One way to determine this is to look at national employment data after the minimum wage was raised.
The minimum wage has been changed 28 times since it was first instituted in 1938. It was lowered twice, in 1964 and 1969,and a couple of times in the 1950’s there were corrections relating to farm labor and manufacturing labor. See the Department of Labor web site: http://www.dol.gov/whd/minwage/chart.htm
Unfortunately the Bureau of Labor Statistics did not start keeping good comprehensive employment data until 1950, which means that we can’t adequately analyze the first couple of raises. But we do have good data since 1950.
A rough stand in to determine the rate of employment is the unemployment rate. If raising the minimum wage effects employment we should see that, to some degree, in an increase in the unemployment rate after the wage is raised.
To make matters relatively easy I look at the month the rate was changed, and the three months after the minimum wage was raised:
The unemployment numbers are from the Bureau of Labor Statistics Database available at:
http://data.bls.gov/pdq/SurveyOutputServlet
Since 1950, the minimum wage has been raised 24 times. The unemployment rate went up 8 times in the month after the wage was raised, went down ten time, and stayed the same six times. So, the unemployment rate went down more times then it went up. The minimum wage was actually lowered twice, in 1964 and 1969. Both times the unemployment rate stayed the same.
So much for the idea that raising the minimum wage hurts employment.