Common Tragedies

Thoughts on Environmental Economics

Uncertainty

Posted by Daniel Hall on April 1, 2008

I have been meaning to post on Marty Weitzman’s ideas about uncertainty and climate change economics, and Paul Klemperer at VoxEU gives me a good opening by writing about the topic today. He argues that uncertainty about the impacts should make us more concerned about climate change, not less:

Although greater uncertainty means climate change might be less bad than we fear – for example, an “iris” effect means increases in cloud cover may slow global warming – it also means it might be much worse. While the central predictions of climate change models are arguably not so much worse than many other difficult problems the world faces, the worst possibilities are far, far nastier.

This argument is a simplified version of the one that Weitzman presents in his paper on the economics of catastrophic climate change (most recent version here, discussed previously here and here).

I got to go hear Weitzman present on his paper a couple weeks back at a World Bank InfoShop event. This was a lot of fun and very informative. I think Weitzman’s paper is a little difficult to grasp when you read it,* but hearing him present it in person made it sound much simpler.

Weitzman’s main argument is that traditional benefit-cost analysis (BCA) can’t calculate the “optimal” amount of social action to take to diminish the risks of climate change, because the calculation is entirely dominated by low-probability, high-impact events, i.e., catastrophic climate change. The upshot is that we should worry less about what is likely to happen, but we should be much more concerned about the worst outcomes.

Weitzman argues that climate change has two key features that it impossible to conduct traditional benefit-cost analysis:

1. It is a problem with “structural uncertainty”

2. It is a problem that poses “unlimited downside disutility”

Weitzman argues that any problem that possesses these characteristics is not going to be amenable to conventional BCA.** In the context of climate change the first point basically means that there are “unknown unknowns” about the science of what will happen. The second point essentially implies that the very worst outcomes of climate change could include the (effective) extinction of life on Earth. This leads to a situation where the relatively unlikely but devastatingly costly outcomes are completely dominating the cost-benefit calculation.

For readers who like to think in ‘graphs’ I found the following mental exercise helpful for getting a grasp on the intuition: Imagine a probability distribution with climate change outcomes — perhaps temperature change — running along the horizontal axis. Very far out on the right are the highest (and most catastrophic) levels of change; they are also very unlikely. Now imagine a second plot that uses the same horizontal axis (temperature change in this case) and plots the ‘disutility’ from any given level of change. At very low levels the disutility is very low*** but it goes up faster and faster (exponentially) at higher levels (out on the right side). The ‘expected impact’ from any level of change is essentially the probability of a given outcome multiplied by its cost. Note that if the curve of damages is rising faster than the curve of probability is falling off then every step you take further out is getting more costly in expected terms. The calculation becomes impossible because it just runs off towards infinity. This is essentially the situation that Weitzman claims we are in: the ‘structural uncertainty’ of the problem (we don’t know what the probabilities are and we don’t even know what distribution to use) means the tails of the probability distribution are not going down fast enough to get rid of our concern about the ‘unlimited downside disutility’.

This is scary partially because it implies we don’t know what risks we are running — is it a 1% chance of catastrophe? 0.1%? One-in-a-million? Even this might be higher than most people would feel comfortable with if we’re talking about extinction.

But this is also where the paper frustrates many people, because it doesn’t tell us what to do in response. It highlights the inadequacy of traditional benefit-cost analysis, but doesn’t suggest what should replace it. Suppose we could cut the chance of catastrophe from 1% to 0.5%. If we are literally talking about extinction here then I suspect almost everyone will think it is worth spending a very great deal indeed — nearly all global resources in fact — in order to cut the odds in half. And the same logic would apply if we were talking about taking the odds from 0.5% to 0.1%, or from one-in-a-thousand to one-in-a-million, because when you are talking about preventing the ultimate disaster then paying almost any price will look like a good deal. But since the whole point is that we don’t know what the risks are and we don’t know how to quantify them then we will never know what buying more insurance is getting us and that is very frustrating.

Another criticism of Weitzman is that perhaps climate change doesn’t actually have ‘unlimited downside disutility’. There are basically two ways to view this. The strong version is that your disutility is capped by your death. (This may not be very reassuring to most readers.) The weaker version is basically that regardless of how bad things got some people would still survive and adapt and get on with things. The quote I have heard is something along the lines of, “Well, even if we all end up living miles underground in caves, that will still do wonders for the interior design industry.”

Where does that leave us? My sense is that mainly Weitzman wants to increase the intuition that catastrophic events can be the most important factor by far when considering action. But what is he actually recommending specifically? Well, not much in his paper, but stay tuned for one intriguing answer in a subsequent post.  (Now up.)

*Indeed, I found myself in good company in this regard: Nobel prize winner Tom Schelling, one of the discussants at the event, noted that he read the paper 5 or 6 times without ever feeling that he was sure what it was saying.

**At the panel he also discussed the reasons he thinks climate change is the biggest problem we face with these characteristics, because of both greater uncertainty and disutility.

**Or even negative; perhaps a little warming would be good for us.

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5 Responses to “Uncertainty”

  1. [...] I was happy to see in Daniel Hall’s post today on the subject that I am not alone: Nobel prize winner Tom Schelling, one of the discussants at the event, noted [...]

  2. David said

    It would be nice to point out that Weitzman himself has the “cap by death” (or distinction of civilisation as we know it, I think are his words) in his paper. The problem is that while you can do BCA then (you got rid of the infinity), you results are super, super sensitive on what value you attach to existence of civilisation while at the same time that clearly is a very badly researched number, if at all. So, I think Weitzman argues, you get very little by this sort of cutting of tails of the distribution, all you do is make your results dependent on a some other number that you do not really understand well.

  3. [...] Common Tragedies explains why regular cost-benefit analyses fall short when it comes to tackling climate change: Catastrophic changes, rather than gradual changes, cant be priced in a rational model. And overlooking catastrophic changesor any other negative impacts of global warmingis precisely what the adaptation crowd led by Bjorn Lomborg is all about, argues SolveClimate. Meanwhile, Dot Earth dives into the recent scuffle over ocean temperatures and what it says about global warming. [...]

  4. Tom Fuller said

    Erm, excuse me, but I have not seen any description–any–of an extinction level event associated with global warming scenarios. The catastrophic 20 metre sea-level rise that is an extremely unlikely event, if it should occur, would happen over a protracted time period. Apart from that, what is it about global warming that is in any way shape or form predicted to rise to this level of impact? I’m really curious. I’ve been following the literature for some time and I have never seen anyone claim that global warming would wipe out the human race, or even human civilization.

  5. Daniel Hall said

    David:

    Thanks for pointing that out, it is a good clarification. The point I was trying to make about the “weaker version” of the criticism about the magnitude of the disaster is that you may believe that you can place a maximum value on the cost from climate change (perhaps you have engineered a spaceship that will rescue a fragment of humanity) and so you are willing to run the risk if it is small enough.

    Tom:

    This is kind of the point of Weitzman’s paper — we don’t know how the climate system will respond and there may be (likely are?) “off-model” effects we don’t understand right now. So you can speculate about the “clathrate gun hypothesis” as Paul Klemperer does in his VoxEU piece or some other mechanism but part of the intuition is that if there is something really bad out there then we likely don’t know the mechanism for it right now. This is obviously another frustrating aspect of Weitzman’s paper because it is basically immune to criticism about failing to propose a causal pathway.

    To be fair to Weitzman I should point out that he does not actually discuss “extinction of all human life” in his paper; it is more along the lines of David’s description of extinction of civilization as we know it. He does discuss the probabilities of a world warmer by 20 degrees Celsius (assuming a specific probability distribution for climate sensitivity which of course could be some entirely different distribution). 20 degrees C probably wouldn’t wipe us out but it would make the world a very, very, very different place.

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