A higher minimum wage doesn't have to kill jobs.

The 13 U.S. states that increased their minimum wages on January 1 saw higher employment growth, on average, than the states where the minimum wage didn't change, according to an analysis by the Center for Economic Policy Research, a progressive think tank.

Four states passed laws to raise wages, while nine others had automatic wage increases pegged to inflation. The employment rate rose 0.99 percent, on average, in those states in the first five months of 2014, according to the CEPR. Employment rose by just 0.68 percent, on average, during that same period in the 37 states that didn't raise wages.

These employment rate gains are the difference between the average employment rate during the first five months of 2014 and the average employment rate during the last five months of 2013.

The chart below shows the data, which builds on research first done by Goldman Sachs.

As you can see, all of the states that raised the minimum wage, with the exception of New Jersey, have seen positive job growth. Washington D.C., which CEPR didn't include in its analysis, raised its minimum wage from $8.25 to $9.50 on July 1.

CEPR's study is the latest to debunk the common argument that raising the minimum wage is an economy killer. Earlier this week, Andy Puzder, CEO of CKE restaurants, the parent company of Hardees and Carl’s Jr., hypothesized that a higher minimum wage would increase youth unemployment and cause all sorts of economic problems.

“Government needs to get out of the way,” he told Yahoo! Finance. “If government gets out of the way, businesses will create jobs and wages will go up."

But economic research has shown this simply isn't the case. Take San Francisco, where the minimum wage, $10.74 an hour, is one of the highest in the country. The city has seen faster job growth than any other big city over the past 10 years. Likewise, Washington state, which has the highest state minimum wage in the country at $9.32, has seen faster job growth than any other state.