By next year, if you walk in a restaurant or gas station in Copenhagen, you might no longer be able to pay with cash. The Danish government is considering allowing some stores to stop taking paper money. It’s the next step as the country starts to get rid of cash completely: The central bank doesn’t print bills or make coins anymore, many banks don’t carry cash, and almost all adults have a credit or debit card.

Will places like the U.S. follow? Experts argue there are several reasons to get rid of paper money–like the fact that it might be able to help foil crime and force people to pay their taxes. In most countries, the majority of cash is used to hide secret transactions; in the U.S., only about 10% to 15% of paper money is used in the legal economy. The government misses out on hundreds of billions of dollars of taxes every year–not even counting the informal economy–because people get paid in cash.

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Still, while moving to electronic money might make things harder for criminals or tax evaders, it’s unlikely to eliminate the underground economy. “People will always find new ways to cheat,” says David Wolman, author of The End of Money. “Most money by value is already electronic, and we all know that there’s plenty of illicit activity involving digital money, ranging from garden-variety credit card fraud to colossal schemes orchestrated by the likes of Bernie Madoff. It’s all zeros and ones.”

And if the government–or potentially hackers–can track where people are spending money, that poses obvious challenges for privacy. “The privacy issue is enormous,” says Wolman. “We should be fighting for it in the already-very-digital present, let alone worrying about it in the highly hypothetical cashless future. But the fact is that no monetary system is perfectly safe. The issue is reducing risk and perceived risk sufficiently so that consumers/citizens feel comfortable enough using that system.”

Getting rid of cash does have other benefits. In Denmark, the move to let some stores stop using it was motivated by the fact that it costs those businesses money (it’s worth noting that for now, even if the new proposal passes, places like hospitals and grocery stores will still have to accept paper bills). It’s also obviously insecure: In the U.S., retailers lose around $40 billion a year because of the theft of cash (banks lose another $30 million or so in robberies).

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Without paper currency, it’s also easier for governments to change fiscal policy. Denmark already has negative interest rates; if you put money in the bank, you pay a fee. That helps encourage people to either spend money, or invest it. (Cash spoils this plan, since people can decide to hide it under a mattress and ignore the government’s interest rates.)

In Denmark, the transition may be easier to make than in other places. “It’s a wealthy and tech-savvy country, for starters,” says Wolman. “I also think a strong sense of civic-mindedness may factor into this kind of decision, or at least the decision to have more honest discussion about the economic and social costs of cash.”