Climate Damages and Discount Rates
In this post from the book net-zero:
How much should we care about future climate change damages? Utility, discount rates, the legacy of a severed head and the fight between a Lord and Nobel Laureate.
The elephant in the room: discounting is boring no matter how many severed heads you talk about.
Maybe, but I think the discount rate is one of the three most important numbers required to understand climate change. So here is my opening gambit:
The discount rate is what I call a dial of doom or boom.
The economic sensitivity which defines how much value we place on future generations.
Dial it up and climate damages seem small and manageable and justify little action today.
Dial it down and climate change threatens our future prosperity and warrants immediate action.
By the year 2100, I estimate in the book, net-zero, that climate change and air pollution could wipe out in excess of $40 trillion dollars of global income (annual GDP). Let’s assume that this number is ballpark correct (we will revisit damages in a future post) and use it to better understand how big an economic problem climate change actually is.
$40 trillion sounds like a lot. It’s nearly half of today’s annual GDP and about 10% of all the accumulated wealth in the world. But at the same time the year 2100 is a long way off. Won’t we all be super rich and zooming around in flying Lamborghinis by then?
One of the many difficulties in conceptualising the impacts of climate change are the timescales involved. Humans are used to making decisions seconds, days, or years into the future.
So how do we compare the magnitude of damages decades or centuries ahead with problems today?
First economists use something called utility in an attempt to quantify happiness or satisfaction.
Jeremy Bentham, an 18th century English academic whose philosophy revolved around the greatest happiness for the greatest number of people, introduced the idea of utility to economics. Bentham’s ideas were very progressive for the time, advocating individual and economic freedom, separation of church and state, equal rights for women, decriminalisation of homosexuality and the abolition of slavery. And it’s not just his legacy which was preserved; Bentham left specific instructions that he should be medically dissected before being embalmed and displayed “in the attitude in which I am sitting when engaged in thought”. His body remains on show in the foyer of University College London to this day and has even been wheeled out to attend special university council meetings. However, his mummified head is now kept under lock and key after students at rival university Kings College London kidnapped it and demanded a charitable ransom of £100 for its safe return.
Jeremy Bentham’s Head after a short stint as a football for the team at Kings College London. Taken by Ethan Doyle White.
Bentham’s idea of utility is a measure of happiness, satisfaction, or usefulness of our actions and modern welfare economists study how the allocation of resources can impact social utility today and in the future.
Economists use consumption spending as a proxy for utility based on a logarithmic relationship; they assume happiness rises with increasing incomes, but the added happiness gets smaller and smaller.
So because most economists assume solving climate change is more costly than doing nothing (another future blog, spoiler: it is and it isn’t), we must decide how much we reduce consumption and utility today to slow climate change and to increase utility for our future selves and future generations.
Estimating the magnitude of this trade off requires we take our future dollar damages ($40 trillion in 2100) and convert them into the dollar equivalent utility today.
So next economists use discounting to convert future money in to the equivalent of today’s money and utility.
Money today is worth more than the same amount of money in the future. That statement sounds wrong, but imagine if I asked you whether you wanted £100 now or £100 in one year’s time. If you took the money now you could deposit it in the bank, earn 3% interest, and in one year you would have £100 plus another £3. If you took the money in one year your missed opportunity cost was the accumulated interest.
That 3% difference may seem pretty small in the grand scheme of things, but imagine how 3% per year compounds on an 80 year time horizon. A quick sum tells us £100 invested for 80 years at 3% annual interest grows by more than 10x to £1,064. Put it another way £1,064 of damages in 80 years’ time are worth £100 today. The discount rate turns future climate change damages into the equivalent loss today and has a very significant bearing on the required urgency of dealing with climate change.
Okay but what discount rate should we use?
There are two schools of thought on this.
Option 1: The Prescriptive Approach
The first approach is to use a purely market based rate or opportunity cost. This theory points to the fact that spending money on climate change solutions is just like any other investment. You spend money today and you receive a benefit from lower damages in the future. Therefore climate change spending must compete with other investment opportunities across the economy such as investing into machinery, infrastructure, buildings, companies, real estate, or human capital (eg education or health).
A leading proponent of this descriptive approach is William Nordhaus, a Nobel winning climate change economist, who typically applies 4-5% discounting in his calculations.
However, the problem with using a descriptive approach is that there are very few assets traded in the market which provide a return for longer than 30 years and so it doesn’t fully reflect the time scale of the problem. There are frictions, uncertainties, and distortions in the market which means the rate is never true. We are also making investment decisions impacting future generations who do not trade on today’s markets and have no influence on the market rate.
Option 2: The Prescriptive Approach: The Ramsey Equation
The second school of thought is to calculate the discount rate based on the value we place on future generational welfare and the rate at which wealth will increase. The leading proponent of this prescriptive approach is Nicholas Stern, a British economist who has written extensively on the financial impacts of climate change. The most common determinant of this social discount rate is the Ramsey equation:
The Ramsey Social Discount rate
The easy bit
Let’s start by first explaining the second part of the Ramsey equation which is the least controversial. This sets the discount rate equal to the growth rate times something called the elasticity of marginal utility.
Setting the discount rate to the same level as consumption (or GDP) growth means that damages remain proportional to incomes. So if future generations become wealthier and better able to pay for higher damages we are still comparing like for like. In other words our $40 trillion of damages in 2100 may be half of today’s GDP, but because I assume GDP grows at ~2% per year it is only 5% of GDP in 2100.
By using the rate of consumption (or GDP) growth to discount future damages we can compare like for like.
The elasticity of marginal utility takes the concept one step further to also consider the relative utility.
Lets start by first imagining that you got a pay rise at work and could eat out twice a week instead of just once, that second night out will probably bring you nearly as much pleasure or utility as the first, but next imagine you went from eating out 6 days to 7 days a week, you might still enjoy that 7th meal but it would certainly not bring as much pleasure as adding the second. This is the logarithmic relationship between utility and consumption we mentioned earlier.
The same principles apply to climate change damages. Losing 5% of your $75,000 annual income in 2100 will hurt a lot less than losing 5% of your average $12,000 income today because each percentage point of income brings less utility for your wealthier future self. The principle is that providing for basic needs of food, shelter, and health creates far more utility than upgrading from a Porsche to a Lamborghini (even if it can fly).
Adding the elasticity of marginal utility multiplier (typical value of 1 to 2) acts to discount damages faster than consumption (or GDP) growth to account for the fact that we care less about losing money when we have more of it in the future.
The hard bit
So far so good, but now for the first part of the equation which is more controversial and more mind boggling. The pure time preference is an added element of the Ramsey discount rate to represent the fact that we value having something sooner rather than having it later even if we make no financial gain in the process. This represents the impatience of humans. Essentially those who argue for a higher pure time preference in relation to climate change, also argue that we should value the welfare of current generations higher than future generations.
Nordhaus makes the argument that we have less anxiety for our great grandchildren than our children because they are more remote and have our children and children’s children to look after them. We can’t worry about everyone into an infinite future so the pure time preference rate must be positive and he uses a value equivalent to 1-2%.
On the other hand, Lord Stern argues the only reason we should value future generations any less than current generations is the remote possibility the human race doesn’t exist in the future. He uses a 0.1% pure time preference based on a worst case 10% chance humans don’t last another 100 years.
Many famous economists argue for and against the pure time preference rate.
Throughout the book, net-zero, I base all calculations on a total discount rate of 3% real (excluding inflation). Generally social discount rates range between 1-3% and market discount rates range between 3-6%, so our estimate is a compromise between the descriptive and prescriptive methods and a compromise between Stern (1.4%) and Nordhaus (4.5%).
A 3% real rate of return also represents the weighted average return or interest paid by global bills, bonds, and shares over the last 100 years excluding price inflation. This is the real return of a market investment, on a very long term view. This is the long run opportunity cost or discount rate using a market based descriptive approach. It is also the current market rate of return for low risk, large scale investment projects such as wind and solar farms in developed countries.
A 3% real rate of return also tallies with the prescriptive approach. If we assume 2.4% growth with 1.2x elasticity of marginal utility and 0.1% pure time preference our discount rate comes to 3%.
But why side with Stern on the pure time preference? I would argue if we are trying to find the best course for humanity then having something sooner rather than later becomes rather meaningless because humanity is effectively infinite on our time horizons. Therefore barring an extinction event the time preference should be zero.
Ramsey Social Discount Rate for the book ‘net zero’, Stern and Nordhaus. Stern given in Stern review. Nordhaus doesn’t explicitly use the Ramsey method but approximated the elements in his review of the Stern report.
So what does this mean for our $40 trillion climate change damage estimates?
Well if we estimated damages at 5% of GDP by 2100 and 9% of GDP by the year 2150, this is the equivalent of around 4-5% of GDP in today’s money after discounting at our 3% rate. In other words losing 5% of GDP in 2100 or 9% of GDP in 2150 will feel like losing 4.5% of GDP today and forever.
Using our same damage projections Lord Stern’s discount rate would argue the losses are closer to 6.5% or more in today’s equivalent and Nordhaus would argue they are equivalent to less than 0.5% of today’s income. This gives you an idea of why climate change is such an intractable problem. The long time periods create such uncertainty that the smallest change in assumptions can completely alter the outcome. Are we warranted spending 6.5% of GDP or more to solve climate change and air pollution or should it be less than 0.5%?
Chart showing how our projected climate change damages increase with rising temperature over time. Black line shows forecast damages per capita as a percent of forecast GDP per capita. Orange line shows future USD damages discounted into today’s money as a percentage of today’s GDP per capita – equivalent utility. We use a GDP per capita growth rate of 2.4% and a discount rate of 3%. The chart also shows our discounted damages using the Stern discount rate (1.4%) and Nordhaus discount rate (4.5%). We leave the investment rate fixed at 25% of GDP so consumption and GDP changes are equivalent.
Is 3% discount rate a fair compromise? Should we use a pure time preference? Should we fade the discount rate to reflect uncertainty? Is there something better than income we can effectively use to measure utility?
How many times a week do you eat out?
For more resources on discounting see Christian Gollier’s book ‘Pricing the Planet’s Future’ in the bookshelf.