Latest Issue of Science News


Math Trek

'Discounting' the future cost of climate change

Economists develop new methods to quantify the trade-off between spending now and spending later

Sponsor Message

To figure out how much we should spend fighting climate change, economists have some questions for you: How much would you be willing to spend now to make your child $100 richer in the future? What about your grandchild in the farther future, or your great-great-great-great-great-grandchild in the very distant future?

The health of the planet may hinge on the answers. Most economic analyses of climate change have concluded that we should be spending only small amounts to combat climate change now, ramping up slowly over time. This conclusion mystifies most climate scientists, who argue that immediate action is the only way to forestall dreadful consequences. And at the heart of the disagreement are these very questions, about the value of future generations’ welfare in monetary terms.

The worst consequences of climate change are likely to unfold only over decades or centuries — in other words, in our children’s or grandchildren’s or great-great-great-great-great-grandchildren’s lifetimes, not ours. The decision of how much to spend now to avert climate changes hinges on assessing how much it is worth to us now to prevent that future damage. Since most of us would prefer money now over money later, economists typically figure that we’re willing to spend only less than a dollar now to prevent a dollar’s worth of damage in a year, or in a decade. The percentage less is called the “social discount rate.”

The key is figuring out what this percentage should be. In the short term, there’s a straightforward way to do it: use the market rate on loans. After all, if you can get a bank loan at 5 percent, then getting a dollar in a year is essentially equivalent to getting a tad over 95 cents now. That means that, economically, it would make sense to spend 95 cents today if doing so would save you from a problem that would cost you at least a dollar a year from now. In other words, a dollar of future impacts has gotten discounted to 95 cents today.

Play this out over many years, though, and the consequences are peculiar. For example, at a 5 percent annual interest rate, a penny that belonged to Julius Caesar would have expanded to the bogglingly huge sum of 3 – 1041 dollars today — more than the entire world economic output over the last 2,000 years multiplied by the number of stars in the sky. So the brutal arithmetic of discounting (at a 5 percent social discount rate) would shrink any imaginable catastrophe today to far less than a penny in Caesar’s time, and an economist would have therefore recommended that Caesar not spend even so tiny an amount to avoid it.

Besides being absurd, this little calculation is a mute in the trumpet of economists alarmed about climate change. Any constant social discount rate (like the 5 percent rate used above) leads to exponential growth, which is explosive over the long term. So even at moderate social discount rates — for example, 2 to 3 percent — economists have a very difficult time justifying significant spending in the present to fight climate change. Invest the money instead, economists would advise, and our descendants will be rich enough to live well despite the damage from climate change.

One of the few exceptions is Nicholas Stern, now at the London School of Economics. In 2006, he wrote the The Economics of Climate Change: The Stern Review and concluded that we should immediately invest 1 percent of world GDP to combat climate change. Otherwise, he said, the resulting climate chaos could cost 20 percent of world GDP per year. In order to reach this conclusion, though, Stern had to set the social discount rate at near zero.

Many economists, even those sympathetic with the report’s conclusions, howled at this assumption. After all, people do much prefer a dollar today to a dollar next year or a dollar a hundred years from now.

So economists seemed to be on the horns of a dilemma: Either accept an assumption that many argue is economically unjustified (a near-zero social discount rate), or conclude that we should just accept climate change without much of a fight. (A third alternative is perhaps even less appealing to economists: accepting that their calculations simply can’t illuminate the question.)

Now Larry Karp of the University of California, Berkeley, building on a large body of research, has proposed a solution: Start with real human behavior. Studies have shown that given the choice between $100 now or $103 in a year, most people will go for the immediate hundred bucks — no surprise there. But now suppose the choice is between $100 in 20 years or $103 in 21 years. According to traditional discounting theory, the “cost” of waiting a year would be the same now as 20 years from now, so impatience should still reign. But in reality, people are often willing to wait: 20 years, 21 years, what’s the difference?

This difference points to an alternate theory known as “hyperbolic discounting”: The farther into the future we look, the fuzzier our view. We’re much happier to have good stuff now than later, so our short-term discount rate is high. But we hardly distinguish between goods in the pretty far future and goods in the very far future, so our discount rate in the future is far lower.

Hyperbolic discounting has a powerful impact on the math of climate change, because it implies that we’ll spend almost as much to reduce the impact on our great-grandchildren as on our grandchildren. In that case, the long-term consequences of our actions, even those hundreds of years out, no longer fade to complete insignificance as they do with a constant social discount rate. Because, Karp says, it’s those really long-term impacts of climate change that are most horrifying, "many models show that you’re willing to spend a heck of a lot more to stabilize the risk of climate change under hyperbolic discounting.”

But hyperbolic discounting comes with a nasty downside, one we also see in real life: It encourages procrastination. Essentially, we imagine that we’ll be more patient in the future than we are today. (In 20 years, for example, we’ll be willing to wait a year for the extra three bucks, even though we’re not willing to right now.) So the perfect solution will always appear to be: Spend nothing to combat climate change now, but start to do so real soon, in that mythical future time when we acquire patience.

The problem with this “perfect” solution is that we can’t force our future selves to follow through on the plan we make now. To find the true best strategy, then, we’ve got to find one that we’ll choose to follow through on when the time comes.

Karp created a simple model of climate change as a multistage game and forced the players to assume that future generations will use the same strategies as they do. So if we procrastinate, we can expect our future selves or descendants to procrastinate too. In Karp’s model, each player has a simple choice to make: For a given level of greenhouse gases, is it worth spending money to stabilize that amount, or shall we just continue with business as usual? By assuming that all generations would follow the same rule to make their decisions, Karp could then play the game forward and see the consequences of each strategy.

He found that, unlike with traditional discounting, his model offered no single, best strategy. Nevertheless, Karp says, it’s clear that in his model, the range of levels of greenhouse gases at which it’s a good strategy to stabilize is much broader than with constant discounting.

Karp has yet to apply hyperbolic discounting to a more sophisticated model, and its potential to help make sense of climate change economics isn’t yet clear. But in any case, Karp argues that new approaches like his are desperately needed to capture the important considerations around fighting climate change. “Lay people and climate scientists aren’t concerned with whether greenhouse gases are going to reduce gross world product by 1 percent or 3 percent in a few decades,” Karp says. “Existing models are really good at answering that uninteresting question, but only economists care.”

Note: To comment, Science News subscribing members must now establish a separate login relationship with Disqus. Click the Disqus icon below, enter your e-mail and click “forgot password” to reset your password. You may also log into Disqus using Facebook, Twitter or Google.

X