Bernie Sanders and Hillary Clinton debate at the Brooklyn Navy Yard in New York on Thursday. REUTERS/Lucas Jackson

A confusing exchange between Hillary Clinton and Bernie Sanders in Thursday night's debate in Brooklyn left unclear where Clinton stands on an important question for voters in the Democratic presidential primary: the $15 hourly minimum wage.

Clinton's position has been consistent, but it's a complicated one. While she has given her support to specific labor movements advocating for a $15 minimum in particular areas, she thinks the right minimum level nationwide is $12 an hour.

"I have supported the fight for $15," she said Thursday in CNN's debate. "I have said from the very beginning that I supported the fight for $15."

"I think the secretary has confused a lot of people," Sanders rejoined. "I don't know how you're there for the fight for $15 when you say you want a $12-an-hour national minimum wage."

[Read more: The Brooklyn Democratic debate transcript]

Clinton has been making the same argument since last year. In June, she told workers organizing in Detroit for a $15 hourly minimum they she supported their efforts.

"I want to be your champion. I want to fight with you every day," she said, without endorsing a $15 national minimum wage.

[Read more: How the $15 minimum wage could become a new dividing line in the 2016 primary]

Instead, she called on local governments to make that decision. "We need more cities and states to follow the lead of Los Angeles and St. Louis and New York," she said, listing a few jurisdictions where policymakers have increased the minimum wage. In California and New York, the minimum wage is set to rise to $15 an hour. Aldermen in St. Louis sought to increase the minimum to $11 an hour, but so far, the courts have stymied them.

Clinton's position accords with that of the Obama administration and some liberal economists, who worry that a $15 minimum wage could put workers out of a job in many parts of the country where wages and retail prices are generally lower. In those areas, businesses hoping to serve more customers and sell more products by hiring more workers might find that the additional sales don't make up the cost of the $15 hourly wage. They might hire fewer people as a result.

[Read more: It’s Hillary Clinton and Barack Obama versus liberals on the minimum wage]

For example, Arindrajit Dube, an economist at the University of Massachusetts, Amherst and a vocal supporter of increasing the minimum wage, argues that local governments set the minimum in the neighborhood of half the median wage in their jurisdiction to align minimum wages with prices.

Clinton's campaign restated her position Thursday night. Clinton "encourages states, cities, and workers through bargaining to go even higher, including a $15 minimum wage in places where it makes sense," a release from the organization stated.

Others argue in favor of a $15 national minimum wage, including former Labor Secretary Robert Reich. He's written that while increasing the federal minimum wage to $15 might result in fewer people working, it's wrong to employ people for less than that amount anyway.

While Clinton believes $12 an hour is the right federal minimum, she is not steadfastly opposed to the idea of a $15 hourly minimum nationwide. On Thursday, CNN's Wolf Blitzer asked if she would sign a bill from Congress setting the federal minimum at that level (something that would be politically improbable). "Well, of course I would," she said.

Correction: An earlier version of this post incorrectly stated the minimum wage in St. Louis. While aldermen voted to increase the minimum to $11 an hour last year, a state judge later threw out that vote. The issue is now being decided by Missouri's Supreme Court.