Ellsberg, Knight and Climate Change

Placed before you are two urns. Each contains 100 balls. You are given a clear description of the first urn’s contents, in which there are 50 red balls and 50 black balls. The economist running the experiment is tight-lipped about the second, saying only that there are 100 balls divided between red and black in some ratio. Then you are offered a choice. Pick a red ball from an urn and you will get a million dollars. Which urn would you like to pull from? Now try again, but select a black ball. Which urn this time?

Most people plump for the first urn both times, despite such a choice implying that there are both more and fewer red balls than in the second urn.


Why do most people plump for the first urn both times? Because, as the saying goes, “Better the known devil…”.

This is the well known Ellsberg paradox, of course. If you’ve studied micro, decision theory, probability or behavioral economics, you’ve probably come across it.

But climate change? What does the Ellsberg paradox have to do with climate change?

The experiment may seem like just another of the cutesy puzzles beloved by economists. In fact, it reveals a deeper problem facing the world as it struggles with climate change. Not only are the probabilities of outcomes not known—the likelihood, say, of hurricanes in the Caribbean ten years from now—nor is the damage they might do. Ignorance of the future carries a cost today: ambiguity makes risks uninsurable, or at the very least prohibitively expensive. The less insurers know about risks, the more capital they need to protect their balance-sheets against possible losses.
In May State Farm, California’s largest home-insurance provider, retreated from the market altogether, citing the cost of “rapidly growing catastrophe exposure”. Gallagher Re, a broker, estimates that the price of reinsurance in America has increased 50% this year after disasters in California and Florida. Few firms mention climate change specifically—perhaps a legacy of Republican attacks on “woke capitalism”—but it lurks behind the rising cost of insuring homeowners against fires, floods and hurricanes.


The key phrase in that excerpt is this one: ambiguity makes risks uninsurable. Another way to put it is: ambiguity (uncertainty) means a risk can no longer be called a risk.

Why? Because risk… and have a sip of coffee before reading this next bit… risk is about certainty. Nope, not a typo! Risk is about certainty. Well, ok, I’ll kind of put you out of your misery. Risk is about the absence of uncertainty.

Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated…. The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating…. It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.

Knight, F. H. (1921) Risk, Uncertainty, and Profit

How bad will the impacts of climate change be? How bad will hurricanes get? When will parts of Mumbai go under water? How long before Maldives ceases to exist? There is only one answer to this question: we just don’t know.

Then how do we price the risk associated with these events? We can’t, which is why home insurance firms in California are exiting form the market. This is where I and the article disagree a little bit, for it goes on to say that when it comes to climate change, reality isn’t quite as bad. We can resolve the uncertainty, in other words, by guessing how bad things may get.

How do we guess? By taking a look at how climate change affected the planet in the past. These changes can be deciphered by studying things such as the Arctic ice cores, for example. Or oceans. For a given change in x (say carbon dioxide emissions), this is how y changed (say patterns seen in the Arctic ice-cores).

But this will, at the end of the day, still be a guess. What we are saying is that because this is how things played out in the past, this is how things will play out in the future. Well, maybe. And maybe not!

As I’m fond of telling my students when I explain the concept of value-at-risk, predicting I will not die tomorrow because I haven’t died so far isn’t a great idea. Or predicting the height of the waves on some beach in South East Asia (given the data of the past hundred years) wouldn’t have worked out so well on the day the tsunami struck in 2004. Both those examples have their own problems, I will happily admit – but the point I wish to make is a simple one.

The future doesn’t always look exactly like the past. We can, at best, reduce some of the uncertainty. Not resolve it. And when you can’t resolve uncertainty, you can’t price it, and when you can’t price it, you are going to struggle with a viable insurance market.

The article goes on to say as much, but along a different dimension: political uncertainty. As they put it “there is no model that can predict whether policymakers will pull the levers that are available to them to prevent such fires from happening”. Indeed.

And worse: policymakers can sometimes not only not pull all the available levers, but they can go out of their way to prevent others from using them.

Policy can also prevent a proper accounting of risk. Californian regulations forbid insurers from using the latest climate models to set prices, since protection would become more costly. Premiums must be based on the average payout over the past 20 years, rather than the latest science. Shying away from ambiguity is understandable. Sticking your head in the sand is plain foolish.


If price is a signal wrapped up in an incentive (and I think it is), then a good way to figure out how seriously markets are taking climate change is to look at the price. But for that, price discovery mechanisms must be allowed to flourish!