Discounting the future, yet again

Felix Salmon gnashes his teeth at yet another incorrect report on discounting and the Stern review, by David Leonhardt in the New York Times.

Using his discount rate and other assumptions, a dollar of economic damage prevented a century from now is roughly as valuable as 7 cents spent reducing emissions today. (In fact, it’s less than that, because Stern adds another discount rate, called delta, on top of eta.)
Leonhardt says that “spending a dollar on carbon reduction today to avoid a dollar’s worth of economic damage in 2107 doesn’t make sense” – but this is a straw man, since Stern never comes close to saying that we should do such a thing. Leonhardt also spends a lot of time on the academic qualifications of Stern’s opponents, but neglects to mention that Stern himself, a former chief economist of the World Bank, is actually a real expert on discount rates, and understands them much better than most economists do.

Salmon is right, both about the Leonhardt piece and, unfortunately, about the limited understanding of discounting issues on the part of economists in general.

Leonhardt’s error follows a column by Hal Varian which, while not strictly wrong, was ambiguous enough to lend itself to this misreading. And the same error has been made by lots of Internet commentators who have enough economics that I would have expected them to know better.

But even economists who avoid the obvious error of confusing the pure rate of time preference with the money discount rate, as Leonhardt has done, have been badly confused about this question, being led astray by a presumption that the money discount rate has to be fairly high. There are a number of reasons for this.

First, standard practice in benefit-cost analysis is to use high discount rates, often as high as 8 or 10 per cent, and this seems to work reasonably well (by no means perfectly) in terms of selecting good projects and rejecting bad ones. But this is a paradigm case of “being right for the wrong reasons”. In a typical project evaluation, the project’s proponents (in the case of infrastructure, usually engineers) have a lot of influence over the projections on which cash flows are based, and they tend to be biased upwards (mostly by ignoring things that might go wrong). By contrast, economists usually get to choose the discount rate, and they almost always go for a high rate. If an economically correct discount rate is applied to cash flow estimates with a pervasive optimism bias, too many projects will pass the test. But using a high discount rate offsets, on average, the bias in cash flow projections. This is far from a perfect approach, but it’s hard to implement a better one. However, it leads you badly astray in the case of climate change, where the big risks of unforeseen bad outcomes arise with the do-nothing option.

Second, there’s a belief that market rates of discount are high and that we should follow the market. The problem here is that the premise as false at least for the obvious choice of market rate, namely the rate of interest on high grade bonds, which has averaged about 1 or two per cent. This is much lower than the rate of return to equity, which seems to be what most economists have in mind (at this point we need to start thinking about the equity premium). But, on the face of it, the bond rate is the appropriate rate for discounting riskless flows of either cash or utility. The best way to deal with risk is not to use a risk-adjusted cash rate to convert risky cash flows into certainty equivalents using expected utility or some more general model.

Third, it’s commonly assumed that individuals display high rates of time preference, and therefore so should society. In fact, individual behaviour on this score is inconsistent, with some decisions implying unreasonably high rates of time preference and others low or negative rates. More importantly, the putative fact that individuals have high rates of time preferences implies almost nothing about the social rate of time preference, for a couple of reasons. First, individuals are mortal whereas (except for a small probability of nuclear annihilation and similar disasters) society is not. To quote Richard Tol and his co-authors in 2006 paper in Environmental Science and Policy

The PRTP is the ‘utility discount rate’,which reflects our time preference for utility. Estimates of utility discount rates for individuals are almost always positive – an estimate of 1.5% is considered plausible for the UK for instance (HMTreasury, 2003) – for the simple reason that humans prefer good things to come earlier rather than later. Given the inevitability of death for individuals, a preference for benefits to accrue earlier rather than later is entirely sensible. At the social level, however, the arguments are more nuanced, and indeed whether or not the PRTP should be equal zero has been debated by philosophers and economists for decades. Cline (2004), for example, proposes to use a zero PRTP in evaluating climate change policies. Reasonable ethical considerations suggest using a zero PRTP—a positive PRTP involves placing a lower weight on the welfare of future generations, which is impartial and contrary to intergenerational equity. However, there are also persuasive arguments for employing a very small positive PRTP.�

We can sharpen this up a bit by observing that the average annual mortality probability for adults is around 1.5 per cent, suggesting that this factor alone is sufficient to explain positive time preference.

A more fundamental problem is that individual time preference is relevant to optimal individual consumption profiles, but not to the equitable distribution of resources between different age cohorts. I doubt that many gen X-ers (certainly not the esteemed Paul Watson) will agree that, having been born earlier, baby boomers like myself are entitled to a higher weight in social welfare calculations. But there is no other coherent basis for using a positive social rate of time preference. You can’t discriminate between generations without discriminating between people who are alive at the same time.

You can read my general summary of the issues here

Note: I’ve been a bit mischievous in a couple of places above. The phrase “right for the wrong reason” is quoted by Leonhardt, and comes from Marty Weitzman’s excellent review of Stern, where he observes that Stern tends to overweight known risks as a way of dealing with unknown ones. I’m just making the point that this kind of offsetting bias is widely prevalent, and is incorporated in the unexamined assumptions of most economists on discounting.

Also, while I’ve quoted Richard Tol in support of Stern’s position (as indeed Stern did) he’s strongly criticised Stern and (on my blog) has repeatedly denounced the idea that a zero social rate of time preference could ever be appropriate. He has also claimed that the correct rate for both individuals and society is between 2 and 4 per cent, whereas the quote above suggests 1.5 per cent for individuals and either zero or “a very small positive rate” for society. I’ll leave it to Tol to reconcile these positions; I’m happy to endorse the passage I’ve quoted.

* Discounting and the social cost of carbon: a closer look at uncertainty by Jiehan Guo, Cameron J. Hepburn, Richard S.J. Tol and David Anthoff, Environmental Science & Policy, 9(3): 205-216

74 thoughts on “Discounting the future, yet again

  1. You should reference the paper as Jiehan Guo and her co-authors, she was the lead author of the paper.

  2. Hi – it is not obvious to me that the market risk premium (“MRP”) is necessarily relevant to discounting cash flows from the point of society as a whole (i.e., weighing social benefits against social costs). As I understand the Capital Asset Pricing Model (and assuming CAPM accurately describes returns on equity), a corporation’s cost of equity is the return required to compensate investors holding a diversified portfolio for the incremental non-diversifiable risk that the investor is exposed to when investing in the corporation. The cost of equity therefore only makese sense in the context of evaluating projects that compete to raise capital from the equity market. It does not seem obvious that CAPM (and therefore the MRP) is necessarily relevant to an evaluation of social costs and benefits, especially when future generations are involved. The “social discount rate” could well be higher or lower than the MRP. Until I read Professor Quiggin’s paper explaining discounting from an economist’s perspective, it was a mystery to me how the public sector would go about evaluating social costs and benefits. That said, I’m not an expert on corporate finance and discounting. Just saying it is not obvious to me that the MRP is necessarily relevant to discounting social costs and benefits.

  3. JQ, I am new to this subject in one sense and have been surrounded by it my entire career in another. The juxtaposition has sparked my interest, so I wondered if you could humor a few questions I have.

    First, you’ve given a robust case for the PRTP value that Stern uses. What about risk aversion and consumption growth- would you endorse his choices there? If so or not, to what extent is the appropriate justification ‘offsetting bias’ vs. ‘objective’ analysis. I have seen very long time series data that suggest very stable per-capita consumption growth of slightly more than 2% (though weakening sharply in the 70s and 80s). What type of impact would it have on Stern’s recommendations of using that assumption along with a somewhat higher risk aversion parameter but the same PRTP? To what extent is that sensitivity problematic?

    Two other things. First, do you think that a Ramsey formulation of discount rates is sensible at all in light of the asset return puzzles? And finally, it is my impression that the use of a US only data series to calculate risk premia raises the specter of significant survivorship/selection bias. Perhaps you can comment.

  4. David, I’ve added a full reference. I assume you didn’t mean to claim that the views I quoted should be imputed to the senior author alone.

    Given this impressively well-informed comment I assume you are pretty closely involved with the paper. Can I request that, if you intend to continue participating, you at least use a verifiable email address. If you don’t want to be identified, I’ll happily keep your name confidential, but I don’t really like debating with

  5. Apparently the IPCC thinks there is a range of choices between early, late and no mitigation. In a sense dial up your preferred climate. See for example
    What we then need are economic measures that go with each scenario eg per capita GDP under 500 ppm. It may turn out that there is a best path using several discount rates. Intuitively I think that path is mitigate hard for the next decade.

    However that’s still too technical. A better criterion is ‘what sort of world do you want your grandchildren to be living in when you pass on?’ ie zero discount for the next 20,30,40 years. The indicators might be qualitative rather than financial; not the value of the average house but whether food and energy costs prevent that generation from ever owning their home.

  6. I agree with Hermit. One way that it would be possible to investigate this argument about discount rates into future generations further is simply to ask people and get a good idea about how much people really care about the next generation. Obviously some people are going to not care at all about anything, and others are going to be in the next generation should be better than this one category, but it would be interesting to know what some of the central tendency measures are. My guess is that most of them would be around 0 — I think most people don’t want the next generation to be significantly worse off on any grounds than this one, and most people are probably willing to make quite some sacrifices to keep it this way — probably quite a bit more than the rather small estimates that are offered as to the cost.

  7. Lets do a thought experiment.
    We are the world citizens in 2030. Temperature is up by 1 degree and reduces our utility by w utiles in 2030.
    We should be compensated by those in the past who caused the damage, and lets say for the sake of argument that we are happy to be compensated with money . (We may prefer that the temperature had gone up 0.5 degrees with $y of compensation rather than 1 degree with $x of monetary compensation, in which case it’s a different ball game, but for now assume we are only asking for, and are happy with $x compensation).In a just utilitarian world the CO2 emitters of the past will have set aside money so that we can in 2030 be compensated for our utility loss. But which CO2 emitters are responsible for our utility loss and should pay to compensate us? If there had been zero CO2 emissions for the previous 10 years, then I’m guessing the temperature would probably be at 2007 levels in 2030, so therefore you could argue the 1 degree temperature rise was totally the ‘fault’ of the CO2 emitters from 2020 to 2030 so only they should pay. Or is it the fault of all CO2 emitters over the last 2 millenia, or is it 4% the fault of 2029 emitters, 4% the fault of 2028 emitters, ….. and 4% of the fault of 2007 emitters. Or should it be something else.

    When economists do the calculations of what the optimal CO2 tax should be so as to maximise intertemporal world utility, what is the implicit assumption as to which CO2 emitters in which time periods should pay? Is it, to use the example above, that the compensation for the disutility experienced in 2030 is allocated equally over all tonnes of CO2 emitted back to present day.

    Of course the optimal CO2 tax calculation has the added complication of the temperature and hence disutility of future generations being reduced because the CO2 tax reduces emissions. And this depends as JQ points out on the elasticity.
    But what I’m wondering about here is exactly which polluter should be held responsible for, and pay for the damage.
    This question doesn’t directly relate to the discounting issue, but its the question that arose as I read these posts.

  8. I’m not an expert on the CAPM, but my understanding is that a higher discount rate should be attached to risks that are correlated with the market (or alternatively, risk neutral valuations should take into account correlation with the market). Does Stern take this into account?

  9. John: This is not a bit mischievous.

    First, Guo et alii do not present any empirical evidence on the pure rate of time preference. We just restate the opinion of HM Treasury in this matter. The paper in fact does not have any position on discounting. It does a number of what-if exercises. Your interpretation of our work is completely wrong.

    Second, you repeat your “everyone thinks that the market rate of discount is high, but I have data that show this not to be the case” without showing the data or referring to a paper that has such data. Your claim was hollow at first, but the many repetitions make it ridiculous.

    As I said before, present your data and a decent analysis, submit it to the AER, and if it gets accepted I will nominate you for the Nobel Prize until you get it or die. I hope this is not interpreted as a cheap comment; empirical evidence for a low PRTP is so earth shattering that it is worthy of the big one.

  10. Richard, just to clarify, is the endorsement of zero or very small positive PRTP for social discounting, quoted above, the position of the authors (my reading) or your summary of HM Treasury? If the latter, why did you criticise Stern for inconsistency with Treasury when he adopted a very small positive PRTP?

    On your second para, I honestly believed that data on the real US bond rate was readily available and that the fact that this rate has averaged between 1 and 2 per cent was well-known. You can check the current rate here. 30-year bonds are returning 4.75 per cent nominal. The headline rate of inflation in recent years has been about 3.5 per cent and the core rate about 2.5 per cent, so the real rate is somewhere between 1.25 per cent and 2.25 per cent. For comparable historical data covering lots of countries, look at Mehra and Prescott and Siegel.

    As regards publishing in AER, my articles there so far haven’t put me in contention for the big one, but maybe you’re right about the opportunity presented in this debate. I’ll give it a go!

  11. John, HM Treasury has a Green Book that recommends a Weitzman-like discount rate for all projects by the UK Government. See reference in the Guo et al. paper. Stern deviates on two counts. He uses exponential discounting rather than hyperbolic. And he uses a low discount rate right from the start.

    Yes, bonds have low returns at present. What makes you think the market is at equilibrium? There is this big country to your north. It’s called China. It’s buying US bonds in astonishing amounts.

  12. Richard, what ever happened to “that’s the price and who am I to say”? Perhaps you should point me to the appendix with the exceptions.

    JQ, probably you should be using index linked yields (TIPS) and, in any case, the 10 year. This is the benchmark long-bond now as considerable liquidity has been drained from the 30 year vertex. TIP yields have oscillated around slightly over 2% since 2003 (with extremely little volatility of late).

    I agree with Richard though at least in the sense that using contemporaneous bond yields is demonstration of little, (though my lack of gospel faith in the efficiency of markets affords me that luxury). The fact that current bond market yields typically underpin gaga bullish arguments about equity markets strengthens my resolve in this respect. And, it has to be said, historical real rates, at least in the US, have been higher than current yields, and especially so over the last 50 years. What that says though is not clear- the same period over an international data set shows significantly negative term premia.

    It is also worth pointing out- again- that productivity growth over a very long term period is slowing somewhat, (excepting the reacceleration that has occurred, at least in the data, since the mid-90s). Combined with a substantially negative demographic input, that suggests decreased growth potential and concomitantly lower real interest rates going forward.

    JQ, since you didn’t like my previous questions, I’ll try another. Presumably the economic parameters that drive discount rates also drive observed savings behavior. Indeed, according to Weitzman, this is one of the critiques of Stern- that his parameter choices are not consistent with empirical savings behavior. Yet the savings rate in the US has been negative for 21 months straight as of yesterday- this as the economy is at full employment and with consistently robust yoy real wage gains.

    So here’s the question- who’s edict leads to government policy that maximizes social welfare: the philosopher king’s or the all-mighty consumer? Is consumer behavior represent the wisdom of the collective or does that ‘wisdom’ actually lead to our following one another like lemmings over a cliff?

  13. Majorajam, I was indeed going to mention TIPS, which tell much the same story. Actually, while nominal rates have been a lot higher over the past 50 years, real rates have been about the same.

    I need to work more on savings, but obviously our savings in the past have been sufficient to generate a growing capital stock. Of course, there’s a big debate over whether negative household savings rates here and in the US are real or a statistical illusion.

    The big question is, in a sense, not so hard to answer. Governments ultimately tend to do what voters want. I’m optimistic that voters will support a response to climate change that protects the interests of the currently young generation and of future generations, including their interest in inheriting a natural environment that hasn’t been destroyed. Richard, if I understand him correctly, doesn’t think voters will or should support such policies. We’ll all get to see over the next 20 years or so.

  14. Fair enough. I am aware of the controversy over savings rates, at least as it pertains to arguments about capital gains. It is quite conceivable that the appearance of rising net worth contributes to savings behavior- or lack thereof- but ludicrous, in my view, to suggest it represents savings, especially in the aggregate. Multiples can’t go to the moon. Furthermore, it is easy to illustrate how non-productive asset based credit growth- e.g. a leveraged buyout, a mortgage- increases appraisal based net worth without creating any wealth. The argument is so twisted it would disappear behind a corkscrew.

    I also can’t help but note the overtones of legitimation that has a wide swath of the punditry and even academia rushing to explain away unprecedented savings rates against the backdrop of sedate acceptance of inflation statistics. Never mind the exploding balance sheets and derivative and security markets, Asia is subsidizing consumer products and therefore inflation is tame.

  15. Since there’s an identity linking the current account deficit to the gap between domestic savings and investment, a lot of these concerns are implicit in my post on revising priors. I find it hard to believe all this can be sustained, but it has already lasted longer than I would have thought possible.

  16. Household saving ratios in Australia and US (I think) use NET savings/disposable income. While net saving by households is negative over quite a run of periods in both places, GROSS saving is positive.

    The difference between net and gross measures is depreciation, which value is estimated, not observed, for the good reason that most households do not calculate depreciation, say, as part of family budgeting. It is not a cash outgoing.

    Could it be that for the same reasons that we use Gross Domestic Product rather than Net Domestic Product as an indicator of growth (a technically superior indicator is hampered by measurement difficulty), we should not take notice of Net Saving, but Gross Saving?

    To loop back to the discounting discussion…. Household decision making about spend / save-invest does not take into account depreciation, especially as the largest depreciable asset, the dwelling, is actually appreciating (well, its the land the dwelling sits on, but its inseparable from the dwelling). This must surely impact on how current generations act wrt to *our childrens’ childrens’ children*.

    * This obviously dates me: its the title of a Moody Blues concept album.

  17. Health economists have been arguing about discounting for some time.
    Summary measures of population health (2002) (below) has 3 articles on discounting from p. 657 on. Murray’s review p. 677 on is particularly pertinent.

    Click to access 9241545518.pdf

    There is also evidence for time preference with regard to health from surveys.

  18. Majorajam: You do need everyting spelled out, don’t you?

    US treasury bonds are a logical place to look for the risk-free rate of return that people require. But the bond market is a market, with supply and demand that fluctuate; prices vary as a result. Therefore, it is unwise to look at the bond rate at any instant, and assume that it is equal to the long-term average bond rate.

    The present bond rate is not a reflection of the low time preference of the people of the US (who are borrowing money as if there is no tomorrow) nor is it a reflection of the low time preference of the Chinese Central Bank — it rather reflects an attempt to postpone the pain an exchange rate adjustment, and thus may be interpreted as a sign of a high time preference of the Chinese.

  19. Richard,

    There’s no question that doesn’t lend itself to a good story- my comment here as elsewhere regards your prodigious proclivity to tell one (although naive is probably a more apt modifier). To be clear, I have no qualms with your position that you cannot assume a contemporaneous yield to be equilibrious- indeed I endorsed that view in the post that you responded to. My problem is with your contradictions- to claim on the one hand to be above subjectivity while making subjective interpretations of data and history at every turn. It’s high farce, and this last was the granddaddy of them all.

    How does it go again? The Chinese Central Bank has a high time preference? Are you sure you read the tea leaves correctly? Because the last time I checked, the Chinese could buy as many dollars as they chose and still not purchase a single T-bond. Even if you didn’t make that critical distinction, surely an appropriate interpretation is that the currency intervention is an export subsidy, to be pitched down a black hole and thus evidence of a low time preference, (hardly the only such evidence- see their savings rates). As for your initial assumption, it may interest you to know that the literature has it that the effect of Chinese buying of T-bonds was estimated to depress yields around 30 basis points. Is that sufficient to make Stern’s assumptions look laughable?

    But pointing out the peculiarities of this particular naivete is beyond the point. The point is that, as a stickler on the ‘rules’, you really ought to steer clear of Pandora’s box. For if you really want to start interpreting prices through the lens of Asian currency intervention, then surely it becomes incumbent on you to examine all manner of considerations from pension fund, insurance and banking regulations, to benchmarking, to career risk, to the rise of dc plans, changes to tax law, exchange rate paradigms, restrictions on capital flows, etc. etc. etc. Each and every one of these non-return/time preference trade-off considerations affects the funding costs of the US government and others, in some cases considerably, and focusing on one because it works in the direction of your conclusions just plain makes you look silly.

    How’s that for spelling things out.

  20. I’m afraid not, JH. In fact, it will put you in contention for the IgNobels unless you have a very good market failure story to tell.

  21. Majorajam: I admit defeat. The current bond yields are clear evidence that both Americans and Chinese have a very low pure rate of time preference. I will include you in my nominations.

  22. On my way to work, I thought of an introduction to the great Majorajam and Quiggin paper:

    Since at least Aristotle, scholars have believed that people’s pure rate of time preference is substantial (and argued, apparently in vain, that it should be lower). While Aristotle based his belief on introspection and anecdotical evidence, more recent studies used sophisticated econometric techniques to reach essentially the same conclusion: People are myopic. In this paper, we add a single observation that overthrows 3,000 years of learning: People are not myopic.

    I hope this will get me an acknowledgement in the most amazing paper ever written.

  23. Why not JQ?

    One element for our time preference is that we realise $1 today can be invested and we will have more tomorrow. So we go and invest our money. And our relative preference for today’s dollar should be dictated by what we think we will have next year. That is — the expected return.

    That will be higher than the zero-risk return because we (correctly) note that some risks are worth taking. So we take double the possible return if we have 3/4 chance of getting it.

    There are additional reasons for our time preference — for example we try to fit in our spending decisions with our life plans. If we have the money now we can do that better. And of course there’s the whole dying thing. But that isn’t absolute because we do value passing on money to our children, so our personal time preference is already compassionate towards future generations.

    Of course different people have different time preferences. If you’re relatively good at investing you will have a higher time preference. If your money/time requirements are more accute (ie you’re about to starve to death) then you will have a higher time preference. But I don’t see how we get an average by assuming that everybody is an infinitely bad investor (and therefore will rationally only choose zero risk investments).

  24. JH, you’re confusing the intertemporal rate of substitution with pure time preference. This is the same error made by many of Stern’s critics.

  25. Richard, my article will begin “From Aristotle (BCE 300) to Guo, Hepburn, Tol and Anthoff 2006 scholars have argued that the rate of social time preference should be zero or very small ….” So you’ll get not only an acknowledgement but a citation!

  26. John H:

    The required/expected rate of return also includes a risk premium. That is why one would look at the risk-free rate of return.

    John Q:

    Again, Guo et al. do not argue for or against any discount rate. Jiehan just faithfully reflects the range of reasonable opinions.

  27. Hmm, in your comments to this blog you don’t seem to include “zero” in the range of reasonable opinions. Can you clarify whether or not zero is a reasonable choice for the rate of time preference in making social judgements?

  28. A zero rate of time preference has been advocated by such people as Aristotle, Augustine, Aquinas, Smith, Marx, Ramsey, Koopmans, and Majorajam. It is therefore in the range of reasonable opinions. I mean, who would call Marx unreasonable?

    My main objections are (1) that one cannot use one rate of pure time preference for climate change, and another rate for other policy; and (2) that a democratic government is constrained by the will of the people, and the 8 eminent scholars above are not representative in any sense.

  29. Richard,

    Agreed on (1), but this does not mean that they should have to use the same discount rate. As per Weitzman, if we take into account the correlation of returns to climate change spending with the overall economy, which is likely to be relatively low, the appropriate discount rate is significantly closer to the risk free rate than the equity rate appropriate for other policy. Weitzman plugs a coefficient of .5 for effect, which, given inputs I gather you would be much in favor of- the empirical risk free rate and equity risk premium- yields a Stern-esque discount rate of 1.7%.

    As per (2), I’m wondering if the paradoxical nature of steadfast observance to 3000 years of carefully chronicled myopia has occurred to you? From the sounds of it you appear to believe this is a bad thing.

    Incidentally, for my own part, my argument is not for philosopher king inputs or particular techniques for deriving empirical time preferences, but for appropriate consideration for empirical risk aversion, especially to extreme events, or more quantitatively, ex-ante uncertainty. That this leads me to conclude for policy I feel to also be morally appropriate, I put down to serendipity.

  30. Majorajam: Again, you are right. Weitzman is a great admirer of Stern, that is why is calling him names in public. Weitzman argues for a declining discount rate, and that is the same thing as a constant discount rate. My simple brain cannot see the paradox. Human nature has not changed since Aristotle, but that is only 100 generations ago.

  31. I could give two figs what Weitzman thinks of Stern. I’m pointing to relevant analysis he gave in his paper and the summary I gave is accurate- please check it for yourself. While you’re at it you can climb down and pick up your toys.

    As for Weitzman’s endorsement of a declining discount rate, it is not contradictory to the segment of his paper I summarized, merely (and rightly) speaks to uncertainty around the point estimates. I am interested you felt it necessary to bring that up, given that this line of argument favors lower estimates of constant discount rates over any horizon and more so the farther out you look, (asymptotically approaching the lower bound on r). That works against your professed outrage of Stern’s implausibly low discount rates, so here again, you’re tying yourself in knots.

    Speaking of, I’m happy to hear that your cognition of dissonance has not reached critical levels. From the sounds of it you might just come unglued if it did.

  32. Richard, if you’re opposed to philosopher kings seeking to override the democratic will of the people, why don’t you refrain from public criticism of Kyoto, which is supported by the overwhelming majority of Europeans and Australians, and even by 75 per cent of Americans in this poll. Or is this yet more cognitive dissonance?

  33. JQ — the intertemporal rate of substitution is only one element of how we determine the time preference.

    Tol — I know there is risk in investments. That’s why I said “expected” return. That is, the possible return times the probability it will happen. If you have a 50% chance of getting $100 then your expected return is $50. The fact that you’re getting a return on taking a risk isn’t important… the important issue is that $1 today is worth $1.10 tomorrow. So if I have a choice between $1 today or $1.09 tomorrow, I’ll pick $1 today. What’s wrong with this scenario?

  34. The other way around JH. The pure rate of time preference is a parameter which contributes to the determination of the intertemporal rate of substitution under given market conditions.

  35. ???

    Whatever causes the expected return I can find in the market — it isn’t just me! But I am a person who sees the market expected return and then makes decisions based on this information.

    Let’s personalise this — if you had an expected return of 10% a year (I can get you more, but that’s a different story) and you knew that you wanted to spend money in one year then what would you prefer:

    1. $100 now
    2. $105 next year

  36. I have been trying to understand how to specify “sustainability” in economic terms. You may be able to help answer some questions?

    Is seems to me that economic models are models of reality created in the minds of economists. Economists try to refine their model so that their model represents reality. It seems to work quite well when measuring transactions in the market using units of currency.

    I am involved in investing in biological systems. The transactions in biological systems could be measured in units of energy, water, nutrients and growth and death of the various interacting species. I concede that the models that biologists make of biological systems are also just models in the minds of biologists.

    However when I try to apply the concept of discounting to biological systems, I run into many inconsistencies. For example, should I spend an hour to eradicate a pest the first time I find it on my land? Or should I not worry about it until some time in the future when it eventually breeds up to a level where it causes significant economic loss of say thousands of hours per year to control?

    How far into the future is “Sustainable”? What discount rate should be applied to investments to ensure sustainability?

    Models of biological systems are a bit more complicated than models of economic systems in that we live within and are dependant on biological systems.

    As a manager of investments in infrastructure for the provision of water to produce food for humans to eat, how far into the future should I look?

    What discount rate should I use to compare two options the industry faces?
    Should we invest now to make water distribution infrastructure last into the future?
    Should we run down our infrastructure and maximise our profit to existing shareholders and not worry about the huge cost of refurbishment, some time in the distant future?

    Kev Kelly

  37. JH,

    Your hypothetical does not account for risk. If the 10% return of which you speak is ‘risk-less’- which certainly would be miraculous- then it goes without saying that you would choose option 1. If however, the 10% expected return is not risk free, and option number 2 is, then the answer is ambiguous- it falls to your own personal risk aversion.

    The ultimate rates of return available in the economy then are determined by the risk free rate, which is largely a function of economic growth potential, and the degree of social risk aversion. As there is a market for risky assets, the lower the collective preference for these, the higher the effective discount rate on their expected cash flows, the higher the required/expected returns. The market clearing discount rate for ownership interest in economic enterprise is the equity risk premium (which in equilibrium, i.e. some stable level of implied preferences, equates to the return to these investments).

    In the case of public investment or spending, the appropriate discount rate hurdle to should not be the equity risk premium, according to Tol and Quiggin amongst others, but a lower rate consistent with a government’s cost of capital, (in effect a risk spreading argument). Milton Friedman might not agree. In any case, according to portfolio theory, it is incumbent upon a pricing model to consider the degree of diversification of a project, and global warming spending is likely to be favored by a discount rate far closer to the risk free rate than the rate appropriate for equity under such an approach, (and considering the applicable time table).

    So, indeed, discounting the costs and benefits of this project is very much a problem of determining a justifiable prtp, equilibrium bond long bond yield, risk free rate, equity risk premium, aggregate income beta, etc. depending on how it is approached.

  38. I take your point that people are risk-averse. However, the fact that we choose an expected return of 10% (with some risk) over an expected return of 5% (with no risk) shows that the difference more than compensates for our risk aversion. I would suggest that it is possible to get a significantly higher rate of return than the risk-free rate with a very low level of risk and that is born out by people’s investment decisions. Most super funds invest in shares, not just government bonds.

    I wouldn’t have thought it mattered what issue was being discussed (public or private investment etc). Irrespective of who commits what action, we’re talking about the effect on normal people who will either be richer or poorer. The question is whether those people prefer $1 now or $1.05 next year.

    And the government’s cost of capital is the same as the private sectors. It’s just that the risk-free and the risky element are separated and the govt only reports the risk-free rate. The risky element will normally appear as a higher rate, which is (in part) a form of insurance against the risk. But the government self-insures. The total cost should be similar. And then you have to add the deadweight loss of the tax raised for the government spending.

    But that’s a moot point here because the issue we’re discussing isn’t an issue of government spending, but individual adjustments to changed circumstances (eg need for more insurance or higher electricity prices).

  39. You may feel ‘more than compensated’ but that misses a critical distinction between an individual investor and aggregate investment behavior. First, it will be useful to actually add the dimension of risk to your hypothetical. To keep it discrete, let’s assume the choice is between a 100% probability of 1.05 and a 75% chance of 1.1 against a 25% chance of 1.03. Now, this attractive sounding hypothetical may be a no brainer for you- you may consider that the risky asset’s increased expected return “more than compensates” you for the risk taken. But your revealed preference does not preclude others from selecting option 1. In reality, there is a continuum of investors out there, and some have what you may consider to be a remarkably low tolerance for risk.

    Adding a layer of complexity, in the real world, there is a market for risk and return profiles. That market facilities the dynamic interaction of revealed preferences with prices/discount rates and hence expected returns (in particular, investors bid up and down the price of risky investments- e.g. shares- based on preferences that can be illustrated by the above hypothetical. The higher the aggregate risk aversion, the fewer dollars/investors are interested to buy a risky asset- e.g. a share- the lower the share price, and- all else equal- the higher the earnings yield/return to your investment).

    As regards the distinction between the cost of capital for public and private projects, this is also an argument about risk- in particular Professor Quiggin’s argument (he’s got the article for free on his site if you’re interested). When one investment has a lower risk profile than another, investors/dollars will prefer the lower risk investment, and this will push up its price. Another way to say the same thing is that this lower risk investment will require a lower discount rate to ‘clear markets’ than a higher risk investment.

    Hope it helps.

  40. John. Take a look at the paper by Roger Guesnerie (Sustainable development and cost benefit analysis). He argues that long run value for a discount rate for environmental goods should be close to zero with rather non conventional but compelling arguments. Note that if the Willingness to pay of future generation for an environmental good increases dramatically with the availability of this good, this tends to support the idea of a zero discount rate in his framework. I believe that it is a reasonable assumption: Look at WTP for salmon in Ireland (where i live). In our fishery, 1 salmon was caught last year, 13 two years ago, 35 three years ago, and 2000 15 years ago. You can draw a nice curve. More and more members of this fishery go to Russia (5000 sterling a week) just to flyfish. You can also draw a nice curve. Others go to Iceland (up to 1000 dollars a day the licence only). This supports the hypothesis.

    I heard R. Tol claim that Stern’s work was an outlier. But Tol did some meta analysis with a very high selection bias (mainly his own stuff actually). I did not find him very convincing.

  41. Christophe: Can you kindly specify “very high selection bias”? As far as I know, I included every study published in English. Although the paper you refer to is quoted very often, you are the first to suggest that I overlooked some papers.

    Majorajam: Weitzman discounting is not the same as exponential discounting with a low discount rate. In fact, Weitzman starts with a high discount rate. That implies that the discount factor rapidly falls from unity.

    John H: Sorry for giving such a basic answer. On this blog, it is hard to know who actually understands something. Climate change is such a weird investment, that I prefer not to use a money discount rate (e.g., the expected return on investment) but rather go back to the first principles of myopia, risk aversion, and inequity aversion and then work up to the appropriate discount rate again.

  42. Hey Tol, you ever heard of a yield curve? How about a bond price? If you have, you should know that you can indeed express time varying exponential discount rates as a single discount factor, (or constant exponential discount rate- the yield), in the context of a particular problem.

    Weitzman produces formulations of declining exponential discount rates. The formulation which you are banging on about declines in t according to uncertainty around point estimates of Ramsey taste parameters. The second which appears to the formulation he would most closely endorse declines in t between the equity discount rate and risk free rate as configured by the correlation of the project with the economy. Both get you closer to a Stern discount rate, (and hence analytical conclusions), then it appears by your wild-eyed incredulity that you are willing to concede.

    Btw, you didn’t answer JQ’s question. If the masses know better, then certainly it is not your business to try to persuade them as regards Kyoto, etc.? Or is it that the masses know better when it suits your prejudices?

  43. To be clear, the point is that Weitzman’s discount rate formulations fatally undermine the objections to Stern’s taste parameters that denialists are so invested in (albeit while also repudiating Stern’s approach). It is furthermore that an equivalent single discount rate could be derived to approximate his formulations if someone was so inclined, and that such a comparison would come closer to substantiating Stern’s conclusions than those of his critics based on the illustrative number I cited before (1.7% at 100 years with b=.5 – a parameter that, though Weitzman didn’t get to it, should also be biased downward to reflect uncertainty and by the same logic as his formulation of Ramsey under discrete uncertainty). That illustration, given the length of time it will take for returns to emissions reductions to materialize and without even incorporating the effect of declining discount rates on the far earlier weighted net costs of emissions reductions, should speak volumes to those of us who care to listen. Whether or not that includes Richard Tol or Tim Curtain is another question entirely.

  44. Majorajam, for once I agree: I did not answer JQ #33. Here we go.

    I do not care much about stated preferences. Revealed preferences are far superior. I care even less about superficial polls. While it is true that the overwhelming majority of the people support Kyoto, it is also true that the overwhelming majority is against higher fuel prices. Take your pick. The best poll was the one that showed that 70% of US Republicans support Kyoto because they thought that Bush supports Kyoto.

    You do not need to lecture me on Weitzman discounting. I’m a professor of environmental economics, and I teach that stuff. Of course there is an equivalence. Equivalence does not mean identical, though; and equivalence in 2100 does not imply equivalence in 2010.

    Weitzman discounting has been applied to cost-benefit analysis of climate change, by the Guo et al. paper that JQ seems to like, by Newell and Pizer, by Nordhaus and Boyer, by Reilly. These four papers agree: Weitzman discounting calls for modest action on climate change, and not for Stern-like action.

  45. And revealed preferences require the sage wisdom of someone like you to uncover, right? What a happy coincidence. Professor Quiggin has pointed out that real long term bond yields in the US support Stern like discounting, but that is insufficient. Meanwhile, people being against higher fuel prices- presumably akin to their being against death by spontaneous combustion- contradicts their position on a policy with self-evidently positive and negative ramifications. Terrific. Thank heavens you were there to navigate us through the treachery of the democratic process.

    As to your simplification that other CBAs use “Weitzman discounting” and are in perfect harmony about the implications of said, it is rather insufficient, isn’t it? Because, depending on the parameter values chosen, such a methodology could yield Stern, less than Stern or even, God forbid, Tol. Presumably, there’s a bit more to it.

  46. Majorajam, pls pay attention. There is a large body of literature on revealed time preference. John Q has not contributed to that literature, and neither have I. I read it, though, but JQ did not. My contributions to the revealed preference literature has to do with tourism and trees.

    I should have been more specific. CBA, with Weitzman discounting calibrated to reproduce observed short-term discount rates, produce results that contrast Stern. Of course, one can calibrate Weitzman discounting to reproduce Stern, but that is cheating.

  47. Majorajam — you misunderstand the concept of expected value. The expected value already factors in the probability. So if you have 75% chance of getting $100 then your expected value is $75 (not $100). And I agree it’s the total return that’s important to our discussion, and that’s why it’s appropriate to look a the expected return in the market and not just for me. You correctly point out there is a market for risk/return… taking the risk-free return for the time value of money ignores this. And I fully understand risk dynamics… but you miss my point about public v private risk. If the behaviour is the same, the risk is the same. It’s just that the government can hide it’s risk-premium by self-insuring as so it looks less risky. Not true.

    Richard — I understand the instinct to not use money discount rates — it seems to imply that money is more important than the environment. But money is simply a measure. We could do the entire excercise measuring the benefits and costs in apples or utiles or haircuts… but those are inefficient stores of value to use and we already have a very easy to use option — $$. I can see no good reason (rather than emotional reason) not to use the market discount rate (+ a value for no-growth time preference).

    If we can buy people a tree now for $10 or give invest $10 (with an expected return of 100% over a generation — note: expected return) and give $20 to the next generation to buy two trees — which situation is better for the future generation? Even if the future generation buys something other than trees… they are still better off (because the other thing gives them more pleasure than two trees).

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