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. 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. 🙂

  2. 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.

  3. 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.


  4. 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?

  5. 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).

  6. 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.

  7. 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.

  8. 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.


  9. 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.

  10. 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?

  11. 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:-


  12. 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?

  13. 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.”

  14. 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.


  15. 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.

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