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What limits central banks from setting highly negative interest rates if needed? Is it only that people can take out a lot of cash and put it in a vault, or are there other reasons?
If we had removed cash and only had electronic money, could central banks set interest rates highly negative, for instance, -10%? Could they set it to -20%? Or would people just have started to use other means of value, like foreign currencies, crypto currencies or gold?
Pretty much yes. It is because cash carries implicit zero interest in itself. In practice interest rates can be little bit negative because having all your money in form of cash could be dangerous (you might get robbed, also it’s not easy to store let’s say 20000e at home etc.).
However, if a country would went cashless the central bank could in principle set interest rate to any value they would like even -10%. In that case there is really no any other way how people could avoid the negative interest rate if they want to hold the money.
Since this is a question about central banks... they would not want to do this because it would push many ordinary people to put their savings in highly speculative assets, potentially destabilizing the economy. It is/was already a bit of a concern even with near zero, never mind mildly negative interest rates. There's a fine line between "kickstarting the economy" and setting up a large portion of the population to speculate in the junk bond market and/or housing.
Also, wealth inequality will probably go up faster as well (in the long) as more smaller investors get wiped out, although that's seldom a concern for central banks, given their usual mission.
As for hoarding cash in such an environment... that's not without risk either, because the authorities could decide to counter that with some kind of demonetization (see India, and numerous other historical examples.)
Also, in a democracy, weird stuff might happen, like the Swiss left- and right-wing populist parties threatening to put to a referendum a redistribution of the central bank profits into the pension funds (who blame the central bank for their losses.) That would basically negate the effect of the negative interest rates, as far as the pensions funds are concerned. In fact, it would act like a redistribution from others to said pension funds, ultimately.
What stops it are the basic laws of supply and demand.
A highly negative interest rate means that someone will pay you to take their money. There are very few people willing to offer credit on those terms.
This is the equivalent of me offering someone 100 dollars today and asking for 90 dollars in return tomorrow, with the added risk of not receiving all of the money back. There is nothing in it for me.
Central banks would in that case would be giving free money to private banks, which certainly would not pass on negative interest rates to borrowers, for reasons outlined above.
