# Discounting, cost-benefit analysis and climate change

In the debate about climate change, people talk a lot about the cost of not doing anything, but they more rarely talk about the cost of the various policies that have been proposed to mitigate climate change. In order to determine what to do about climate, we have to engage in a cost-benefit analysis, which by definition considers both aspects of the question. Cost-benefit analysis is a method that economists often use to determine whether a policy should be adopted. It consists in estimating a trajectory over time for both the costs and the benefits that can be expected of the policy in question. For instance, if the policy consists in creating a carbon tax, the costs would be a rise of the price of energy, while the benefits would be a reduction of the damages resulting from the emission of greenhouse gases into the atmosphere. If the benefits outweigh the costs over the period of time under consideration, then adopting that policy could make sense, but otherwise it does not.

In the case of policies to mitigate climate change, the period of time under consideration in a cost-benefit analysis is very long because, according to the models scientists have developed, the worst consequences of climate change won’t really take place until a century from now or so. I think there are very serious concerns about whether it’s realistic to think that we can estimate with any accuracy how the costs and benefits of any policy would evolve over such a long period of time. (To be clear, when I say that, it’s a huge understatement. What I really think is that, if people knew how the economic models  used to make such monumental policy decisions work, there would be riots in the streets.) However, for the purposes of this post, I will just assume that it’s possible. Now, even if we can estimate a trajectory over such a long period of time for the costs and benefits of a policy such as the adoption of a carbon tax, there remains the question of how we should discount both costs and benefits in the future. In the case of the debate about climate change, since economists think that most costs of a policy to mitigate it would be incurred during the initial period, while most benefits would accrue far in the future, the question is how benefits that would be enjoyed only by future generations should be discounted or even whether they should be discounted at all.

If the discount rate you are using in a cost-benefit analysis is $r$, it means that the value of a cost or benefit that accrues in the future is reduced by $r$ every year. For instance, if the discount rate is 1% and the policy under consideration is expected to produce a benefit of \$1 billion a century from now, then when compared to a cost incurred today this benefit would only be worth \$1 billion/1.01100 ≈ \$369 million. Some people think that we should not discount benefits that would accrue to future generations at all because it’s immoral. The idea behind this claim is that future generations are not worth any less than us and, therefore, there is no reason to give more weight to a cost we’d have to incur than to a benefit that would accrue to them if we adopted a policy to mitigate the effects of climate change. In other words, on that view, any discount rate other than zero would be incompatible with intergenerational justice. I think that virtually every economist would agree to reject that claim (even Nicholas Stern, whose report on climate change was criticized for using a discount rate that was deemed too low, used a non-zero discount rate), if only for the reason I’m about to explain, but in my experience most people find it compelling, so I think it’s useful to explain why that can’t be right.

The problem with that claim has to do with the fact that, as a result of economic growth, people in a century from now will be a lot richer than us. You may be tempted to say that we can’t assume that productivity will continue to increase, but you have to realize that, if it did not, climate change would not even be a problem. Indeed, the models that are used to predict what is going to happen if we keep emitting greenhouse gases into the atmosphere assume that GDP per capita will continue to grow, which is precisely why they predict that greenhouse gases emissions will continue to increase unless we do something. If economic growth stopped, emissions would not continue to increase and, as a result, there would no problem to mitigate in the first place. In his book on climate change, William Nordhaus assumes that GDP per capita will on average grow at a rate of approximately 2%, which after a century corresponds to a factor of approximately 7.2. In other words, according to the models used to predict the evolution of climate, people a century from now will on average be 7.2 times richer than us.

Now, this is relevant because pretty much everyone, including people who claim that we shouldn’t discount benefits that accrue to future generations, agrees that we should give more weight to costs incurred by relatively poor people than to benefits enjoyed by relatively well-off people. The reason is that we generally assume that, although well-being increases with income, the rate at which it does also decreases with income. What this means is that a cost/benefit that is equivalent to the same amount of money is worth more for someone who is relatively poor than for someone who is relatively well-off. For instance, a loss of income of \$5,000 is worth a lot more for someone who makes \$20,000/year than for someone who makes \$145,000/year, i. e. approximately 7.2 times more. (Remember that, according to the models used to predict the effects of greenhouse gases emissions, that’s how much richer than us on average people will be in a century.) For the guy who only makes \$20,000/year, this could make the difference between sending his kids to a decent school and sending them to a shithole, whereas for the guy who makes \$145,000/year it may just mean that he’ll have to wait a little longer before he buys another Mercedes.

Suppose we are considering a policy that would increase the income of people who make \$145,000/year by \$5,000/year, but decrease the income of people who make \$20,000/year by \$3,000/year. For someone who makes \$20,000/year, \$3,000/year is 15% of his income, which is pretty low to begin with. On the other hand, for someone who makes \$145,000/year,  \$5,000/year is only 3.4% of his income. Assuming the number of people who make \$145,000/year is the same as the number of people who make \$20,000/year, if we used a discount rate of zero in the cost-benefit analysis for that policy, we’d conclude that we should adopt it because the benefits outweigh the costs. However, I’m sure that almost everybody would agree that it’s crazy, because it would clearly be extremely unfair to adopt that policy.  Yet, as far as the discount rate that we should use is concerned, there doesn’t seem to be any relevant different between this case and the inter-generational case. Thus, if you think that we should discount the benefits that would accrue to people who make \$145,000/year in this case, then presumably you should also say that we should discount the benefits that would accrue to future generations from policies that mitigate climate change.

Obviously, there are a lot of complications involved in a cost-benefit analysis of policies to mitigate the effects of climate change, which I didn’t even mention. For instance, I completely ignored the issue of distributive justice, which is obviously important. Even in a century from now, some people still won’t be as rich as Westerners are today, so just looking at the average can be misleading. Indeed, this post doesn’t deal with any of the aspects of the debate about discounting that are really interesting and, as I already noted, I don’t think what I have said is controversial among people who are familiar with cost-benefit analysis. But I hope to have convinced you that the discount rate should definitely not be zero, despite the intuition that, in my experience, many people have when they first hear about discounting. Not only is it not immoral to discount the benefits that would accrue to future generations from that kind of policies, but insofar as they will be relatively better-off compared to us, it would be immoral not to discount them. Of course, this point alone doesn’t really have any obvious implication for what you should say about policies that purport to mitigate the effects of climate change, but it’s still something that people should realize.

It’s interesting that, in my experience, people who are inclined to say that we should use a discount rate of zero for the cost-benefit analysis of policies designed to mitigate the effects of climate change are typically liberals/progressives. Indeed, given that liberals/progressives are ordinarily more averse to inequality than other people, that’s exactly the opposite of what you’d expect if they were consistent. Conversely, I wouldn’t be surprised if, upon reading this, some conservatives suddenly became more concerned about inequality, at least in the context of the debate about climate change. People seem to be making a difference between the ordinary case and the intergenerational case, but I can’t think of any reason to be more/less tolerant of inequality in the latter than in the former. If you think that we should care less about people who are relatively better-off, as I think you should, then I think it shouldn’t matter if they’re already alive or if they’re not born yet.

## 8 thoughts

1. Nikolas says:

Even as an ardent environmentalist, I believe cost benefit-analysis definitely has a place in environmental policy (see this good, albeit short, article from 1996: http://www.env-econ.net/recommended_reading/Arrow_BCA.pdf). Moreover, Venter et al.’s 2016 paper in Nature suggests that economic growth is good for the environment as a whole. I would be interested in seeing you tackle the difficult question of how we quantify the benefits of climate change policy (perhaps taking into account popular policy making methods such as contingent valuation).

1. Thanks for the paper by Arrow et al., as well as the Nature reference, I’ll read that when I have some time. I definitely think economic growth is a good thing for the environment and maybe I will write a post to explain why. As for cost-benefit analysis, I think that in some cases, it’s essentially meaningless and perhaps I will also write a post to explain why. On the discount rate specifically, as I say in the post, I haven’t even touched on what I take to be the really controversial and interesting aspects of the debate. It’s a really complicated debate that involves a lot of different questions and I hope that I will have the opportunity to discuss some of them in the future. I often disagree with environmentalists, so if I write more about those issues and you think I’m wrong, I would love to get some pushback from you.

2. Brendan Long says:

One of the environmentalist claims is that climate change will disproportionately hurt poor people, and environmentalists also generally prefer higher taxes in the right. Doesn’t this switch the calculation back, so we’re taxing rich people now to help future poor people?

1. Well, as I said in my post, I was totally ignoring the issue of distributional justice. When you take it in consideration, which you definitely should, things rapidly get a lot more complicated. My only goal with this post was to argue that, to the extent that future generations will be richer than us, that’s a reason to discount the damages they might have to suffer if we don’t do anything about climate change. But, clearly, even in a century from now, not everyone will be richer than people in the West today.

3. Esso says:

Is it possible the reason for low discount rates in some studies is that they’ve factored in rising costs of effective interventions to climate change as it progresses and economy grows? The price of energy at least goes up as economy grows.

1. I may be missing your point, but cost-benefit analyses of climate change mitigation policies typically try to determine whether doing something now would be worth it, so the fact that the cost of effective interventions rises the longer we wait is usually irrelevant. Of course, you can also do a cost-benefit analysis of doing something at some later day, in which case the cost will be higher, but I don’t see what this has to do with the discount rate. As far as I can tell, if the discount rate is low in some studies, it’s because they use the prescriptive approach to discounting instead of the descriptive approach, which for reasons I don’t have time to explain right now results in a lower discount rate.

4. MG says:

Paragraph 4 of your piece – two questions (asked seriously, not rhetorically): (1) is it not the case that it’s the stock of greenhouse gases in the atmosphere that matters, rather than the flow and (2) is not the consensus view that the stock is already problematic, such that only a reduction in the stock, and not just in the rate of the flow, can prevent catastrophic climate change in the future (because of feed-back loops and the like)? If (1) and (2) are true (or false, in the way I’ve phrased them), then even if economic growth doesn’t continue and, let’s say, the flow reduces to zero, climate change might still be a problem.

1. As far as I know, it’s indeed the stock of greenhouse gases in the atmosphere that matters, but it’s definitely not the consensus view that, even if the stock just remained at the current level, climate change would be catastrophic.