There are slight differences, depending on how I describe the change in the minimum wage.
Here is the change in employment per dollar increase in the minimum wage, which doesn't account for increasing incomes over time:
Here is the change in employment per 100% increase in the minimum wage, which doesn't account for the increasing effect of the minimum wage as it increases (eg. if the minimum wage was 2 cents/hour, we wouldn't expect a doubling to have an effect on employment):
Here is the change in employment given an increase in the minimum wage roughly equal to the average wage. (eg. if there were no minimum wage and a new minimum wage was enacted, set at the average wage level, this would be the effect on employment). Of course, this would not be a linear relationship, as very low levels of MW would have little effect, and if we tried to implement a MW as high as the average wage, the labor market would implode. So, this way of addressing the effect is imperfect, but probably gives a decent result, given the typical level of the minimum wage, and it helps to scale the effect without the problem of inflation or changing MW levels, compared to the previous two charts.
It might give better results to do a regression against both the change in MW and the level, but I don't want to get too complicated for this post:
So, depending a little bit on how we measure it, we see a very large effect among teenagers, a negligible effect on middle-aged workers, and a somewhat strong effect on older workers. This is basically intuitive, since teenagers and very old workers would be more likely to be working in low-marginal-productivity jobs. The results for 25-54 year olds tend not to be statistically significant, because only 1-3% of these age groups are working at low wages at any given time. In recent years, 8% to 18% of teens have been working at or below minimum wage at any given time, so a change in the price floor has a statistically significant effect on them. The one surprising outcome here is the apparent positive effect on 20 somethings in the last chart. I wonder if there is a substitution effect happening there, where teenagers are priced out of work, which leads to a recasting of the lost jobs into more productive jobs that slightly older workers with more experience and dependableness can perform. This could be pointing to a mitigating factor that keeps the negative effect on employment from being worse. Low productivity workers are put out of work, and so if there are some higher productivity workers who are available for those jobs, there could be a contrary effect where there are more jobs for those workers.
Over a long period of time we have seen labor force participation decline among young people. The minimum wage hasn't risen over this time relative to average wages, but we do see the LFP rate decline as new minimum wage increases are implemented. A combination of the effects of the minimum wage and cultural changes appear to be leading young people into schooling as a substitute for entry level employment. This probably relates to the internship issue I recently considered, and the distinction between training through work or school. Wage floors force workers to seek employment status signals outside of actual employment. They have to try to build up enough personal capital to be productive enough to earn a legal wage level. This pushes a lot more young people into extended schooling that is probably not an optimal use of their time. I suspect we would be a lot better off if the pendulum could swing back toward an equilibrium where more young people gained skills and status on the job. A lot of effort and resources are being put into schooling that costs young people a tremendous amount. The attitudes of most students about school content suggests that it is an expensive signal that is not strongly related to the accrual of actual skills. In the alternative world, many young people would be producing instead of consuming, earning income instead of building debts, and likely would gain more skills and status in the process.
Why is it considered enlightened to have a public policy that leads to a bunch of 21 year old kids with $20,000 in debt and 2 1/2 years of classes for a liberal arts degree they're never going to get, but it's inhumane for them to stock shelves for a retailer for a couple of years for $6/hour. It doesn't even look like a contest to me. Instead of letting these kids do what's best for them, we're imposing anti-market biases and bourgeois pretenses on them, to nobody's benefit in the long run.