam o’Shanter
    January 5th, 2007 at 12:39 | #46

    Terje: what do you know about it? Tol confirmed my “weak” argument. Pity also the students at UQ.

  47. jquiggin
    January 5th, 2007 at 14:47 | #47

    As regards the argument from John H. it’s badly wrong. Most obviously, intertemporal utility maximising doesn’t mean we should stop all spending on ourselves unless the rate of return or the elasticity of intertemporal substitution is infinite. I explained all this at length in my paper. As John seems to rely on this claim to derive a reductio ad absurdam, I can’t respond until he starts from a more reasonable point.

    “Pity also the students at UQ.”

    I get sick of this kind of thing from you, Tim. Readers can take a look at my CV, then yours and judge who is likely to be right when it comes to making arguments from authority.

  48. wilful
    January 5th, 2007 at 15:26 | #48

    This is perhaps far too based in the real world, not in some abstract mathematical modelling, but do the doubters really believe that there will be very little or no cost from global climate change? And that early action would be far more expensive than ameliorative action? There seems to be a serious disconnection between arguments over what formulae and figures to use and the real world, where the evidence of the costs of climate change become more apparent daily.

  49. Tam o’Shanter
    January 6th, 2007 at 07:02 | #49

    Wilful: where is the evidence of the costs of climate change that “become more apparent daily”? – like the big drop in the price of oil overnight because of the mild weather in New York?

  50. wilful
    January 6th, 2007 at 08:53 | #50

    Erm, how about the tens of millions being spent on fighting bushfires? The significant reduction in Australia’s GDP due to the severe drought? The cost of all this new water infrastructure, such as desalination plants?

  51. Tam o’Shanter
    January 6th, 2007 at 12:03 | #51

    Dear Wilful: bushfires and drought have nothing to do with “climate change”, they have ben endemic in Australia for millennia, or how do you explain the excellent rains across southern and eastern Africa over the last year and the long term trend in much of that area for increasing rainfall? More water storage would make desalination unnecessary.

  52. Richard Tol
    January 6th, 2007 at 19:51 | #52

    To Roger Jones:

    All scenarios of the World Bank, UN, IPCC and who not have population growth slowing substantially in a few decades from now. Total economic growth would slow too, and probably per capita economic growth would slow with aging. This would reduce the growth rate of energy use; only in a handful of scenarios, this is dominated by a switch to coal as the main energy source.

    And then the spectral window of carbon dioxide saturates.

    So, if you stop looking at the temperature scenarios of the IPCC, and start looking at their first derivatives, you will find that these decades are the ones with the most rapid change.

    You would need to assume massive methane or carbon dioxide releases to reverse this.

    Perhaps my “all” was a bit overdone; “almost all” is more accurate.

  53. January 7th, 2007 at 00:50 | #53

    Did I say that we would stop all spending on ourselves?

    Estimates have already been run using the Stern approach to intergenerational utility maximising showing that the appropriate savings rate is something absurdly high. True, not 100%, but high enough to be absurd. I believe Toll and others have also raised this objection.

    No other analysis is done using intergenerational utility… though most activity will impact on the currently unborn. The conclusions from intergernational utility maximisation are absurd. There is no reason to switch to this strange, unjustified and generally un-used totally revolutionary policy analysis approach.

    Certainly, switching to this radical new approach does not imply that a person cares more about their children.

    Further, even if you want to use the radical Stern/Quiggin approach, the time value of money should still include an expected cost of capital.

    I think it is dishonest to say that The quote used by Tam (which had obvious errors) is the best that the GW non-activists can do. That is patently untrue and presumably only written for it’s insult value.

  54. January 7th, 2007 at 00:59 | #54

    I did indeed say that we’d stop all spending. Mea culpa. I’d written with more nuance previously and I assumed that people would understand the reality underlying the dramatic overstatement. Obviously intergenerational-utility-maximising doesn’t imply zero consumption. At a minimum we need to eat! But it does imply implausably high levels of saving & many absurd policy ideas that nobody would accept.

    I made other points besides this one and it’s dispointing that Quiggin chose to ignore the entire arguments because of a rhetorical flourish.

  55. jquiggin
    January 7th, 2007 at 01:46 | #55

    John, I already responded to the claim by Dasgupta about extremely high savings rates, as did Brad DeLong. Dasgupta’s assumption that economic growth arises solely from capital accumulation (no technical progress) is wrong, as is the implicit assumption of an infinite supply of riskless projections yielding 4 per cent returns (we can see this from the fact that the bond rate is 2 per cent).

    Since you didn’t express yourself in terms of parametric choices, but rather with a general claim that maximising intergenerational utility implied zero consumption, I didn’t know whether this was a rhetorical flourish or a formal (wrong) claim.

    As for your claims about strange, unjustified, revolutionary approaches, I suggest you look at the large literature on intergenerational equity, including the Australian Treasury’s paper on this subject. As I pointed out already, the standard assumption in this literature that equity requires constant proportional tax rates makes sense only on the basis of something like Stern’s assumptions.

    Finally, my statement that the FT letter quoted by Tam was the best the do-nothing lobby can do was a bit unfair, but a lot of the criticism of Stern has not risen above this standard.

  56. Sinclair Davidson
    January 7th, 2007 at 09:58 | #56

    From memory, Sir Partha estimated a savings rate of 97.5% (it might have been 98.5%). Why would anyone believe we’d have any technical progress, if we were saving that amount of GDP? Indeed, the social rate of 0.1% (representing the probability of extinction) would have to increase because we’d all be extinct (from starvation).

    The biggest problem the Greenists have is their continual over-reaching.

  57. Tam o’Shanter
    January 7th, 2007 at 15:59 | #57

    Sinclair said: The biggest problem the Greenists have is their continual over-reaching.
    Exactly. My point about Stern’s discounting appears not to have been understood. Because of the 0.1 social discount rate, damages that would be only 0.5 per cent of GDP in 2100, because of its much higher level then even if the World economy grows at only 2.5 per cent a year, have the high present value of 5 per cent of today’s GDP. Sir Nicolas Stern would have been less disingenuous if he had stated simply that his estimate of costs of not preventing climate change damages would be just 0.5 per cent of likely global GDP in 2100. Our successors would be able to make appropriate adaptation to that level of damage with some ease, whereas his Review asks us to give up one per cent of our much lower level of income now to save half that proportion for our descendants.

  58. wilful
    January 7th, 2007 at 17:41 | #58

    Dear Tam: al the experts disagree with you.

    And this thread isn’t about whether the weather will change, that is (for the purposes of these arguments) a given. The question is what would the costs be. It’s so easy to point to costs already being incurred.

  59. Tam o’Shanter
    January 7th, 2007 at 19:02 | #59

    Wilful: “The question is what would the costs be”. such as? falling prices of oil as the northern hemisphere warms up? there has been NO detectable warming in the tropics, and only a small proportion of the total global population lives in the Southern. Can I suggest you start the process for acquiring a des res. dacha somewhere north of Moscow?

  60. Richard Tol
    January 7th, 2007 at 22:18 | #60

    John Q:
    It is the authority of the argument that counts, not the authority of the one that makes the argument.

    In your particular case, I would be extra careful with saying “take a look at my CV” as they might just do that. Not that this matters.

    I pity the students of the London School of Economics for two reasons, and of U Queensland for one.

    First, despite having at least 50 person years of technical support at his disposal, Nick Stern produced a report that has so many technical flaws that it would fail as a master’s thesis in economics. Someone like that is not fit to teach economics. I indeed think that it is nonsense to grant a PhD for life.

    Second, the technical errors aside, Nick Stern placed political expedience above intellectual honesty — by a selective review of the evidence, taking an extreme position on ethical matters, both without alerting the reader to this, and by refusing to do sensitivity analyses. You seem to applaud this attitude, but I think it disqualifies you and him as honest brokers of scientific knowledge. You abandoned your position as policy analysts, and adopted the position of policy advocates. Advocates have a useful role in society, but they do not belong at university.

    With professors like that, I would think twice before hiring students from LSE or UQ.

  61. January 8th, 2007 at 08:53 | #61

    Richard Tol said:

    “And then the spectral window of carbon dioxide saturates.”

    The spectral window for carbon dioxide is already saturated, which is why the response is logarithmic and not linear or higher (water vapor response to a linear increase in other forcings).

  62. jquiggin
    January 8th, 2007 at 14:53 | #62


    I find this kidn of argument pretty disappointing from you. For a start, it seems strange to say that I applaud Stern’s failure to do sensitivity analysis when commenting on a post that begins “One of the points on which economists generally agree on is that sensitivity analysis is a good thing. ”

    Next, given that you’re using emotive criticisms of opponents to push your case, you’re hardly in a position to accuse others of acting as advocates.

    Third, you’re labelling as “extreme” a view which, as you conceded in an earlier post, has a strong body of support, but which you don’t happen to like. Then you use advocacy of “extreme” positions as evidence of bias. In effect, anyone who disagrees with you cannot have a legitimate position if you argue this way

    Finally, you haven’t responded at all to my substantive point that the approach proposed by Stern yields a discount rate very close to the relevant market rate for evaluating riskless, namely the real bond rate, while the approach you propose is well above the market rate. And as Brad DeLong and Tyler Cowen have pointed out, you can’t fix this hole in your argument by appealing to uncertainty – in this context, uncertainty implies a need for more action, not less.

  63. Richard Tol
    January 8th, 2007 at 20:24 | #63


    The empirical evidence is that people and their governments have a pure rate of time preference between 2 and 4% per year (at least in rich countries); not 0.1%. Saying that Stern’s discount rate is close to the market is just hogwash.

    More generally, you came out strongly supporting the Stern Review — although you did say that perhaps he should have done some more sensitivity analysis.

  64. Chris O’Neill
    January 8th, 2007 at 20:31 | #64

    Timtam from the ministry of truth advises:

    “there has been NO detectable warming in the tropics”

    Sure. Not too many blue dots in the tropics in amongst all the red. From Observed trends and variability in land and ocean surface temperatures, BTW.

  65. Tam o’Shanter
    January 8th, 2007 at 20:44 | #65

    Chris: large swathes of tropical South America and Africa have no data in your chart, while for the Northern Territory your claimed anomaly is 2C. But the BoM shows for about half the NT +0 to +0.5, and for the rest less than +0.15, all within the SEE.

  66. jquiggin
    January 8th, 2007 at 23:10 | #66

    Richard, you still haven’t responded to my point – if the pure rate of time preference is between 2 and 4 per cent (and the elasticity of intertemporal substitution is nonzero) how can the real bond rate be between 1 and 2 per cent as it has been for most of the last century?

    Also, can you point to a summary of the literature supporting your claim?

  67. Chris O’Neill
    January 10th, 2007 at 13:08 | #67

    “large swathes of tropical South America and Africa have no data in your chart”

    “large” meaning 5 dots out of 50 odd in tropical South America and 1 dot out of 80 odd in tropical Africa.

    “while for the Northern Territory your claimed anomaly is 2C”

    NCDC’s chart shows 1C actually.

    “But the BoM shows for about half the NT +0 to +0.5, and for the rest less than +0.15”

    Slowy getting less inaccurate, but still wrong. BoM’s map show +0.5 to +1.0/century for about 40% of NT, +1.0 to +1.5/century for about 50% of NT and +1.5 to 2.0/centrury for about 10% of NT.

    I can see the level of self-delusion it takes to be a global warming denialist (as in “there has been NO detectable warming in the tropics”). You have to believe that 6 out of 130 means “large”, you have to read dots meaning 1C as 2C and you have to carelessly read contour maps.

  68. Richard Tol
    January 10th, 2007 at 23:45 | #68

    John — my earlier post did not get through

    I suggest you start with Newell and Pizer, 2003, JEEM and Evans and Sezer, 2004, Appl Econ Let, and trace the substantial empirical literature on discount rates from there

    you may trace it all the way to Aristotle’s tirade against usury — which he may not have written had the discount rate been lower


  69. jquiggin
    January 10th, 2007 at 23:59 | #69

    Richard, I know the Newell and Pizer paper, but it doesn’t have any reference to the pure rate of time preference. It uses the real bond rate as the riskless discount rate, just as I’ve suggested.

    They use a 4 per cent rate for illustrative purposes, but both the current real bond rate (about 2 per cent) and the historical average for the last 100 years or so (between 1 and 3 per cent, depending on details of the calculation) are lower than this. Assuming that rising incomes account for a discount rate of at least 2 per cent, it’s hard to see any evidence of pure time preference here.

  70. January 12th, 2007 at 09:34 | #70

    I was involved in the preparation of the intergenerational review done by Treasury and I can assure you that it does not suggest that intergenerational utility maximising is an appropriate public policy approach.

    Also, the relevant capital return is not the risk-free rate, but the expected rate. These aren’t the same thing.

  71. jquiggin
    January 12th, 2007 at 13:03 | #71

    Then why the concern about the possibility that tax rates might be significantly higher in 2050 – why not just borrow overseas to finance public expenditure now and stick the grandkids with the bill?

    It struck me at the time that the authors of the intergenerational report didn’t really understand the assumptions implicit in their analysis (for example, much the same people were advocating an 8 per cent real discount rate), and your comment suggests that this view was right.

  72. melanie
    January 12th, 2007 at 22:34 | #72

    #46“Pity also the students at UQ.�

    TimTam. Were you brainwashed at university?

  73. Richard Tol
    January 13th, 2007 at 21:46 | #73


    The pure rate of time preference is the money discount rate minus the rate of risk aversion times the per capita consumption growth.

  74. jquiggin
    January 14th, 2007 at 23:08 | #74

    To restate my point, since the real bond rate is around 2 per cent, the coefficient of risk aversion is 1 and per capita consumption growth is 2 per cent, the implied pure rate of time preference is close to zero. So Stern’s assumptions match market data. I’ve made this point quite a few times, without so far seeing a response from you.

  75. Richard Tol
    January 15th, 2007 at 03:21 | #75

    Sure, John, the pure rate of time preference is zero — this is quite a stunning discovery: 3000 years of economic theory and data proved wrong! — forget about Krugman, I will nominate you for the Nobel Prize from now on

  76. jquiggin
    January 15th, 2007 at 03:58 | #76

    Thanks for this kind nomination, Richard. Unfortunately, it appears that Ramsey, Pigou, Solow, Sen and others have beaten me to this discovery, but I’m glad that you agree (as shown by your substantive non-response) that the case for a positive rate doesn’t stand up well to scrutiny.

  77. Tam o’Shanter
    January 15th, 2007 at 10:22 | #77

    Richard Tol (13th): “The pure rate of time preference is the money discount rate minus the rate of risk aversion times the per capita consumption growth�.
    JQ (14th): To restate my point, since the real bond rate is around 2 per cent, the coefficient of risk aversion is 1 and per capita consumption growth is 2 per cent, the implied pure rate of time preference is close to zero. So Stern’s assumptions match market data. I’ve made this point quite a few times, without so far seeing a response from you.
    Truly JQ as inventor of new new math doth deserve a Nobel.
    He accepts Tol’s definition that prtp = (mdr – rar)*percapconsgrowth, and then provides data, such that apparently prtp = (2-1)*2 = 0; to lesser mortals, (2-1)*2 = 2, which is not “close to zeroâ€?. In fact JQ’s data and Tol’s algebra result in no difference between the prtp and the real bond rate as the correct discount rate of 2%.

  78. Uncle Milton
    January 15th, 2007 at 10:52 | #78


    unfortunately, your sarcasm “Truly JQ as inventor of new new math doth deserve a Nobel” fails immediately.

    “The pure rate of time preference is the money discount rate minus the rate of risk aversion times the per capita consumption growth” means:

    prtp = mdr – rar*percapconsgrowth

    So it’s prtp = 2% – 1*2% = 0

    Of course, as anyone who underatands the concepts knows, it makes no sense to create a variable (mdr – rar), as you have done, since mdr is measured in percentage points (like 2% or 3%), and rar is measured as number, like one or two.

  79. Tam o’Shanter
    January 15th, 2007 at 10:55 | #79

    Uncle: Nonsense; a rate is a rate is rate, and it is 1% for risk.

  80. Uncle Milton
    January 15th, 2007 at 11:23 | #80

    Tam, you are wrong. You are confusing a risk premium with the rate of risk aversion

    The coefficient of relative risk aversion is defined as

    rra = -cu”(c)/u'(c)

    where c is the level of consumption, u'(c) is the first derivative of the utility function, and u”(c) is thr second derivative.

    This is basic stuff.

    The classic reference for why rra is close to one is Ken Arrow (1970), Essays in the Theory of Risk Bearing, Chapter 3.

  81. Uncle Milton
    January 15th, 2007 at 11:34 | #81

    In addition, your argument falls over on your own logic.

    If, as you say, rar = 1%, then your equation

    prtp = (mdr – rar)*percapconsgrowth

    implies prtp = (2%-1%)*2% = 0.0002, which is, in fact, close to zero.

    But your equation is wrong in any case, as is your measure of rar.

    As I said at 78, the correct equation with the correct measure of rar gives prtp = 0.

  82. jquiggin
    January 15th, 2007 at 12:15 | #82

    Thanks for doing garbage pickup on this, Uncle M, but I’m afraid TimTam is a lost cause when it comes to logical reasoning of any kind.

    And while Richard Tol has the mental equipment, it seems that he’d rather engage in cheap shots like #75 than respond to a substantive point that contradicts his views.

  83. Uncle Milton
    January 15th, 2007 at 13:47 | #83

    John, I presume you know Tol and his work. Why is he so determined to play the spoiler? Could it be that Stern did not make enough references to Tol’s contributions to the field?

  84. Tam o’Shanter
    January 15th, 2007 at 13:49 | #84

    Uncle: I am intrigued by this new algebra and arithmetic (JQ is a lost cause in this area). You said:
    “prtp = (2%-1%)*2% = 0.0002, which is, in fact, close to zero”.

    Let us start with 100, then take 2% of that minus 1% of that, which (as I was no doubt wrongly taught) is 2 minus 1 which means one. Multiply that by 2% of 100, which usually equals 2, and we have 2 times one, which in my day equalled 2 and is not “in fact equal to zero”. If the prtp is an absolute number and not a rate as in your #78, then the equation is comparing mixing aples with oranges. Pity again, Milton, no doubt you are an alumnus of UQ.

  85. Uncle Milton
    January 15th, 2007 at 15:03 | #85


    You don’t start with 100.

    You start with the real risk free rate of interest, which, as a factual matter, is around 2% per year. You then subtract from that the product of the coefficient of risk aversion, which is close to one, and the rate of growth of consumption which also, as it happens, is around 2% per year.

    There is no mixing of apples and oranges. You can see for yourself the derivation of the equation for prtp in chapter 1 of any asset pricing textbook.

  86. Richard Tol
    January 15th, 2007 at 19:43 | #86

    Uncle Milton,

    According to the BBC, Stern quoted my work 63 times.


    I do not believe your numbers one bit. Maybe that is because I’m a reactionary. Your numbers do go against 3000 years of research. So, either you have done something truly spectacular and deserve a Nobel Prize — in which case I suggest that you stop blogging and start drafting a paper — or you’re just completely off.

  87. jquiggin
    January 15th, 2007 at 21:25 | #87

    “I do not believe your numbers one bit. ”

    Richard, I’ve used three numbers – the real bond rate (2 per cent), the coefficient of relative risk aversion (1) and the rate of per capita consumption growth (2 per cent) – and plugged them into a standard formula (given by you in #73) to derive the pure rate of time preference (approximately zero). Which of these numbers don’t you believe?

    If you want to disagree, the most plausible line is to claim that the real bond rate is not the proper rate of discount for riskless flows, either because of tax distortions or because of problems associated with the equity premium and risk-free rate puzzles. A case can be made this way, but it’s uncomfortable if you want to rely on market evidence to attack Stern (as, for example, Nordhaus did).

    Thanks for the advice to publish this. I am working on a paper now which will include this point.

  88. Richard Tol
    January 15th, 2007 at 22:49 | #88

    Hi John,

    The real bond rate stikes me as suspect.

    I would not write a paper that includes this point. I would write a paper on this point.


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