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A long, long time ago (in a galaxy far, far away…) I wrote up a summary of two events that I attended discussing the mathematical treatment of catastrophic climate change. The main take away in those sessions was that we’ve severely underestimated the effects of climate change and particularly catastrophic climate change.

Since I went to those sessions, a lot has happened and I’ve spent a fair amount of time thinking about it. My work has shifted to place where I do a lot more work with climate change directly as opposed to by happenstance. There are a lot of what-ifs and options, ranging from “do nothing” to a recent Discovery series that discusses the possibility of terraforming the earth (what a concept!). What I want to know – and I asked John Seo of Fermat Capital back at those sessions – is: where are the insurance companies?

Specifically, where are the big reinsurers, like Swiss Re and General Re? The practical take away of the session is that no matter how small the probability of a catastrophic change is, the expected cost of even a single meter rise in sea level would likely flood a large portion of the 500 largest coastal cities – and as a UN report estimated, the damage to infrastructure alone in the top 50 would be about US$ 500 trillion – that’s $500,000,000,000,000. A lot of that is essential to the functioning of the cities and is covered by flood insurance. It doesn’t matter how big Swiss Re, Hannover Re, Munich Re and General Re are – a pay out of that magnitude would wipe them out completely several hundred times over. Even a hundredth of one percent probability (0.0001%) of a one meter rise in sea levels would yield an expected cost of $50 billion, which frankly put, is a lot of money, even if your net income is $4 billion.

If you were the CEO of a major reinsurer and looking at an expected cost in the tens of billions of US dollars, I think you would go to your actuarial guys and ask, “Given the fact that the major polluters are increasing the risk of the pay out due to catastrophe, can we cost this as a premium?” As soon as one or two of the major reinsurers starts costing premiums for climate change risk, I suspect others would fall into line. Sure it may not make much a difference if on your $90 car insurance premium you’re paying an extra $5 for the risk you’re adding to the climate, but what if the math works out to requiring $300 extra on your $500 home insurance? Would that not give you a strong incentive to reduce the polluting impact of your house?

Ultimately, if governments want to seriously put a dent in climate change through this market method, I’d expect them to legislate this the way the German and Indian governments have approached highway insurance – if you’re travelling above the recommended speed, then your insurer has the right to turn down your claim – or the way the American government has legislated fire alarms – no fire alarm, no insurance coverage. In the meantime, however, it’s a method that allows the internalizing of the climate costs each individual has so far treated as an externality, at a relatively low cost to the environment.

Climate change has been something of an interesting topic here at work for the last few weeks. It’s also spawned a lot of pretty interesting panels and I wanted to take a moment to talk about two that I’ve been to dealing with modeling extremely low probability, extremely high cost events. I’ll post another part in a few days about a couple of conversations I had, based in part on ideas that I’ve been spinning around in my head for a good while.

The first panel starred Marty Weitzman from Harvard, discussing the problem of probability functions. His paper on modeling climate catastrophe discussed the fact that many of the standard climate change modeling exercises used the normal curve as a decent approximation of the chance of a climate catastrophe. His work, however, suggests that: (a) this may not be the appropriate curve to use, given existing empirical data that says catastrophes are becoming more frequent and more costly; and, thus (b) we should use a different curve – such as the Student’s T with far fewer degrees of freedom. The unfortunate consequence is that events at the long end of the tail that earlier had nil probability (and thus zero expected cost) suddenly balloon into infinite expected costs.

Richard Posner was the first to comment on the paper, discussing discount rates more generally referring to his catastrophe book‘s findings. The Judge quibbled slightly with the figures that Weitzman used in his paper, but generally agreed with the findings of the paper. (I later went and talked to him for about 30 minutes about his book, and discovered there was no funding for near-Earth asteroid detection, because it was not politically sexy to do so – so if you all want to deflect a potential Earth-colliding object, you’re on your own.)

John Seo from Fermat Capital was up next, trying to bring a private sector perspective to it. His concern with the paper was that one of Marty’s assumptions (I believe it was choice in the degrees of freedom, but I don’t exactly remember) was essentially a judgment call, and so you could turn the infinite expected cost into zero by flipping a coin and choosing a different assumption. While valid criticism, I agree with Weitzman that he missed the point of the paper, which was that long tail is fatter than people believe, regardless of the exact distribution used. That’s not to say Seo disagreed per se – he is in the business of cat bonds, after all – but he did raise valid technical questions about which curve best approximates past and present catastrophes. I also talked to John twice – which I’ll discuss in another post -

Finally, a very worried looking Tom Schelling applied Marty’s paper to other possible disaster scenarios, and how to best allocate resources to adaptation and mitigation. Schelling brought up the dismal conclusion that if  we’ve got discount rates wrong as implied by Marty’s paper, it’s possible that future populations will be relatively poorer than us and thus less able to deal with climate change than the current generation. That really throws a spanner in the works of current climate change mitigation and adaptation plans, which do defray costs to the future. What’s worrying about Schelling’s interpretation is that Marty looked at the worst-case scenarios in his paper and presentation, and already, we’re seeing worse than worst case scenarios playing out. For example, even as recently as January 2007, the soonest the IPCC was expecting an ice-free Arctic was the 2040s-2050s. However, as the geopolitical maneuvering of last summer showed, the Arctic is likely to be ice-free not in the next half-century, but in the next decade! Or, closer to home for me, the Indian summer monsoon, which was not expected to collapse for the next two decades is expected to see its final downpour this year, with calamitous effects on agriculture in South Asia. (And yes, I’m surprised I could end that terrifying statement with a period and not an exclamation point.)

The second panel some weeks later starred Ken Arrow beefing up some of Tom Schelling’s points about wrong estimations in our current intertemporal utility and cost curves. Arrow took a much more mathematical approach to the problem, deriving the utility and cost curves from first principles, which was perhaps a little more technical than the audience had hoped for. Working through the cost curve was fascinating to me, because it became pretty clear that given our current modeling inadequacies at any point of time beyond a two or three year horizon, civilization could end. At any rate, his work really hammered home the point that if there is a time for action on climate change, it is now, because it’s not clear what will happen even in the next decade.

I’m not entirely sure what Tom Schelling’s comments were – I can’t seem to find the notes – but I have a vague recollection of his talking about some of Arrow’s other work, and how a catastrophe would affect a general equilibrium state. Surprisingly, I found John Seo sitting in the front row as well, and I approached him to talk further about something I had raised earlier. I’ll write more about that later.

So some takeaways from these two panels:

1. Our models of catastrophic climate change are, broadly speaking, underestimating expected costs of climate change.
2. This is because our models have all assumed that the long tail is a relatively thin tail – which empirically, it does not appear to be.
3. Given this, it’s urgent to start work on climate change mitigation and adaptation now as opposed to later, because we don’t know in what shape society will be. This is particularly true of future resource constraints, which may in fact be tighter than current ones.

Next part, I’ll discuss what I talked to John Seo about, which is something that makes sense to me, and something I wish I could do the math out for, but can’t since I don’t have a good enough model.