One of the most under-appreciated aspects of the climate change problem is the so-called “fat tail” of risk. In short, the likelihood of very large impacts is greater than we would expect under typical statistical assumptions.

We are used to thinking about likelihoods and probabilities in terms of the familiar “normal” distribution—otherwise known as the “bell curve.” It looks like this:

Roughly 68 percent of the area falls within the region bounded by 1 standard deviation below (-1 sigma) and above (+1 sigma) the “mean” or “average,” and a substantially greater 96 percent of the area falls between two standard deviations below (-2 sigma) and above (+2 sigma) the mean. So given this statistical distribution, we would expect values to fall *above* the +2 sigma (two standard deviation) limit only about 2 percent of the time. Call that the positive “tail” of the distribution.

There are many phenomena that follow a normal distribution, from the heights of adult men in the U.S. to the day-to-day fluctuations in summer temperature in New York City. But the predicted warming due to increased greenhouse gas concentrations isn’t one of them.

Global warming instead displays what we call a “heavy-tailed” or “fat-tailed” distribution. There is more area under the far right extreme of the curve than we would expect for a normal distribution, a greater likelihood of warming that is well in excess of the *average* amount of warming predicted by climate models.

An important new book, *Climate Shock: The Economic Consequences of a Hotter Planet,* by Environmental Defense Fund senior economist Gernot Wagner and Harvard economist Martin Weitzman, explores the deep implications this has for the debate over climate policy.

Here’s the blurb I wrote for the book (a shortened version of which appears on the back cover):

Think climate change is a low-priority problem? Something to put off while we deal with more immediate threats? Then *Climate Shock* will open your eyes. Leading economists Wagner and Weitzman explain, in simple, understandable terms, why we face an existential threat in human-caused climate change. The authors lay out the case for taking out a planetary insurance policy, without delay, in the form of market mechanisms aimed at keeping carbon emissions below dangerous levels. —Michael E. Mann, author of *The Hockey Stick and the Climate Wars*

The “insurance policy” analogy is appropriate here. We don’t purchase fire insurance on our homes because our homes are *likely* to burn down. Far from it in fact: less than one-in-four homeowners are likely to ever experience a house fire. We purchase fire insurance because we understand that, even though such a catastrophic event is unlikely (less than 25 percent chance of happening), if it *did* happen, it would be catastrophic. So it is worth hedging against, by investing money now—in the form of fire insurance.

Let us consider, in that context, the prospects for warming well in excess of what we might term “dangerous” (typically considered to be at least 2C or 3.6F warming of the planet). How likely, for example, are we to experience a catastrophic 6C = 11F warming of the globe, if we allow greenhouse gas concentrations to reach double their pre-industrial levels (something we’re on course to do by the middle of this century given business-as-usual burning of fossil fuels)?

Well, the mean or average warming that is predicted by models in that scenario is about 3C, and the standard deviation about 1.5C. So the positive tail, defined as the +2 sigma limit, is about 6C of warming. As shown by Wagner & Weitzman (see figure below), the likelihood of exceeding that amount of warming isn’t 2 percent as we would expect for a bell-curve distribution. It’s closer to 10 percent!

In fact, it’s actually even worse than that when we consider the associated *risk*.

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