Guest post by Mark Freeman

On 11^th 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?”, 4^th 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

14^th January 2019