Most obviously, such a system would make moving money easier. Properly designed, a digital fiat currency could move seamlessly across otherwise incompatible payment networks, making transactions faster and cheaper. It would be of particular use to the poor, who could pay bills or accept payments online without need of a bank account, or make remittances without getting gouged.
For governments and their taxpayers, potential advantages abound. Issuing digital currency would be cheaper than printing bills and minting coins. It could improve statistical indicators, such as inflation and gross domestic product. Traceable transactions could help inhibit terrorist financing, money laundering, fraud, tax evasion and corruption.
The most far-reaching effect might be on monetary policy. For much of the past decade, central banks in the rich world have been hampered by what economists call the zero lower bound, or the inability to impose significantly negative interest rates. Persistent low demand and high unemployment may sometimes require interest rates to be pushed below zero - but why keep money in a deposit whose value keeps shrinking when you can hold cash instead? With rates near zero, that conundrum has led policy makers to novel and unpredictable methods of stimulating the economy, such as large-scale bond-buying.
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A digital legal tender could resolve this problem. Suppose the central bank charged the banks that deal with it a fee for accepting paper currency. In that way, it could set an exchange rate between electronic and paper money -- and by raising the fee, it would cause paper money to depreciate against the electronic standard.
This would eliminate the incentive to hold cash rather than digital money, allowing the central bank to push the interest rate below zero and thereby boost consumption and investment. It would be a big step toward doing without cash altogether.
Digital legal tender isn't without risk. A policy that drives down the value of paper money would meet political resistance and - to put it mildly - would require some explaining. It could hold back private innovation in digital currencies. Security will be an abiding concern. Non-cash payments also tend to exacerbate the human propensity to overspend. And you don't have to be paranoid to worry about Big Brother tracking your financial life.
Governments must be alert to these problems - because the key to getting people to adopt such a system is trust. A rule that a person's transaction history could be accessed only with a court order, for instance, might alleviate privacy concerns. Harmonising international regulations could encourage companies to keep experimenting. And an effective campaign to explain the new tender would be indispensable.
If policy makers are wise and attend to all that, they just might convince the public of a surprising truth about cash: They're better off without it.