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A customer uses an Apple iPhone to pay via the Apple Pay system.Bloomberg

The move to a cashless society is about much more than just consumer convenience. As nice as it is to be able to buy a coffee without fumbling for change, the economic transformation from ditching paper money has the potential to reach far deeper than that.

Picture a world where you might have to pay banks to hold your money. Where regulators could at times make it punitively expensive to save.

Mind you, this would also be a world where recessions would be rare and brief, where inflation would be non-existent.

At least, so goes the theory. It rests on the new powers that central bank policy-makers would be able to wield in a society dominated by electronic, rather than paper, money.

Miles Kimball, a professor of economics at the University of Colorado at Boulder, has become one of the best-known advocates for this vision. He has outlined how it might work in several academic papers, as well as blog posts and presentations to central banks.

He pictures a world where the widespread use of electronic money would make it relatively easy for banks to impose negative rates on savers during times of economic stagnation – in other words, to charge depositors for holding their money.

Why would this be a good thing? Central banks chop rates in a recession to discourage the hoarding of money and encourage borrowing and spending. This has been standard practice for decades.

The problem comes when interest rates are already at zero, as they were in much of the world in the years immediately after the financial crisis. At this point, known as the zero bound, policy-makers cannot cut rates further because savers can evade the sting of negative rates by withdrawing their money from the bank and holding it in paper bills.

However, if electronic money becomes the norm, that option will no longer be available. People won’t be able to shelter their savings in paper form, so policy-makers will be able to take rates as far as they want into negative territory without fear of consumers fleeing for cover.

The ability to pull rates deep into negative territory could have important advantages for policy-makers if the economy becomes stuck in a long period of stagnation.

During such bleak periods, businesses are reluctant to borrow, even at an interest rate of zero, because they don’t know if they can make a profit by investing in new equipment. Ordinary people put off buying cars and homes because they’re afraid of what will happen next. Instead, everyone tries to save.

One way to get the economy moving again is to send a strong message that this is not the time to save, but to invest and spend. And nothing sends that message better than negative rates, which punish savers and reward those who borrow money to purchase goods or build new ventures.

According to Prof. Kimball’s presentations, negative rates would only be used rarely and in cases where simply lowering rates to zero hasn’t been enough to deliver the jolt of stimulus required to restore economic growth. The United States might have benefited from negative rates immediately after the financial crisis, and Europe, which already has mildly negative rates in some cases, could arguably benefit right now from much deeper negative rates to break out of its economic funk.

Governments don’t need to rule out paper money to make this come to pass, Prof. Kimball says. So long as electronic money is dominant, authorities could simply impose fees on paper money when it is deposited at a bank to make its return match that of its electronic cousin.

To be sure, this sounds intrusive and complicated to administer. But the benefits would be much larger than the rare bouts of pain, Prof. Kimball argues.

Recessions would not linger, because strongly negative rates would jolt the economy back to growth in short order. And central banks would no longer have to target a minimal level of inflation to ensure they have room to cut rates before hitting the zero bound. With the new-found ability to impose negative rates, they could instead aim to bring inflation to zero.

Not everyone is convinced. Former U.S. treasury secretary Larry Summers, Gauti Eggertsson and Ella Getz Wold of Brown University and Ragnar Juelsrud of Norges Bank recently collaborated on a working paper that casts doubt on the notion of negative rates as a policy tool.

Their paper, published in January, looks at the experience of Sweden, which became the first country to introduce negative interest rates in 2009. The experiment has not been as successful as its designers hoped. Instead of falling, some bank lending rates went up. The researchers suggest that negative rates appear to impair bank profits and can lead to a contraction, not an expansion, of the economy.

But the debate continues. Ruchir Agarwal and Signe Krogstrup of the International Monetary Fund wrote a blog post this past week arguing that a system such as the one proposed by Prof. Kimball could work if properly implemented. For now, the one thing that is clear is that a cashless society could have much broader implications for policy-makers than most of us realize.