One of the strangest financial scandals of recent years has been the selling of payment protection insurance. PPI is a curious form of insurance that meets loan repayment obligations for people who become ill or jobless.

Now, there is an honourable tradition of insurance being bundled with a loan. The practice is discussed in the Code of Hammurabi, which is nearly 4,000 years old. This ancient Babylonian law code includes 282 clauses on “bottomry”, which functioned as payment protection insurance for maritime merchants. Hammurabi specifies that a merchant who borrows money to fund a ship’s voyage is not obliged to repay the loan if the ship sinks.

That was a sensible enough arrangement but there are two objections to PPI in its modern form. One is that such policies were often sold to people under false pretences, including those who would never have been eligible for repayment. For this reason, British banks have had to repay tens of billions of pounds in compensation.

But the economist has a rather different complaint about PPI: it’s that even when it is not being mis-sold, it’s poor value for money. There are many other insurance products that are also poor value: mobile phone insurance, for example; or cancellation insurance for tickets; or collision damage waivers for hire cars. These products may not technically be being mis-sold but they are certainly being mis-bought.

To see why, let’s step back and ask ourselves what insurance is for. Classical economics has an answer: people are risk-averse, which means that they will pay good money to reduce the variability of outcomes they face. If home insurance guards against the loss of a million pounds when my house burns down, I’m happy to buy the insurance even though the insurance company expects to make a profit from it.

But this risk aversion emerges from the fact that money is worth more to poor people than to rich people. Gaining a million pounds would make me rich but losing a million pounds would make me poor. I should not gamble a million pounds on the toss of a coin, because the million pounds I might lose is more precious to me than the million pounds I might gain.

As so often with classical economics, this is an excellent description of how we should behave. It is not such an excellent description of how we actually do behave. Risk aversion can only explain why we insure large risks. It cannot explain why we insure small ones. This is because risk aversion turns on the idea that an extra pound is worth more if you are poor than if you are rich. But having to replace a phone is not going to make the difference between poverty and wealth.

In one of my favourite economics articles, written in 2001, the behavioural economists Richard Thaler and Matthew Rabin point out that anyone who rejects a 50/50 gamble to win £10.10 or lose £10 — apparently a reasonable enough taste for caution — cannot possibly be doing so because of risk aversion. (The degree of risk aversion necessary would mean that the same individual wouldn’t risk £1,000 on the toss of a coin for all the money in the world.) Risk aversion simply cannot explain why anyone would turn down that fractionally favourable gamble. And it cannot explain why anyone would insure a mobile phone.

A better explanation is that we tend to view risks in isolation. Rather than telling ourselves “a lost mobile phone would lower my lifetime wealth by 0.005 per cent”, we tell ourselves “it would be so annoying to have to pay for a new mobile phone”. Isolating and obsessing about risks in this way is arbitrary and illogical. But that does not mean we don’t do it.

At this stage, I would like to introduce you to the idea of a money pump. A money pump is a person whose irrationalities can be systematically exploited for financial gain. The simplest money pump is a person who prefers an apple to a doughnut, prefers a doughnut to a chocolate bar, and prefers a chocolate bar to an apple. Just offer them an apple in exchange for their doughnut plus a penny. They will accept. Then offer them a chocolate bar for their apple plus a penny. Then offer them a doughnut for their chocolate bar plus a penny. They end up with their original doughnut and are three pence poorer. Repeat for ever.

Money-pump arguments are sometimes deployed to object that people cannot be irrational, otherwise they would be bankrupted by money pumping. But economists are increasingly coming to realise that, instead, we should be looking for money pumping in action.

Given our anxiety about small risks, what would the money pumping look like? It would be an insurance policy focused on the narrowest possible slice of risk. It would be sold alongside another product or service, often at the last moment. It would be marketed by creating anxiety and then offering the product to make the anxiety go away. In short, it would look like the collision damage waiver, the extended warranty, and PPI. These bespoke slices of insurance are among the largest money-pumping projects in the modern economy. No wonder the banks abandoned their principles to join in.

Written for and first published in the Financial Times.

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