Of discount rates and candy-canes

“The time has come,” the Walrus said,

“To talk of many things:

Of shoes and ships and sealing-wax,

Of cabbages and kings,

And why the sea is boiling hot,

And whether pigs have wings.”

Lewis Carroll, Aliciae per speculum transitus

WUWT By Christopher Monckton of Brenchley | January 11, 2019

Dr Mark Freeman (January 4) wrote that the 5% intertemporal discount rate recommended by the Nobel-prizewinning economist William Nordhaus for appraising the net welfare loss or gain arising from investment in measures intended to abate global warming was, if anything, too high. Dr Freeman said he and his colleagues had recently published the results of a survey of almost 200 economists with “expertise in intergenerational social discount rates … to be used by governments when … determining climate change policy”. The survey had concluded that Nordhaus’ rate was too high.

In this reply, I shall begin by explaining what an intertemporal discount rate is and why it is used. The bird-in-the-hand rule states that a dollar in our billfold today is worth more to us at present than a dollar in the sticky pocket of our sticky grandson 100 years hence. To work out how much more that dollar is worth today than the day after tomorrow, one begins by estimating the flow of incomings and outgoings from today until a chosen future date. Next, one purges the figures of inflation, so that all the dollars in the ledger are at today’s prices.

Now comes the discount rate. From experience, we can predict that predicting the future is uncertain. Accordingly, if we want to reassure ourselves that a hefty investment we are thinking of making today is prudent and likely to convey a healthy net welfare gain over the chosen period, we discount the future cashflow at a chosen annual intertemporal discount rate so as to convert it to what is called “present value”. Present value is the discounted sum of the annual net inflows or outflows throughout the term of the proposal.

The higher the discount rate, the more the uncertainty there is and the less likely it is that the calculation will show our investment to be net-profitable. The reason is that the bulk of our proposed investment is upfront, in the form of capital expenditure to build our factory or railroad, while the bulk of our hoped-for reward will arrive only after the factory is delivering its shoes or ships or sealing wax, or after the railroad is carrying passengers or cargo.

As a guide, the minimum commercial overall or “social” discount rate is Nordhaus’ 5% (see Nordhaus 2008; Murphy 2008). The U.S. Office of Management and Budget uses 7%. A submarket overall discount rate appears unduly to favor future generations at the expense of our own: in practice, however, it harms future generations by making the economy in our generation less efficient, greatly reducing the inherited wealth we are able to bequeath to them.

Therefore, since most of the outgoings in a proposed investment will be in or near the present, whatever discount rate we choose will not make much difference to the present value of our proposed enterprise’s cost. It will, however, make a large difference to our income from the distant future. That is why high discount rates reduce the likelihood that our present-value calculation will show our proposed investment to be worthwhile.

The overall or “social” intertemporal discount rate comprises two parts: the utility discount rate and the consumption-growth rate. A typical commercial investment will tend to allocate half the discount rate to the former and half to the latter – say, 2.5% for each half, or 5% in all, which, approximately, is Nordhaus’ discount rate.

However, the Stern review (2006) of the economics of climate change for the then Socialist government in Britain, chose an overall discount rate of just 1.4%. 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.

Stern’s utility discount rate (also known as the pure rate-of-time preference), which describes a lower weight on the future simply because it is the future, was only 0.1%. The astonishing pretext for this absurdly low utility discount rate was not explicitly stated in the review itself, but was subsequently revealed in Dietz+ (2007), of which Stern was a co-author. Laughably, Stern had assumed a 10% probability that global warming would end the world by 2100.

Garnaut (2008), in his me-too economic report for the then Socialist government in Australia, adopted an overall discount rate similar to that of Stern. Many other economists have done likewise, as Dr Freeman points out. 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.

Which raises the questions that should always be asked by anyone proposing an intertemporal investment: How much will the proposed investment cost upfront, and what return will I eventually get for my money?

A small child entering a candy store with a handful of coins has the rationality to ask: “How many candy-canes can I buy with this, Mister?” How much global warming that will otherwise eventuate will any present or proposed abatement measure – however piously intended – actually abate, and at what unit cost?

The “integrated assessment models” used by economists in attempting to justify excessive diversion of taxpayers’ and fuel-users’ money towards attempts to make global warming go away are incapable of answering the candy-cane question. Most economists do not know enough climate science to calculate how much global warming a given mitigation measure will abate, and most climate scientists do not know enough economics to do the calculation for themselves.

Governments, panicked by shrieking, lavishly-funded environmental-fanatic lobby groups, do not trouble to ask the candy-cane question. The French Government did not ask the candy-cane question when in 2018 it proposed to inflict additional taxes amounting to $3 billion a year on gasoline and diesel.

Had M Macron asked that preliminary question, without which – as will become apparent – there is simply no point in fussing about the intertemporal discount rate, the costed answer would have revealed to him the egregious futility of his proposal. As the costed French example will amply demonstrate, no policy to mitigate global warming by taxing, trading, regulating or reducing emissions, however piously intended, is at all likely to be cost-effective solely on grounds of the expected net welfare gain from that mitigation.

The French Government had proposed to increase gasoline tax by 0.029 euros per litre and diesel tax by 0.065 euros per litre from January 2019. France uses 1.6 million barrels a day of oil (IEA). Each barrel yields ~31 U.S. gallons of fuel, of which 20 gallons are gasoline and 11 gallons are diesel (IEA). At 3.7854 litres per U.S. gallon, the product of the 44.243 billion litres annual gasoline consumption in France and the 0.029 euros per litre tax increase is 1.283 billion euros a year. The product of the 24.334 billion litres annual diesel consumption and the 0.065 euros per litre tax increase is 1.582 billion euros a year. Total additional revenue – and thus the total welfare loss occasioned to the citizenry by the Government’s proposal – would thus have been 2.865 billion euros a year.

Mean fuel tax increase is 0.042 euros per litre, or 3% of the 1.46 euros per litre mean retail price of gasoline or diesel in France prevalent at the time of the protests of winter 2018.

Fuel is a Giffen-good: demand is inelastic in the face of price increases. Raising its cost by 3% does not cut consumption by 3%. Here, 1% is optimistically assumed. Since France’s CO2 emissions from gas and diesel are ~200 million tonnes per year (International Energy Agency; worlddata.info), the proposed tax increase might cut global CO2 emissions by 2 million tonnes a year, or 0.006% of global CO2 emissions of 32.5 billion tonnes a year (IEA).

Importantly, since the mean atmospheric residence time of CO2 is ~125 yr (IPCC 2013), abatement only affects the 3 parts per million by volume per year (NOAA 2018) business-as-usual perturbation in concentration, of which 0.006% is 0.00018 parts per million by volume per year.

Radiative forcing from doubled CO2 concentration, the mean of the midrange estimates in 15 CMIP5 ensemble members (Andrews et al. 2012), is 3.346 W m^(-2). Since reference sensitivity to CO2 is an approximately logarithmic function of the proportionate change in concentration, the coefficient in the CO2 forcing function is 3.346/ln(2), or 4.83.

Reference sensitivity to doubled CO2, before allowing for temperature feedback, is the product of the CO2 forcing and the Planck sensitivity parameter, currently 0.3 C° W^(-1) m^2 (Schlesinger 1985): i.e., 0.3 x 3.346=1 C°. Since CMIP5 predicted midrange equilibrium sensitivity to doubled CO2 is 3.4 C° (Andrews 2012), the implicit midrange transfer function that allows for the operation of temperature feedback is the ratio of equilibrium to reference sensitivity: namely, 3.4 C° / 1 C°, or 3.4.

Since expected business-as-usual global CO2 concentration (NOAA 2018) at end 2019 will be 413 ppmv, the expected welfare benefit in global warming abated by the proposed French fuel tax increase would be 3.4 x 0.3 x 4.83 ln[413/(413-0.00018)], or 0.000002 C°.

The direct welfare loss arising from any strategy to mitigate global warming by abating emissions of greenhouse gases is the cost to taxpayers and consumers of fuel and power. Opportunity losses are additional. The direct welfare benefit of any such policy is the value of the global warming abated. Indirect benefits are likewise excluded here, brevitatis causa.

The ratio of the direct welfare benefit of a mitigation strategy to the warming abated by the strategy is the strategy’s unit abatement cost per Kelvin abated. Derivation of the unit abatement cost allows direct comparison to establish which – if any – of competing mitigation strategies is cost-effective.

The unit abatement cost of the French proposal is the cost of abating 1 K global warming by strategies whose benefit/cost ratios are that of the proposal: namely, the ratio of 2.865 billion euros per year to 0.000002 K, or 1.4 quadrillion euros per Kelvin abated.

The cost of abating all of the 4.2 K global warming predicted for this century on the RCP 8.5 scenario (IPCC 2013, fig. 1.25) would thus be 1.4 x 4.2=6 quadrillion euros. At 7.5 billion global population, the annual per-capita abatement cost would be 8000 euros, or approaching 90% of the 8950 euros global mean annual per-capita income in 2016 (World Bank).

The French example, by no means untypical in its high cost and low effectiveness, illustrates the principal reasons why no mitigation strategy is at all likely to deliver a net welfare benefit solely on grounds of global-warming abatement. The cost is absurdly high, but the quantum of business-as-usual CO2 emission and concentration and hence of global warming abated in return for the expenditure is necessarily very low – and low not only by comparison with the high cost but also in itself.

The above calculation assumes that, per impossibile, the midrange rate of global warming currently predicted by climate models is correct. Since that warming rate, owing to the error of physics on which it is based, is approximately thrice the legitimate expectation, the true expected welfare benefit in the shape of global warming abated by the proposed French fuel tax increase would be 1.3 x 0.3 x 4.827 ln[413/(413-0.00018)], or 0.0000008 C°. Then the cost of abating 1 K global warming by measures of equivalent cost-ineffectiveness would be the ratio of 2.865 billion euros per year to 0.0000008 C°, or 3.6 quadrillion euros.

We have answered the candy-cane question that the French Government, like nearly all governments worldwide, does not take the trouble to ask. Answering that question reveals at once the futility of wielding intertemporal discount rates in the vain hope of providing a rational economic justification for measures to make global warming go away. For the above calculation assumes a zero discount rate. Any positive intertemporal discount rate will have the effect of reducing whatever minuscule net welfare gain might be conceived to have arisen from forestalling 0.0000008 C° of global warming in return for the very substantial welfare loss in the cost of the proposed measure.

The “Democrats” in Congress have begun to realize that any “climate action” against the small, harmless and net-beneficial anthropogenic warming that is likely to continue for the next century or two is unjustifiably expensive and egregiously ineffective. Their original ambition to prevent the funding of the Republican party by the coal-mining and coal-burning industries, formerly among the Republicans’ biggest donors, has already been achieved. Now they are proposing a “new green deal” to finish off the free market altogether.

Their proposed “fee-and-dividend” scam, which, like others of its kind, is being presented as a “cost-free” or “no-regrets” measure, involves a large and annually-increasing additional tax levied upon fossil-fuel corporations until they go bust. This is Mr Obama’s “war on coal” on steroids. But the State will not retain the money it has thus grabbed from the corporations. Instead, the money will be divided up among the populace in the form of a cash dividend. Millions of jobs will be created in “renewable” energy, just like that. There will be motherhood and apple pie all round, with extra cream and jam and chocolate sprinkles.

Here are just some of the costs of the “Democrats’” “cost-free” fee-and-dividend scam. Affordable, reliable, continuous, base-load, high-density, low-environmental-impact energy will be replaced by costly, unreliable, intermittent, part-time, low-density, high-environmental-impact windmills, solar farms and suchlike wondrous boondoggles. The lights will go out all over the nation. Millions of jobs will be destroyed. Tens of millions will starve (historically, this is the usual consequence of extreme Socialism).

After all, it’s working elsewhere in the world. Just look at the Third World, which is largely unelectrified. Chiefly owing to lack of access to electricity, mean life expectancy in the Third World is 60 years. In the electrified West, it is 80 years. Some 1.2 billion people – a sixth of the global population – have no access to electricity – “access” being defined, I kid you not, as the ability to turn on a single 60-Watt bulb for four hours a day (IEA).

Some 4.5 million people a year die in some-filed huts because they have no electricity to cook with. Another half million, all of them women, die in childbirth for lack of electricity. Half a million neonates ditto. Several million more die each year because they cannot get treatment in a hospital with electricity, or because they cannot keep food or drugs refrigerated, or because there is no electricity to pump clean water to them or drive sewage-disposal plants, or because they cannot run air-conditioning by day or heating by night.


Yet the World Bank and the IMF will no longer lend to third-world countries for digging coal or building coal-fired power stations, and from next year there will be no lending to poor countries for oil and gas extraction either. The Dark Continent will stay Dark.



I end, as I began, by looking briefly at the science. If Napoleon had bothered to stick his nose outside the Elysee Palace and check in with his totalitarian comrades at the European Commission in Brussels, the unelected Kommissars would have told him that, not so long ago, they commissioned some research to find out just how many lives would be lost in Europe if global warming were to continue unchecked.

To their horror, they found that the more global warming happened the more lives would be saved. For, as every schoolboy knows, it is colder weather, not warmer weather, that is the big killer. Warmer weather saves lives.

There is a horrifying recent example from my own country of what happens when electricity prices are hiked so much that poorer families can’t afford to turn on the heater. There was a brief cold snap last winter, and 25,000 more excess winter deaths than usual resulted, chiefly because those who are less well-off can no longer afford electrical power or heating oil because global-warming policies have made these essential commodities six times costlier than they would be if the free market had been allowed to work without governmental interference. When the gilets jaunes took to the streets in France, set fires and threw cobblestones, they had very good reason to complain at their government’s policy.

As for the discussion of discount rates, it is pointless unless and until one has first asked and credibly answered the candy-cane question. Slowly, infinitely slowly, my team is convincing the few open-minded governments in the world that they should ask that question and replace the anti-scientific, uneconomic hysteria of current intergovernmental climate policy with a rational economic approach.

In the long run, the use of reason will triumph against the current epidemic of irrationality. But how many more tens of millions must die in third-world countries, and increasingly in Western countries too, before common sense and common humanity prevail?