Cash also plays a role in the illegal immigration problem that bedevils countries like the United States. It is incredible that some politicians talk seriously about building huge border fences, yet no one seems to realize that a far more humane and effective approach would be to make it difficult for U.S. employers to use cash to pay ineligible workers off the books and often below the minimum wage. Jobs are the big magnet that drives the whole process.

This is from the introduction to Kenneth S. Rogoff, The Curse of Cash. Rogoff is a prominent economics professor at Harvard University and former chief economist at the International Monetary Fund.

At a recent Liberty Fund conference in San Antonio where I was the discussion leader, and where chapters from Rogoff constituted 30% to 40% of the readings, I highlighted Rogoff’s thoughts on immigration. I had missed this passage above until my friend Jeff Hummel pointed it out.

Here, though, are the parts I did highlight in the discussion questions I suggested. They cover the same territory:

Whatever one’s position on legal immigration, few would argue with the proposition that under normal circumstances, countries have a sovereign right to control their borders and to determine their immigration policy. The issue is becoming increasingly prominent across advanced economies. Some US politicians are proposing extreme measures, such as building a giant razor wire fence across the US-Mexican border, much as Hungary has done and other European countries are considering. Yet there seems to be precious little awareness of how much more difficult and risky it would be for employers to routinely hire illegal workers if they could not pay in cash, and how phasing out paper currency might prove a far more effective remedy than the alternatives being considered.

To be clear, I strongly favor allowing increased legal migration into advanced economies. Any economist who takes income and wealth inequality seriously realizes that, despite the enormous progress of the past three decades, differences across countries simply swamp the within-country inequality that Thomas Piketty and others worry about. The 2015 Nobel Prize winner Angus Deaton, author of the 2013 book The Great Escape, has forcefully made this point. International migration from poor countries to advanced ones create massive welfare gains for the immigrants. The issue is likely to become an even more important humanitarian concern if, as likely seems the case, climate change makes some parts of the world that are now densely populated uninhabitable. One can hope that enabling countries to better control their borders might lead to a more rational debate on immigration policy, though I admit that might be optimistic.

Rather than ask the question I asked the participants, I’ll lay out the tension between these two passages.

On the one hand, Rogoff favors the right of the U.S. government to decide who enters and who stays. On the other hand, he favors more legal immigration and makes the case for it beautifully and succinctly. But he wants to cut down on illegal immigration and sees the elimination of $100 and $50 (and possibly $20) bills as an effective way to do so.

Here’s the problem. If Rogoff is right that eliminating these high-denomination bills will substantially reduce illegal immigration, then his policy will also substantially reduce the “massive welfare gains for immigrants.” The only situation under which the massive welfare gains would continue is if legal immigration increased a lot. He and I can both hope that we would have a more rational debate on immigration policy that would lead to, say, an additional one million or two million people a year allowed to immigrate to the United States. But Rogoff admits that that is optimistic.

So, realistically, where are we? Either the U.S. government does not eliminate high-denomination bills and that facilitates illegal immigration along with the huge gains to immigrants from being able to work at higher-wage jobs or the U.S. government does ban those bills and those massive gains become smaller. Much as Rogoff might hope for more legal immigration, it’s clear that if choosing between the two alternatives I have laid out, he would choose the one that reduces those gains and, therefore, preserves some of the massive inequalities.