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Oklahoma Gov. Mary Fallin signed into law on Tuesday a measure that would ban cities in her state from increasing their minimum wages above the state's. It's been hailed as move to protect jobs — but the evidence that it will actually do so is heavily disputed.

When President Obama raised the issue of a minimum wage increase in January, the U.S. Chamber of Commerce came out against the idea. "One need not resort to a polygraph test to prove that proponents know raising the minimum wage destroys jobs," the Chamber wrote on its blog. "Simple logic will do." That logic? Increased wages mean that less money is available to hire employees, so employers will lay people off.

The Chamber's argument — which is by no means a new one — was bolstered by a February study from the non-partisan Congressional Budget Office, which estimated that the increase Obama sought, $10.10 an hour, could cost between a few thousand and a million jobs nationally by the end of 2016. (Oklahoma's 1.2 percent of the country's population suggests the state would lose around 12,000 of that million jobs.)

Shortly after that report was released, the editorial board of The New York Times came out in favor of Obama's proposal. "One 2013 study," the board wrote, "… compared the experiences of businesses in neighboring counties in different states and found less turnover in states that had raised the minimum wage." What's more, the Times notes, higher wages mean more spending power.