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The case to get rid of paper money

FORTUNE — Kenneth Rogoff thinks we would be better off with bitcoin, or something like that, probably.

Rogoff became famous — and infamous — a few years ago for his book, This Time in Different, on the dangers of debt. He, along with his co-author Carmen Reinhart, concluded that when countries take on a lot of debt their economies tended to slow down.

It was later discovered that the conclusion of the book was based, at least partially, on some mistakes the two economists made in Microsoft Excel. Others have pointed out that Reinhart and Rogoff may have gotten the sequence wrong. Slow growth might lead to higher debt, not the other way around.

But that didn’t matter. Rogoff’s book was enthusiastically embraced by the half of Washington that hates spending and social welfare programs. And it caused the other half of Washington to question their beliefs.

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Now Rogoff wants to take away all our money. He’s out with a new paper this week, published on the National Bureau of Economic Research’s website, arguing that the economy would be better off without coins, dollars, and other physical forms of money. Bitcoin for all, I guess, or some national version of it.

Technology buffs have been trying to get rid of paper currency for a while. Fortune wrote a cover story on the topic about a year ago.

Rogoff’s main point has to do with the Federal Reserve and recovering from recessions. To stimulate the economy, the U.S. central bank has cut interest rates all the way to zero, because it was a bad recession and there was a financial crisis and interest rates weren’t all that low to start with. The Fed is also buying bonds, which has driven some people a little bit crazy, but let’s put that aside for now. At best, these stimulus programs have helped the economy a bit, but not as much as many people would like.

The problem is, with interest rates already at zero, they can’t go any lower. Or can they?

Rogoff argues that, if we only had virtual currency, interest rates could dip below zero. Negative interest rates seem fun, until you consider the consequences.

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Yes, with negative interest rates, banks pay you to take out a loan. That’s good for borrowers, as long as banks are willing to lend. But negative interest rates would be terrible for savers, who instead of getting paid money to keep money in the bank — albeit not much these days — would be charged a fee, on top of the ATM and other fees we are already paying. So any money you keep at the bank would slowly disappear.

And that’s the point of Fed stimulus. It’s supposed to get people to spend their money rather than hoard it. But some savers, perhaps quite a few of them, are not likely to change their ways so fast. Instead, they may very well ask for their money back and stick it under a mattress. That would likely crater the banks and crush the economy.

But if there was no paper money, Rogoff asserts, we could avoid such a catastrophe. Virtual money has to be stored in a bank or some other type of financial institution, so you can’t hide it from the Fed.

Although, it seems pretty clear that a system like this would break down. People would print their own money or maybe just barter. Another plus for virtual currency, Rogoff argues, is that it could increase taxes. Without cash, the government could track all transactions, and make sure it gets its cut. Rogoff says it would also curtail illegal activity. He even worries about what affect such a shift would have on the economy.

But who really believes that would happen? People would figure out a way to buy, or more likely sell, cocaine and sex. We’re an inventive species.