French economist Thomas Piketty has been making many headlines in the U.S. with his message that income inequality is not going away and will probably get worse.

Related: U.S. inequality looks like Europe before WWI: Thomas Piketty

Nobel Prize winner Robert Shiller says the U.S. should take action now to protect against this future scenario by indexing income taxes to inequality. He outlined his proposal this month in The New York Times.

"Some measure of inequality is necessary in any functioning capitalist economy," he says in the video above. "The risk is that it will get much worse in the future."

His proposed "contingency plan" would automatically raise taxes on richer people -- but only if inequality gets worse. This system would be dictated by a formula written into the tax code, which would adjust rates continually. Shiller thinks the change might be politically feasible since it wouldn't raise taxes now.

The kinks include an exorbitant top tax rate. Shiller found that in his own 2006 study with Tax Policy Center Director Len Burman that looked at how indexing taxes could have put a stop to increases in inequality starting in 1979 -- by 2006 the top tax bracket would have been taxed at 75%. Shiller advocates a scaled back, much-reduced version of this proposal that Burman presented to the Senate Finance Committee recently.

Related: CEO pay: 'Unbelievably piggish and outrageous,' no matter how you slice it

Shiller says there would be an incentive concern if rates were too high, and that that would be a big mistake.

At the same time, he says, "I don't like high taxes either, but there is this risk that inequality could get horrible in the future ... [this plan] sounds strange but it's actually very sensible ... wealthy people are not necessarily opposed to this. This is in the interest of everyone, you wouldn't want to live as a billionaire in some very unequal society."

In taxing the rich more, how would that help the middle or working class struggling with falling wages and joblessness? Shiller says the earned income tax credit might need to be increased if inequality gets worse. It's currently limited to a little over $5,000 a year.

Related: How to become more successful--by working less

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