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.

A 2011 study reported by Business Insider echoed the 2013 study. A survey of employers found that reducing staff was the eighth-most likely response to a minimum wage increase, behind increasing performance standards, cutting hours, hiring more experienced workers, and postponing other pay raises.

If you look at the history of national minimum wage increases, it's hard to see a strong correlation between increased wages and decreased employment. The graph below shows the annual change in national employment on July of each year (the red line) versus minimum wage changes (gray bars, tied to the right scale).

Minimum wage data from the Dept. Of Labor; employment data from the Federal Reserve.

That 2008 – 2010 stretch seems telling: minimum wages went up as employment plummeted. But you may recall some extenuating circumstances in that time period: the collapse of major financial institutions, etc. In the 1990 – 1991 time period, job growth followed a minimum wage increase. In the 1997 – 1998 period, a minimum wage increase appears to have had no effect on the labor market.

If you look at employment within the state of Oklahoma (for which data only goes back to 1990), it doesn't look much different. The broader economy has an obvious effect on Oklahoma's employment. The effect of national minimum wage increases isn't apparent.

There's a big political benefit to Fallin in signing the legislation: it positions her as a proactive conservative on a politically virulent topic. And, we have to note, it blocks a labor-backed initiative in Oklahoma City that would have raised wages. That will also pay political benefits.

Did Fallin actually help protect jobs in Oklahoma? Simple logic says … that it's difficult to say. It may help protect one job though: Fallin's. She's running for reelection in a contested Republican primary in June, and this signature certainly won't hurt her chances.