Guest post by Mark Freeman
On 11th January, Lord Monckton of Brenchley kindly replied (“Of discount rates and candy-canes”) to a guest post of mine on WUWT concerning Nordhaus’ choice of discount rates (“Is Nordhaus’ discount rate really too low?”, 4th January). This is a response to a number of issues around the choice of the social discount rate that Lord Monckton raises.
In my original post, I highlighted that there are two fundamentally different positions on social discount rates (SDRs). The “normative” position is concerned with how governments should discount – working it all out from first principles. Lord Stern in the Stern Review and the UK Government primarily take this approach. The “positive” position says that we should take discount rates directly from financial markets or the rates of return available to private capital. The US Government and Nordhaus largely adopt this method.
Let me start with a real risk-free normative discount rate. There are many approaches that could be taken here, but a standard extended Ramsey Rule method would be as follows. The discount rate would have three components: a utility discount rate that potentially includes a societal catastrophe adjustment + a wealth term – a precautionary savings term.
Taking these in broad-brush terms, the utility discount rate without societal catastrophe adjustment expresses (roughly) how the present value of life itself changes the further we look into the future. Many people think that life has an intrinsic value and should not be discounted. This was Stern’s view and the modal response of our experts. Christian Gollier at Toulouse uses the line “I am not a sexist, I am not a racist, and I am not a timeist” to capture this view. In this case, the appropriate utility discount rate is zero. Others argue that, in practice, we value life in other parts of the world less than in our own country. We provide little help when starvation occurs in Africa, for example, because of agent-relative ethics (see, for example, the discussion in Section 6 here). If we discount based on geographical distance, then there is an argument that we should also discount on temporal distance. There is also an argument that calculations that apply a utility discount rate of zero place too high a burden on the current generation. HM Treasury takes a utility discount rate of 0.5%, which is also our experts’ median response.
The utility discount rate might be increased to account for the possibility of societal catastrophe; society may not be around in the distant future (nuclear war / pandemics / natural disaster / etc.) to enjoy the benefits of today’s investments. Stern adds on 0.1% to the discount rate to adjust for this effect. The higher this risk the higher, not lower, the discount rate. Lord Monckton’s statement that “Laughably, Stern had assumed a 10% probability that global warming would end the world by 2100” is not quite right. Stern does assume there is a 10% probability (1-0.999100) that society will not exist in something like its current form to receive the benefits from climate change mitigation a century from now, but he does not assume that any societal collapse is caused by climate change. In his own words, it captures “the possibility of some exogenous event that would render future welfare calculations irrelevant” (p. 15 here). Second, if he had assumed a lower risk of societal collapse, then his discount rate would be lower not higher. The statement that Lord Monckton makes: “All these me-too economists choosing zero or near-zero utility discount rates and consequently submarket overall discount rates are, in effect, assuming that global warming is likely to destroy the world” is therefore not accurate.
The wealth term captures a “reverse Robin Hood” argument. Most economists believe that the world will continue to get wealthier. Given this, climate change mitigation transfers money from the relatively poorer present to the relatively richer future. The more we care about intergenerational inequality (through the elasticity of marginal utility of consumption) and/or the more we think society will get richer, then the higher the social discount rate should be. Lord Monckton states that “Stern started from the assumption that annual per-capita consumption growth would be depressed by global warming from 2.5-3% to an average of 1.3% over the 21st century.” This is true, but our responses are higher: 1.6% median real per-capita annual growth. As we state in our paper, “This is close to the 2 percent growth rate of consumption per capita in the western world for the last two centuries (Gollier 2012) and the 1.6 percent growth rate in GDP per capita over the period 1900 to 2000 in non-OECD countries (Boltho and Toniolo 1999)” (p.120). So, while these forecasts may be falsified with the benefit of hindsight, they are not obviously unrealistic at this stage, nor out of line with historical precedent.
Finally, although we may think that the future will be richer than today, we cannot be sure. There is macroeconomic uncertainty about the distant future, meaning we might be much richer or poorer as a society than we currently expect. Under a standard economic precautionary savings argument, this uncertainty drives down the discount rate. Because the precautionary savings component is generally believed to increase with the time horizon, this causes the discount rate to decrease with the maturity of the project. This is the declining discount rate effect that I briefly described in my original blog, and that HM Treasury incorporates into its guidance.
Then we come to the question of project, as opposed to macroeconomic, risk. Should social discount rates be risk-adjusted and, if so, how so for a climate change mitigation project? Historically, some Governments have used the Arrow-Lind principle to argue that all social discount rates should be risk-free irrespective of the risk of the project. This view is going out of fashion, with the French, Dutch and Norwegian governments now all incorporating a project risk premium. In my personal opinion, adding such a risk premium is appropriate.
In Lord Monckton’s post, and the original article that I responded to, reference was made to the “positivist” real 7% discount rate recommended by the OMB in the US. But let’s go back to the original documentation on this, which can be found here. First, this guidance is looking somewhat dated given the many advances in this literature over the last fifteen years. But, even taking it at face value, it states that “For regulatory analysis, you should provide estimates of net benefits using both 3 percent and 7 percent”. The 7%, they argue, is an appropriate rate when government spending displaces the use of capital in risky projects in the private sector. The 3% rate reflects a real risk-free Treasury yield for when government spending affects private consumption.
Theoretically, the 7% rate would be appropriate if (i) if governments choose to price risk in the same way as markets, and (ii) climate change mitigation projects have similar risk characteristics to the average investment in the private sector. After all, in the private sector, we do not apply the same discount rate to all projects but instead, through the Capital Asset Pricing Model, adjust for the project beta. In my opinion, neither of these assumptions obviously holds true. The Interagency Working Group on the Social Cost of Carbon felt that the 7% rate was not appropriate for climate change mitigation. The upper rate was reduced to 5% (incorporating a project risk premium) and a lower rate of 2.5% was added alongside the 3% rate. The 2.5% rate, as well as allowing for declining discount rates, reflected the theoretical possibility that climate change mitigation is a hedging (negative beta or insurance) investment and so should offer lower rates of return than are given by Treasury securities. This has been argued by some in the academic literature. A recent paper by Dietz, Gollier and Kessler, here, is the current state of the art on this question and they argue that the risk premium should be positive.
In practice, the French government allows the risk premium to rise with the project horizon because of increasing project risk over time, offsetting the declining discount rate effect of precautionary savings, meaning that the overall French social discount rate is horizon-independent at 4.5% real (for a beta=1 project). In Norway, both the risk-free component and the risk premium decline with project maturity. As a consequence, the discount rate drops from 4% at the short end to 2% at horizons of 75 years or more. The Dutch rate is 3% real, including risk. But as Dietz et al. also argue, as project beta increases so do the expected benefits of climate mitigation projects and, overall, the estimated NPV of climate change mitigation projects increase compared to a risk-free analysis.
So, what approach does HM Treasury in the UK take? It incorporates a term that combines both the risk of societal collapse (which is a component of the risk-free discount rate) and a CAPM-type risk adjustment. “The risks contained in L could, for example, be disruptions due to unforeseeable and rapid technological advances that lead to obsolescence, or natural disasters that are not directly connected to the appraisal. L also includes a small premium for ‘systemic risk’ because costs and benefits are usually positively correlated to real income per capita”. HM Treasury recommends a discount rate of 3.5% real at the short end declining to 2.5% after 75 years. See Appendix 6 for the discussion of all these matters here.
Of course, Stern argues strongly against any positivist approach. “It must surely, then, be clear that it is a serious
mistake to argue that the SDR should be anchored by importing one of the many private rates of return on the markets (or a rate from government manuals, or a rate from outside empirical studies). Yet it is a mistake that many in the literature have made … Such an approach is entirely inappropriate given the type of nonmarginal choices at issue and the risk structure of the problem, and in light of developments in modern public economics,
which encompasses social cost-benefit analysis and which takes account of many imperfections in the economy, including unrepresented consumers, imperfect information, the absence of first-best taxes, and so on” (p. 13 here). Not all agree with him on this point, Nordhaus for one, but this is a mainstream opinion.
Overall, a real risk-free social discount rate of 2% for intergenerational projects seems, to my co-authors and me, to be highly defendable. There are good arguments to add a premium onto this if you are discounting expected cash flows from risky projects, and this might get us close to 5% (we do not survey on this point). But, within the context of existing government guidance where risk premiums are included, this looks to be towards the upper estimate. This is reflected in the take-away from my first blog post that Nordhaus lies at the top end of economists’ views on these matters without being an outlier. And Dietz et al., would say that allowing for risk in the discount rate but not in the expected cash flows will bias any NPV estimate downwards. Stern, by contrast lies at the lower end of the distribution of expert opinion in a purely risk-free environment.
Mark Freeman
14th January 2019
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Once you argue for such low discount rates, you are self-evidently arguing wrongly somewhere. 2% allows you to invest in just about anything provided you assume some sort of benefit in the future, but that is – self-evidently – nonsensical.
The errors in this discussion are two-fold – they ignore opportunity cost and they massively underprice risk.
We do not have infinite resources, so opportunity cost is vital – indeed, that is why we have discount rates, to allow us to compare our use of resources. Should we spend a billion on preventing malaria or a billion on preventing climate change? Should we spend a billion getting richer or a billion preventing climate change?
Government discount rates ignore opportunity cost because doing so allows them to spend our money how they want, by assuming they have no capital constraints. But they have resource constraints – every extra doctor is one fewer policeman or teacher for example. So 2% is simply silly, because we can get higher returns elsewhere. This is then looking at IRRs rather than NPVs.
As for risk, using 2% makes no allowance that the cashflows are wrong about the benefits. The idea that investing in climate change projects is close to risk-free as investing n a US Treasury is, is absurd. There is a reasonable chance that not only will the investment not make us richer, but it will make us poorer by the wasted cost and the opportunity cost of the investment. This is obviously not a risk-free investment, yet 2% suggests that it is. Again, self-evidently it must be wrong.
Far too many clever people are spending far too much time trying to justify things that cannot be true. Our knowledge of the climate and the economy are both rudimentary, and the claim that investing very large sums based on that knowledge is close to risk-free must be false.
Well put.
+10
Agreed! +10 more!
Errors. I wonder if the error in picking a particular discount rate is small compared with the error in estimating the cost of a particular course of action.
A respected writer on railway projects always multiplies the initial cost of the project by “pi” to get the actual final cost. I am a little more conservative and use “e”, Euler’s number.
If government is involved, use the higher multiple, quantity squared.
Still too conservative David, try pi to the e.
Quantity squared? 😉
With government, we should probably square any final result to get the true cost!
I will assert that the fact that a period is long (inter-generational) should not affect the level of the discount rate. The value of the outer periods are automatically adjusted with the rate. And I assert there is no reason for a special “social” discount rate because there is no such thing as “social” spending. There is only fiscal spending. Money is not more special or less special based on what the spending is for. Nobody is trading between future lives and current lives.
Wealth is expected to increase in the future only because of investments which increase production, which are made based on the expected future benefits — adjusted with the “temporal exchange rate” that is also known as the discount rate. And we already have a very clear signal on what that temporal exchange rate should be. Furthermore, since EVERY dollar that the government spends (even the ones it makes up as it goes) comes out of the economy, there is nothing special about “government money.”
Arguments that we need to invest in climate mitigation now because of the future benefit of saving the world need to consider the competition. We might also invest in gene therapy. Or desalination technology development. Or nutrition research. So when someone asks what’s the harm in addressing climate change just because it might not turn out to be that big a deal, do they really not understand that resources expended building windmills can’t also be expended on something else that might have had an actual benefit to mankind?
Of course, Dr. Freeman is correct about Lord Monckton’s logic failures. And I’m afraid I haven’t taken the time to understand all the finer points of Dr. Freeman’s piece. (For example, a paywall hides the reason why Jensen’s Inequality might imply risk-free rates should be lower for longer terms.)
But laymen like me will nonetheless reject experts’ calculations to the extent that they have “prescriptive” or “normative” bases, because it’s a fatal conceit to think that “working it all out from first principles” is something that academics and bureaucrats—or anyone else for that matter—has the competence to do.
That’s not just ideology; it’s the experience of many visitors here who, like me, have repeatedly dug into experts’ reasoning and found it seriously flawed.
This is nonsense on steroids. Human lives that may be lost in the future are 100% speculative, unverifiable and not even identifiable. Claiming that their utility discount rate should be zero is idiotic. Over 40 million “future” humans are killed every year, possibly over 1.7 billion over the past 45 years. These are real lives, that were really killed before they were born. Their utility discount rate and that of all their potential children, grandchildren, etc. was 100%.
I wonder what “the modal response of [your] experts” would be on the utility discount rate for these future lives. How do you square a willingness to spend whatever it takes now to save speculative lives in the future, while allowing >40 million real future lives to be legally snuffed out each and every year.
+10
As Mr. Middleton says, it’s entirely consistent with the way we make other value assignments for us to distinguish between the values we assign to speculative future people and those we assign to identifiable present-day people.
Moreover, this is true even if we don’t consider the unborn to be people. Even if we knew the names and faces of every worker on a large construction project like the Grand Coulee dam, for example the value that in planning we’d place on the lives they are statistically likely to lose is less than we’d be willing to spend to save the life of a known person who is, say, trapped in a mine shaft.
Since we thus distinguish among the values we put on present, identifiable people’s lives, it’s not self-evident that ethics militates against similarly distinguishing between identifiable present and speculative future lives.
“although we may think that the future will be richer than today, we cannot be sure.”
With this post, it appears that we have fuzzy economics to augment fuzzy climate science. The risk of governments taxing and spending now to prevent future unknowns based on economists opinions is dangerous in my view. Governments taxing and forcing more expensive and unreliable energy onto a population, especially a poor population in the name of climate change will keep that population poor and less able to cope with whatever natural or unnatural disasters come their way. The future is much more likely to be richer and more resilient to disaster than today with the availability of low-cost energy.
Mark: Thanks for this authoritative and informative article. Your wrote: “Most economists believe that the world will continue to get wealthier. Given this, climate change mitigation transfers money from the relatively poorer present to the relatively richer future. The more we care about intergenerational inequality (through the elasticity of marginal utility of consumption) and/or the more we think society will get richer, then the higher the social discount rate should be.”
This clearly expresses the fundamental basis for selecting an appropriate social discount rate. However, no one seems to notice that this implies that DIFFERENT GROUPS AND DIFFERENT COUNTRIES ARE LIKELY TO COME TO DIFFERENT CONCLUSIONS (mathematically or intuitively) ABOUT AN APPROPRIATE SOCIAL DISCOUNT RATE. Having watched the economic growth of China over the past several decades, I suspect it is impossible for any developing country to fail to aspire to do the same thing. If India aspires to follow China’s footsteps, they won’t spend a lot of money today to prevent their much richer and technologically-capable descendants from being forced to adapt to climate change. And less affluent citizens of developed countries probably should reach the same conclusion.
When one looks at the path deliberately and knowingly chosen by the Chinese over the past few decade- horrendous conventional air pollution, massive environmental problems, electricity generated mostly from coal – it is obvious that they cared most about economic growth and were happy to let their richer descendants clean up the messes they have made.
On the other hand, in developed countries, liberal academics, environmentalists and others already worried about sustainability are worried that their descendants will be worse off because recent generations have plundered the planet’s resources. They feel morally obligated to leave the planet unchanged and not add to the burdens on their descendants. They calculate or intuitive a low social discount rate. However, they live in a world that isn’t likely to agree with their conclusions and almost certainly won’t do so in practice. The voluntary nationally determined commitments made for the Paris Accord illustrate this. And they are mostly dependent on aid from the developed world that is unlikely to appear on the promised scale.
In short, rising CO2 is a GLOBAL problem that can’t be successfully tackled without recognizing the legitimate local disagreements about an appropriate discount rate – most of which are easier to understand intuitively rather than mathematically.
(Even in the US, we face the certain depletion of the Social Security Trust fund in a decade – a well-understood problem that could be addressed most easily and cheaply today than a decade from now. OR today’s absurd deficit. This issues really show how much less in practice our political system values future consumption over future consumption.)
Shouldn’t discounts only be calculated when you know enough about a project to make realistic costings and predictions? Let’s leave the fuzzy uncertainties of narrow economics behind and see what science is and what it tells us so we can get a broader perspective on what is going on. In science evidence is King, and the aim of science is to formulate hypotheses based on actual evidence and not on mind constructs. Ideally these hypotheses should lead to predictions, and thus be testable. Science is never settled as it cannot seek the “truth”, it works through rational processes of observation, measurement, induction, and deduction, and it warns that both interpolations and extrapolations – especially about the future – are fraught with difficulties and uncertainties, as induction itself is (and as is deduction when it is ungoverned by observation and rationality). In particular, hypotheses should always be publicly tested for reliability, completeness and utility – discounting seems to fail these tests.
So where do constructs, such as discounting, belong? To the costings of well understood projects. Are they realistic and reliable when applied to the immensely complex and only partially understood global climate system? I doubt it and I think it is probably a waste of time to even consider them.
And the benefits of increased temperature and increased atmospheric carbon dioxide are discounted or ignored by most alarmists. Benefits include the fact that global extreme poverty has halved in the last few years. The causes for this wonderful result are many, but increased levels of atmospheric CO2 is certainly one. The price of food has decreased and the cropping rates per hectare have greatly increased – have a look at market prices and volumes internationally. Here in New Zealand we are aiming at wheat yields of an astounding 20 tonnes per hectare, and the wheat is far better than the Arawa variety of the bad old days when the State had bad agricultural incentive/disincentive schemes, as most countries still have (Aussies, take note). We also know that global cooling is bad, very bad. Even in the relatively moderate Little Ice Age, populations were devastated by disease and starvation. It was a very miserable time; may it never recur (but it will).
In my youth agricultural scientists were worried that the level of CO2 in the atmosphere was getting so low that agriculture production would fail resulting in massive starvation. On a smaller scale, local CO2 stagnation causing crops to cease photosynthesis was a real problem. We are now safe from this threat.
This is reality folks, not constructs. We should address pressing and existing problems, not rob the present to give accumulated riches to the future. People in the future will probably will be much better informed, richer and more empowered than we are. Most likely they will not need our “savings”. In any case, not all will be badly affected by even rapid sea level rise. The huge but submerged continent of Zealandia seems to be heaving its way to the surface once more: parts of New Zealand’s East Coast rose 1.5 to 11 metres last year, which will give local residents hundreds of years, if not thousands of years, protection from an encroaching sea. The take home lesson – stick to real science.
America bought Alaska in 1867 for $7.1m. That’s $58.7m in today’s money, using the same discount rate as the Stern Review.
At a discount rate of 7%, they paid $207.8bn in today’s money.
I think that shows how egregious the Stern Review was.
Alaska crude oil production from 1981-2017 was worth $385.7 billion, nominal. If I converted to 2017 USD, it would be worth a lot more.
https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=MCRFPAK1&f=A
https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=pet&s=f005071__3&f=a
All other value derived by these United States from “Seward’s Folly” is 100% lagniappe!
Thank you Dr. Freeman. I read it not for application to climate change, but to the choice of Public Private Partnerships or purely government investment in projects like hospitals or road infrastructure. It is the same debate as to whether to discount at the cost of private capital or some other rate as proposed here. In my experience our governments have wisely chosen to select P3 delivery models, by using a societal discount rate as a comparator to public delivery.