According to economic theory, a higher minimum wage (assuming that it is set above the equilibrium wage) will increase the quantity supplied of labor and will decrease the quantity demanded. This will lead to a surplus of labor, particularly for people under the age of 25, and will increase unemployment.
When a higher minimum wage is enacted, wages will rise for low wage workers. Many of those workers will be under 25. They will want to work more because of the higher wages. This will increase the quantity supplied of labor. However, employers will not want to hire as many people because it is more expensive to hire them. Therefore, the quantity of labor that is demanded will drop.
If the quantity of labor that is demanded drops, fewer people will have jobs. This will mean that the unemployment rate will rise. Again, it is likely that these changes will affect younger people much more than older people. The older people are more likely to already be making high wages, which means that they will not be affected by an increase in the minimum wage.