This is a particularly famous bit of economics. It’s the equation for pricing options, the financial derivatives that contributed to the financial crisis that started in 2008. This equation was devised by an economist called Robert Miller and some of his colleagues. Before Miller devised the equation there was no options market, because nobody knew how to work out what they should be charging. An option is a derivative because it’s a bet on the future price of some underlying financial security or physical commodity, like a crop or a metal.

Before these economists at the University of Chicago worked out the equation, there were some trades that went on in futures and options, but the pricing was a bit haphazard. So when Merton and his colleagues worked out this equation, they put it into practice as a business. They used the university computers to crank through some different prices for different parameter values, and they printed out big sheets that they then sold around the commodities markets in Chicago.

Once they started selling the sheets of information, the prices that traders in the market charged for the options started to converge and were all described by this model. Because there were some really eminent University of Chicago economists involved in it, the US financial authorities decided they could treat options as financial instruments and not as gambling, because it was touch-and-go. For quite a while it looked like the options market was going to be treated like gambling, and regulated the way that the mafia is regulated in gambling in the United States, which is stricter than the financial markets are regulated.

So the credibility of the University of Chicago and the fact that these guys walked around flogging their sheets of prices meant that the options market, as we know and love it today, came into being. In fact, Merton himself put it into practice with a company he set up on Wall Street, called Long-Term Capital Management, which went belly up in 1998 in a kind of dry run for the present financial crisis.

This kind of equation, that brings its own market into being, is called ‘performative economics’. In language, a performative statement is one where the very act of saying it is the action itself. ‘I’m sorry’ is the apology. ‘I name this ship the Queen Elizabeth’ is the naming of the ship. In the same way, this equation was performative. It performed the options markets. Or another way of putting it is that it was self-fulfilling. It brought its own reality into existence. In fact, the term ‘self-fulfilling’, came into social science through a sociologist called Robert K Merton, who was the father of Robert Merton of the equation. There’s something marvellously Oedipal about all of that.

This equation, devised by economists, played a role in creating the markets and the possibility for the financial crisis. A lot of economists are in denial about this. They say, ‘It was nothing to do with us. There were these finance guys. They committed frauds. They did all sorts of crazy things. It’s not economics really.’

I think we have to accept some responsibility, we economists, for the crisis.

‘Models’ are what economists call their stories. Modelling runs very deep in the subject, and models can be really useful. This is the London Underground map. It isn’t remotely a map that would help you find your way around London at street level. As a simplification, as a telling of an essential truth about one way to find your way about London, it’s a really useful model.

There are other models in economics that are incredibly useful too. There’s a whole strand of economics that looks at the economic incentives to get married, who you choose to marry, how many children you have and the timing of your children. Of course that’s not the whole story.

Economists allow that there is room in life for love and for culture, but the economic incentives are actually very powerful descriptions of the way people make some of these very intimate choices. Explaining, for example, the social sorting that goes on through marriage, the way people tend to marry people who are in jobs like themselves and have levels of education like themselves. So models can be useful. They can be dangerous. They can be useful. They’re absolutely fundamental to the way economists work.

‘Normal people would ask for words to explain what the equation means. Economists ask for equations to explain what the words mean.’

There’s a very nice anecdote told by Robert Lucas, who won the Nobel Prize some years ago. All Nobel Prize winners do a little memoir about their intellectual formation, and he told of a conversation he had in the evening with his University of Chicago colleague, Ed Prescott, about the labour market and some aspect of the way wages were set in certain kinds of jobs. They disagreed about it and they went home. The next morning, Robert Lucas went to his department pigeon hole and pulled out a sheet of paper that had an equation on it that came from Ed Prescott, and Lucas said, in the essay, ‘Normal people would ask for words to explain what the equation means. Economists ask for equations to explain what the words mean.’

This use of models, this tendency to formalise, to write things down as equations, is socialised into economists in our training. In graduate school I had a colleague who did a cookery corner in the department newsletter. One week there was a recipe for cookies one week, which ended, ‘Form the dough into convex sets and place in a separating hyper plane. Bake in the oven for twenty minutes.’

So this way of thinking is deeply ingrained, and economists are really poor at communicating in any other way, once you get the habit, the shorthand and the precision that using models brings you.

But dissenting economists, or ‘heterodox economists’, as they would call themselves, blame the use of models and mathematics in itself for the kind of economics that created the markets that we hate, the aspects of capitalism that we don’t like, and of course the financial crisis. They see what’s wrong with the system being largely what’s wrong with economics, and that’s largely mathematics and equations. I’m not sure that’s true.

In 1620 Francis Bacon — the scientist and philosopher, not the later artist — published a book called, ‘A Treatise on Scientific Method: Novum Organum Centurion’, which means ‘the new instrument of science’. This is the frontispiece, the ship sailing through the Pillars of Hercules, out of the Mediterranean, beyond the boundaries of the known world, into that empty territory of scientific discovery.

The first part of the book is all about the myths that mislead people in the way they think about the world, as a prelude to describing a proper scientific method. He calls them ‘idles’, these myths. The one that he thinks is the most dangerous, he calls ‘idles of the marketplace’.

Well, my ears pricked up when I read that. I was really intrigued to find out what he meant by ‘idles of the marketplace’. He means words. In the marketplace is where you go to chat and gossip and mislead your fellow traders and it’s all very ambiguous. He writes, ‘men associate through conversation but words are applied according to the capacity of ordinary people. Therefore, shoddy and inept application of words lay siege to the intellect’. So the use of words, he was arguing, was just insufficiently precise for proper scientific method and for genuine discovery. I think you can see that imprecision of words in some of the very abstract words we use to talk about the economy.

I want you to think about the word ‘capital’ and ask what that brings to mind. It comes from the Latin word for head. In financial markets its use originated in the middle ages and it meant the main bit of money from which other flows of money originated. I don’t know about you but when I think of capital, which is used in lots of ways, something like this comes to mind. It’s a heap of money. It sits there. Maybe it’s some gold bars in the vaults of the Bank of England but there’s a lot of ambiguity, a lot of different meanings of the word ‘capital’. We use it in quite metaphorical ways. We talk about human capital, meaning the level of education or skills that anybody has, or social capital, meaning some undefined thing about the way a society operates, and capital in lots of contexts in describing the way the economy works as well.

This ambiguity clouds quite technical discussions about reform of the banks. Reform of the banks is something that’s very urgently needed, and now I’m going to give you a little economics tutorial about banking.

This is a very simple bank balance sheet. Here’s a bank that has some liabilities on one side of its balance sheet and some assets on the other side of its balance sheet. Its liabilities are some shareholder capital and deposits, because deposits are assets to us but liabilities to the bank that is looking after them for us. On the assets side of its balance sheet, it’s got some reserves that it puts away for a rainy day in case depositors want their money back quickly, and loans, lending out to businesses or to households to buy homes.

This is what banks are supposed to do. They’re supposed to collect deposits from lots and lots of people, and pool that money and put it into useful, productive activities that will pay a return over time, pay back the depositors, and pay a profit to the bank on the way.

Now of course, in real life, banks are not this simple any more. So here’s a slightly more complicated bank balance sheet. I’ve added in the liabilities side, deposits as before, shareholder equity as before, but also debt. In real life, a lot of banks just go and borrow money from other banks to lend out in turn themselves.

On the assets side of the balance sheet, there’s the money they lend out to businesses and householders for homes, as well as the reserves they hold for a rainy day. They also make trading investments themselves, including investments in derivatives, like the options I was talking about right at the start. So this is a little bit more complicated now. Three kinds of liabilities: the deposits, the shareholder equity and the debt, the money that the bank borrows. Three kinds of assets: the reserves, the loans and the investments, the trading that the bank does on its own account.

Now, it might surprise you to know that banks don’t need to hold very much shareholder equity. In fact, before the crisis this would typically be a level of 3% of all the liabilities on its balance sheet. Just 3%.

This means that I could set up a bank with £3,000 of shareholder equity, borrow or find from deposits another £97,000, and most of that, for some banks, was borrowed money. They took in some deposits, but borrowed a lot of it in the capital markets themselves.

So, I’ve only put in £3,000 and I’ve borrowed £97,000. In turn, I lend out some of that for productive investments and keep some as reserves, say a fifth, say 20% I put in proper loans and keep as reserves, and 80% I can gamble in the derivatives markets. Because you don’t have to put up all the money, but only a fraction of it when you gamble in the derivatives markets. With £3,000 of shareholder equity, I can turn myself into an almost million pound business, all of it highly risky. That is exactly what the banks did before the financial crisis.

So the thing about talking about capital is that there are lots of different bits of this balance sheet that people sometimes mean when they use the word ‘capital’. They might mean the reserves. They might mean the shareholder equity. They might mean the investments that the bank makes, because it’s an abstract word and it has a very flexible set of meanings. That means that banks find it very easy to confuse policy makers, politicians, and ordinary people talking about how the banks need to change post crisis.

The point about stepping you through that rather dull tutorial was just to show that if you analyse it — and I didn’t use equations but I could have done it as algebra — if you analyse it and you pin down the meaning of each of those things, you can be very specific and say, ‘It’s the 3% that we’re worried about. That needs to be more like 30% to make the banking system safe.’ Using the words makes it much more ambiguous. Sometimes I think even bankers themselves don’t understand the cloudiness that they’re introducing into the discussion.