Close to zero?

In yet another round of the controversy over discounting in the Stern Report, Megan McArdle refers to Stern’s use of “a zero or very-near-zero discount rate”. Similarly Bjorn Lomborg refers to the discount rate as “extremely low” and Arnold Kling complains says that it’s a below-market rate.

So what is the discount rate we are talking about? Stern doesn’t pick a fixed rate but rather picks parameters that determine the discount rate in a given projection. The relevant parameters are the pure rate of time preference (delta) which Stern sets equal to 0.1 and the intertemporal elasticity of substitution (eta) which Stern sets equal to 1. The important parameter is eta, which reflects the fact that since people in the future will mostly be richer than us, additional consumption in the future is worth less than additional consumption now.

Given eta = 1, the discount rate is equal to the rate of growth of consumption per person, plus 0.1. A reasonable estimate for the growth rate is 2 per cent, so Stern would have a real discount rate of 2.1 per cent. Allowing for 2.5 per cent inflation, that’s equal to a nominal rate of 4.6 per cent. The US 10-year bond rate, probably the most directly comparable market rate, is currently 4.44 per cent; a bit above its long-run average in real terms. So, Stern’s approach produces a discount rate a little above the real bond rate.

Arguments about discounting are unlikely to be settled any time soon. There’s a strong case for using bond rates as the basis for discounting the future. There are also strong arguments against, largely depending on how you adjust for risk. But to refer to the US bond rate as “near-zero” of “extremely low” seems implausible, and to say it’s below-market is a contradiction in terms. It seems as if these writers have confused the discount rate with the rate of pure time preferences.

46 thoughts on “Close to zero?

  1. I think your point is worth making, but Stern (I think) uses per capita consumption growth – 1.3% (baseline) rather than your 2%.

    Also, there is a postscript to Stern available now that deals with discounting. I haven’t had a chance to read it yet but expect it will be interesting.

  2. Cost-benefit analyses that use discounting seem best suited to comparing dollars from Project A with dollars from Project B. As you point out indefinite growth in consumption is usually assumed. In this case the competing projects are business-somewhat-as-usual compared with economic mayhem due to climate change. A sustainability based approach would require an unspecified future generation to achieve prescribed amounts of food, water and energy and that the following generation has the same. In other words a physical steady state which is not discounted to present dollar values.

    I think the killer line from Stern is that CO2 costs all of us $85 per tonne. Coal users take note. However what is needed now is not financial but physical projections.

  3. I think the killer line from Stern is that CO2 costs all of us $85 per tonne.

    That is $0.085 per kilogram. Which for black coal is about $0.085 per of electricity. Which could mean roughly doubling the current retail price for electricity using a tax and then waiting for alternate technologies to bring the retail price down through substitution.

    However I doubt that it is correct to say that CO2 costs us all $85. I assume it is actually saying that $85 per tonne is the cost of avoiding the emission rather than the cost of continuing the emission. The cost of continuing could be zero (skeptics position) or it could be $50 gazillion (alarmist position).

    Also isn’t $85 dollars the merely the marginal cost for harvesting the low hanging fruit? Sorry I have not read the statement in the original context.

  4. You’ll find $85 evidently USD on p16 of the Stern executive summary
    The main report should nail down just what ‘costs’ that entails. That figure would seem to validate sensational statements such as ‘Australia’s coal industry generates over $100bn a year in pollution’. I think these big numbers don’t convey much information. More personal scenarios hit harder eg weekly grocery bill going from x% to y% of household income by 2010 due to climate change.

  5. John, I agree that the implied discount rate is not low here so your point sound. But I think there are very sound, practical arguments for discounting at low rates and for separating out ideas of time preference for consumption from ideas about interest. Suppose for example I ask you about your concern about the welfare of your children at age 50 or perhaps the children of your children at age 20. This amounts to asking you about how you might weigh the environmental consumption utility of your progeny or their kids say in 30-40 years time. Its not a hard question and most parents have some hazy idea about such valuations.

    I think as a practical matter most of us would like to see people this far into the future enjoy the same types of environmental consumptions we do now. Yet even if you discount at 2% you are harving the weight you place on such utilities. It doesn’t sound plausible to me .

    Indeed many parents discount negatively – they place greater weight on their children’s consumption welfare than their own. I notice some migrant and some low income families who make huge sacrifices so their kids will do better than they do. This again suggests very low discount rates.

    So I agree wityh your point about discounting in tthe Stern report but also believe that on matters that affect the environment of the next generation our attitudes suggest low discount rates. It should be able to conduct an experiment to test this idea.

  6. JQ — discounting is traditionally done for two reasons (1) you could invest the money and have more in the future (this is why people look at rate of return on investments such as bonds); and (2) people have a time preference for a number of other reasons (could be robbed, die, time-specific spending). A standard range in public policy analysis is 5-15%. For these two issues Stern uses a discount rate of 0.1%. That’s pretty low.

    Stern then adds the issue of the decreasing marginal utility of money and notes that future generations will be richer than us — so he adds an additional discount factor. If he wants to do that, then fine… but that doesn’t justify his 0.1% figure for the time value of money.

    Harry — your argument is self-defeating. If you care about your children then they are already in your utility function. This doesn’t imply a negative discount rate at all because of point (1) above. If you have a choice of $100 for you now or $100 for your children and you only care about your children — you’ll take the $100 now and invest it and then give it to your children. You will only accept the handout to your children if the handout is as big as the nestegg you could create by investing.

  7. You are confused John H. The question is how I value a beautiful sunset now compared to a beautiful sunset for my children in 35 years. My argument was it was unrealistic to suppose I would value it at half my valuation now. Hence I believe in social discount rates at much less than 2%.

  8. JQ: fair enough, but you do not allow for the variable terminology used by Stern, and his propensity for using one measure here and another somewhere else. For example, his Delta is sometimes the “utility discount rate� or “the annual risk of catastrophe eliminating society� (p.161) or the “pure rate of time preference�, albeit always 0.1, but it does appear in practice to be the actual discount rate that he used for discounting future costs of climate change (p.163).

    Another problem is that his equation 8 (p161) falls apart when n=1, for then it produces 0 at best. Not only that, if n=1, Ut = minus 4.9, and if n=0.9, Ut = plus 20.39, a rather violent swing, while if ignoring eq.8 when n=1, then per Stern (and JQ), Ut = ln(C)= 7.106. How very convenient to assume n=1.

    Stern’s omnipresent biases are also apparent when he constantly admits that climate warming “may� or “could� have some positive benefits, yet claims it “WILL� always have more than countervailing costs, while advancing no evidence whatsoever for the latter. Yet economic historians like Maddison aver that in reality the amazing advancement in human welfare since 1750-1800 is strongly correlated with the global warming that has occurred over the last 200 years.

  9. You are confused Harry. It doesn’t matter whether you’re talking about sunsets, cricket games or money. All of these things can be valued and brought back to a common medium for comparison. There is a price that your children would pay for a x% worse sunset, and that price should be discounted to find out what money is required now to pay your child what they demand.

  10. Yet economic historians like Maddison aver that in reality the amazing advancement in human welfare since 1750-1800 is strongly correlated with the global warming that has occurred over the last 200 years.

    Oh puh-leeze. This is precisely why economists and economic historians must restrict themselves to subject matters they have some credibility in. Not one professional biologist would begin to suggest there is a net benefit to the biosphere from ACC. There is a massively increased risk of extinction.

  11. Harry is right. If you use inherent discounting, you value a sunset of equal utility far less if it is viewed in the future than today. Of course, you can translate all that into monetary terms, as John H suggests, but you get the same answer in the end.

  12. The question is how I value a beautiful sunset now compared to a beautiful sunset for my children in 35 years.

    If we were trading the quality of tonights sunset for the quality of a sunset 35 years from now I think that we would have an easier time making such assesments. However tonights sunset will be what it will be and there is nothing much that you or I can do that will change that. Arguable we can do something about the quality of the sunset in 35 years time (eg smog policy etc) however what we must sacrifice now to influence that is not tonights sunset but something else like the money required to buy different types of cars. So a like for like comparison does not exist and we are stuck with either monetary comparisons or subjective hand waving.

    In any case I will try and watch the sunset tonight with my kids and hopefully I will still be here in 35 years to watch it with them again. I’ll let you know how it compares in 2041. Personally I like the sunset after a good bush fire.

  13. And once you translate it back into money terms it becomes obvious that sunsets aren’t the only thing that your decendents are going to be worried about. There are plenty of things we will be able to leave our children if we love them. If we don’t care — there’s no debate. If we do care — we don’t need the debate.

  14. Fro The Guardian today: “Little more than a month after the prime minister described the report into climate change by the Treasury economist Sir Nicholas Stern as the most important since Labour came to power, the chancellor’s decision to double air passenger duty and to raise duty on petrol by 1.25% was derided by environmentalists and tax experts. The £1bn tax increase amounted to less than 0.1% of GDP, compared with the 1% of GDP Sir Nicholas said would be necessary to curb carbon emissions.Last night tax experts analysing the chancellor’s figures predicted that consumer behaviour would be unchanged.
    Tony Juniper, director of Friends of the Earth, said: “Instead of putting measures to tackle climate change at the heart of the PBR, Mr Brown continues to tinker at the margins. The Stern review set out that urgent action is needed … But the chancellor’s response has been feeble.” ”

    I think the Stern review can now be safely laid to rest, as not even its progenitor believes in it. The increase of 5 quid in air passenger duty still leaves air travel far cheaper than cars trains or the underground even though air travel emits far more CO2 than the others do per person per mile. Stern puit the social cost of carbon at £85 per ton of CO2 (£314/tC); typical carbon emissions per available seat km are 24.32 grams (ANA of Japan, whose ASK were 78 billion in 2004 with total carbon emissions from all its operations of 1.81 million tonnes, or 6.63 mn tons of CO2). Brown’s aviation tax increase amounts to around £215 per tonne C so he appears to be falling short of Stern’s “social cost of carbon” let alone the much higher tax that would be required to reduce air transport in UK, so he must now be considered to be a climate sceptic.

  15. I know that this is basically an economics blog site, but there has been a general acceptance that we have a CO2 problem and as the news release below (from the ABC) implies, perhaps we need to develop a different view of “what to do”. If we accept that economic growth and population growth are the underlying causes of increased pressure on the Earth’s environment, what do we do about these? Debating the validity of Stern’s discount rate seems to be avoiding discussion of “what to do”.

    Environment planning subservient to economic growth: scientist
    The former leader of CSIRO’s resources futures program says Australia has lost the plot on environmental issues.

    Scientist Barney Foran says the State of the Environment report released yesterday shows a continuing decline of awareness and concern about the environment.

    He says it also shows Australia’s concentration on economic issues overshadows concerns about the impact of economic growth and the population increase that underpins it.

    “When you look at all the bits in the report, there’s no doubt that in just about every theme of the report, that’s six out of eight, I have the overwhelming view that we are consuming our children’s and our grandchildren’s future,” he said.

    Mr Foran, who is a visiting fellow at the Australian National University (ANU) Resource and Environmental Studies Centre, says planning for the environmental future is subservient to economic growth.

    “A wonderful graph hidden in the bowels of the report in the human settlements part shows a constant decline in environmental awareness or concern about the environment,” he said.

    “That goes down at a rapid rate of knots as our per capita GDP and our household debt goes up at a great rate of knots.”

  16. May I remind all you economists that the discount rate depends on income? Poor people (in, for example, China and India) cannot afford to weigh the environment of their grandchildren since they are busy keeping themselves alive today. They also do not participate in the market for bonds. Children are their only hope for a future stream of income (in case they live long enough to reap the benefit). And for the libertarians, maybe this means that we need a strong state to impose a high enough tax on air travel?

  17. Mel: “And for the libertarians, maybe this means that we need a strong state to impose a high enough tax on air travel?”

    What the… ???

    If anything, a lower income will create a higher discount rate.

  18. Johns right.

    Lets say you are on the brink of starvation and I offer you one loaf of bread now or ten loaves of bread a year from now. My bet is that you will take the former.

    Esentially you will take the former because if you invest it now (or rather injest it now) then you will be better off in a years time (ie probably not dead).

    This is essentially why richer people (and richer countries) will invest more in environmental protection. The rise of enviromentalism is highly correlated with the rise of affluence.

    When faced with death the future is usually heavily discounted. Although of course there are instances where people will die for a particular cause (typically so their genes may prosper).

    Discount rates imply certain risk assessments and decision costs and using a rate as it applies in one instance to other situations will not always be appropriate.


  19. Actually if Melanie had left out the last sentence (which seems incongruent) then I’d agree with her also. As it stands I don’t see how the question follows from the statement.

  20. My apologies for leaving out some steps in the old cogitational process. Only the rich have the capacity to invest in outcomes further down the track. The other 4 billion can’t afford to. Therefore we must rely on the rich to save the planet. It is interesting, however, that investment in the environment has rarely been voluntary. I’m just looking around me and seeing more investment in metaphorical jumbo jets, far outweighing the carbon markets (as evidenced by increasing emissions). Maybe they think wealth will protect them (or rather their grandchildren)?

    I do have some difficulty with the whole notion of discounting since you can only infer discount rates from the distribution of income (which it is supposed to explain). It also raises the question of what you include in the future “income” that is to be discounted. The world’s rich arguably have a very low discount rate when it comes to increasing private material wealth and a very high rate when it comes to thinking about externalities (many of which do not have a market price) that will affect their grandchildren. Since the rest of us basically cannot rely on the rich to invest the right way, transferring some of the wealth to representative government is a way to overcome the problem (i.e., impose a price on the externality).

    Terje, there are in fact plenty of environmentalists among the poor (viz, the numerous struggles in SE Asia over water-hogging golf courses, or opposition to logging where it eliminates other economic resources of value to the poor). But, individuals cannot express a preference for goods that they cannot afford. And if they cannot express their demands through political channels then they’re stuffed.

  21. But, individuals cannot express a preference for goods that they cannot afford. And if they cannot express their demands through political channels then they’re stuffed.

    “Demand” is a polyseme. In the economic sence it means something quite different than what it means in the political sence. What you have just said is that poverty is a supply problem. So they can not solve this problem in any economic sence without increasing their output. In other words they need economic growth.

  22. Getting back to the original claim on this thread by JQ that Stern’s Review did NOT use a close to zero social discount rate, he should take this up with G. Yohe in the Integrated Assessment Journal (see link in Richard Tol’s last offering elsewhere on this Blog), at p.68 Yohe states catgorically that 0.1 was the rate actually used; this confirms what Stern himself told Tol (loc.cit.), and Nordhaus likewise states that to be the case in his review of Stern (p.8, for link see Tol loc.cit.). Nordhaus adds that Stern’s report was not peer reviewed, and that its “radical revision” of previous estimates of the costs of climate change was due to “its extreme assumption about discounting” (p.6). Nordhaus shows how Stern’s discount rate explains his claim that we are already “now” incurring 20% p.a. cuts in consumption that will continue “for ever” in the absence of drastic cuts in emissions starting “now”. Nordhaus then uses his DICE model to show that the optimal emissions reduction is 6% now, 14% by 2050, and 25% by 2100, which would limit temperature increase by 2100 to 1.8C (p.15). Then Nordhaus shows that Stern’s assumptions imply that we must reduce our current world per capita consumption of US$7,600 to prevent any decline in potential per capita consumption of the world put by Stern at US$94,000 by 2200 but liable to be only US$81,000 absent drastic emissions control now…”while this (transfer from the poorer current generation to protect the much higher incomes of 2200) might be worth contemplating it hardly seems ethically compelling” (p.18). Nordhaus’s conclusion on Stern’s near-zero discounting is sobering: “Imagine the preventive war strategies that might be devised with low social discount rates. Countries might start wars today because of the possibility of nuclear proliferation a century ahead….it is not clear how the globe could long survive the calculations and machinations of zero discount rate military powers…The radical revision of the economics of climate change proposed by Stern does not arise from any new economics, science, or modeling. Rather, it depends decisively on the assumption of a near-zero social discount rate. The Review’s unambiguous conclusions about the need for extreme immediate action will not survive the substitution of discounting assumptions that are consistent with today’s market place” (pp. 20-21). What price for a correction of the opening statements in this thread?

  23. Terje, I think you just moved the goalposts. I don’t think I was discussing the way out of poverty. I thought I was discussing a case of market failure – in which poor and rich alike (but mostly the poor) have to suffer the consequences of heavy discounting of the future by the rich.

  24. Melanie,

    As stated earlier the rich will discount the future far less than the poor. I thought the bread example made that pretty clear. So in what sence are the rich “heavily discounting” the future.


  25. Terje,

    I think you’ve missed melanie’s point entirely.

    melanie doesn’t think that the “rich” are heavily discounting their own futures, rather that they’re heavily discounting your future.

    You’ll be on your own in the new world, sport, and despite your Libertarian Party credentials, you’ll be part of the underclass that you’re rabidly trying to promote.


    Feel free to whine as much as you like about my uncivil tone. I fully understand that it’s a requirement of your libertarian masters that you do so.

  26. SJ,

    If you live in Australia and you own a house then you are amoungst that group of rich people that control most of the worlds wealth. Who do you think the rich people are?


    P.S. Your uncivil tone is outrageous. Please tell my libertarian master that I said so. 🙂

  27. Terje

    Australians who own their homes do not, in any meaningful way, “control most of the world’s wealth”.

    People who inherited entire countries, on the other hand, probably do “control most of the world’s wealth”.

    You ain’t one of them, and your libertarian fantasies ain’t ever gonna make you one of them.

  28. SJ,

    There were several acticles in the media recently refering to a new report that concludes that 2% of the people on earth own 50% of the worlds wealth. The averge wealth of that elite group was US$500,000. If you want to define “rich” as people with a net worth in the billions of dollars then you are talking about an extremely tiny group of people who on aggregate control only a tiny slither of the worlds assetts.


  29. Terje,

    The news reports you saw were referring to this this report from UNU-WIDER (warning, 1.7 MB .PDF).

    It doesn’t show what you seem to think it shows.

    Firstly, it doesn’t have accurate data on the upper tail of wealth distribution:

    Like all household surveys, wealth surveys suffer from sampling and non-sampling errors. These
    are typically more serious for estimating wealth distribution than e.g. for income distributions.
    The high skewness of wealth distributions makes sampling error more severe. Non-sampling
    error is also a greater problem since differential response (wealthier households less likely to
    respond) and misreporting are generally more important than for income. Both sampling and
    non-sampling error lead to special difficulties in obtaining an accurate picture of the upper tail,
    which is of course one of the most interesting parts of the distribution (see Davies and Shorrocks,
    2000 and 2005)…

    As mentioned above, non-sampling errors include both differential response by wealth level and
    misreporting (mostly under-reporting). Wealthy households are less likely to respond to surveys.
    As found here, comparisons with HBS data generally show lower totals for most financial assets
    in surveys. This may be due to differential response and/or under-reporting by those who do

    The SCF [US Survey of Consumer Finances] design explicitly excludes people in the Forbes 400 list of the wealthiest Americans…

    So they acknowledge that the Sultan of Brunei (for example) probably didn’t respond to his survey, and that the owners of Wal-Mart (the Walton family) weren’t even asked.

    Secondly, you’re confusing ownership with control. I’ll give you two examples of why that confusion leads you to the wrong conclusion.

    Example (1): let’s take the hypothetical company XYZ Ltd. Shares in XYZ are widely held, and no individual holds more than 1%. However, the top ten shareholders all know each other and form a voting bloc. The owners of the 90% aren’t organised and half of them couldn’t give a rats. Who controls XYZ corp?

    Example (2): Rupert Murdoch’s influence (just as an obvious example) is out of all proportion to his ownership of the world’s wealth. The members of the Liverpool RSL (or the Miranda RSL, etc) probably collectively own just as much as Murdoch. Who exerts more control – Murdoch or the members of the Liverpool RSL?

  30. SJ and Terje,
    My references to the ‘rich’ were intended to refer to Exxon, Shell, BP, Gazprom, Hyundai, Sumitomo, News Corp, Toyota, CNOOC, etc, etc, etc. The large corporations are the ones which do the lion’s share of investment. It is the discount rate of these corporations – many of which are larger than whole countries – that we need to look at. They are the ones that, as SJ says, are heavily discounting your future (and mine).

  31. Melanie, I don’t know what discount rate is used by the companies you specify. However I expect they intend being around a long time. Hence the inclination to invest.

    SJ, thanks for specifying that when you say rich you are refering to billionairs. I don’t think any of the personalities you mention qualify as libertarians. However if we ever need to discuss income tax scales I’ll be sure to make sure that I keep this notion of rich in mind if we talk about where to position the top income tax threshold.

  32. Thanks for that, Terje. As if we needed any further confirmation that libertarians in general, and you in particular, are absolutely clueless about pretty much everything.

  33. SJ,

    Such relief. I’m glad you don’t sweat too much, we live in a democracy and my opinions are positioned somewhat away from the mainstream. If you agreed with me you would feel lonely. But you are quite safe where you are and you only need to humour me when you are feeling charitable.

    Libertarians just need a bone to chew on occasionally but otherwise we live quite nicely in cages just like the other suckers.


  34. Terje,

    I wouldn’t get upset – it’s a big problem with the climate change issue that unfortunately it attracts some folk who hijack the environmental cause to help them push their ‘politics of envy’ agenda. For some folk the ‘rich’ are always to blame for everything and the best solution is to slap high taxes on everything that moves. It’s an inconvenient truth that the pathway to better environmental performance is for countries to become ‘richer’, and therefore be able to afford the necessary changes.

  35. Terje said:

    “If you live in Australia and you own a house then you are amoungst that group of rich people that control most of the worlds wealth.”


    “There were several acticles in the media recently refering to a new report that concludes that 2% of the people on earth own 50% of the worlds wealth. The averge wealth of that elite group was US$500,000.”

    The former *might* be true but given that the average house value is way less than A$650,000 there needs to be a bit more proof that it really is true. BTW how many people in Australia own a house worth at least $650,000 outright, i.e. without any mortgage?

  36. Chris,

    Your point is reasonable enough but ultimately just a technicality. My key point was that if you do own a house in Australia you are representative of the well to do in this world. The worlds rich are averge suburban doctor, lawyer, engineers and professionals. So if people want to slag off at the worlds rich people they can probably find them down at the local court house, clinic or building site.

    And the context was that SJ suggested that I was going to be part of the worlds “underclass” which I found to be somewhat presumptious given that he has no clue what I am personally worth.

    More discussion on this issue is available here:-


  37. Chris:

    Terje doesn’t know enough to be able answer your question.

    According to ABS 6554.0 – Houshold Wealth and Wealth Distribution 2003/04 dated 27 April 2006 (warning, large .PDF) at page 11, the top 20% of Australian households have a net worth of at least A$655,783, which roughly equates to Terje’s figure of US$500,000.


    Way to miss the point and whine your head off again, libertarian boy. Proportion of ownership does not equal proportion of control. I read Atlas Shrugged when I was about 15. I’ve grown up and joined the “multi-millionaires who aren’t selfish bastards” club since then. What’s your excuse?

  38. Terje wrote:

    “My key point was that if you do own a house in Australia you are representative of the well to do in this world.

    Depending on what “well to do” means here, this was not the original point. i.e. either it’s not the original point or if it is then it’s still not necessarily true. Also not the original point was:

    “The worlds rich are averge suburban doctor, lawyer, engineers and professionals.”

  39. Chris,

    I am not sure what you are trying to say. It seems to be either:-

    i) Terje dones not know what his own original point was.
    ii) Terje has made a point that is wrong.
    iii) Something else.

    Please feel free to clarify.


  40. ii) Terje has made a point that is wrong

    and in attempts to show that that point is right he makes other points which, though they are right, in no way do they show that the original point is right.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s