IMAGINE a world in which tax offices harry people who file their returns promptly; where big supermarket chains pay their suppliers before the goods fly off the shelves and not months afterwards; and where a pre-paid annual gym membership is more costly than paying month by month. It sounds fanciful, absurd even. Yet such a world came a step closer on January 29th, when Japan’s central bank cut the interest rate on bank reserves to -0.1% (see article). Like its peers in Denmark, the euro area, Sweden and Switzerland, the Bank of Japan will charge commercial banks for holding deposits with it. Almost a quarter of the world’s GDP now comes from countries with negative rates. Though they defy convention, they have proved a useful addition to the central-banking toolkit. The lowest deposit rate set by the central bank acts as a floor for short-term interest rates in money markets and for borrowing rates generally. Borrowing costs across Europe have tumbled, helping the fight against deflation and driving down exchange rates.

Emboldened, Haruhiko Kuroda, the governor of Japan’s central bank, this week claimed there is no limit to measures to ease monetary policy. On interest rates, at least, that is wrong. The limit may no longer be zero but it does still exist.

Tiers are not enough

Not so long ago it was widely thought that, if interest rates went below zero, banks and their depositors would simply switch to cash, which pays no interest but doesn’t charge any either. Yet deposits in Europe, where rates have been negative for well over a year, have been stable. For commercial banks, a small interest charge on electronic deposits has proved to be bearable compared with the costs of safely storing stacks of cash—and not yet onerous enough to try to pass on to individual depositors.

That has resulted in an unavoidable squeeze on profits of banks, particularly in the euro area, where an interest rate of -0.3% applies to almost all commercial-bank reserves. (As in Switzerland and Denmark, Japan’s central bank has shielded banks from the full effect by setting up a system of tiered interest rates, in which the negative rate applies only to new reserves.) If interest rates go deeper into negative territory, profit margins will be squeezed harder—even in places where central banks have tried to protect banks. And if banks are not profitable, they are less able to add to the capital buffers that let them operate safely.

That would put pressure on banks to charge their own customers for deposits. Such pressure is already starting to tell. Banks in Europe have started to pass on some of the cost of negative rates to big corporate depositors. Their only ready alternative to stashing large pots of cash is safe and liquid government bonds, whose yields have also turned negative, for terms of up to ten years in Switzerland. Rich personal-account holders are next. The boss of Julius Baer, a Swiss private bank, said this week that if interest rates in Europe go further into the red, it might have to charge depositors.

Retail customers are more resistant to charges, because small stashes can easily be stored in a mattress or a home safe. Savers might stomach a modest fee for making bank deposits, but as rates go deeper into negative territory, they will find ways to avoid charges. Switching to cash is the obvious solution, which is why some have suggested getting rid of banknotes altogether, but it is not the only one. Small savers would use any available form of prepayment—gift vouchers, long-term subscriptions, urban-transport cards or mobile-phone SIM cards—to avoid the cost of having money in the bank.

That would be only the start of the topsy-turviness. Were interest rates negative enough for long enough, specialist security firms would emerge that would build vaults to store cash on behalf of big depositors and clear transfers between their customers’ accounts. Firms would seek to make payments quickly and receive them slowly. Tax offices would discourage prompt settlement or overpayment of accounts: one Swiss canton has already stopped discounts for early tax payment and said it wants to receive money as late as possible. Far from being incentivised to lend more, banks worried about shrinking deposits would be warier of extending credit.

As avenues to avoid negative rates are closed off, human ingenuity will ensure that others open up. It may not be zero, but there is still a lower bound to interest rates.