To piggyback some on what Spoon said about minimum wage
Studies evaluating minimum wage/employment effects are basically a joke. They're like studying the ocean by evaluating waves on a beach. The vastness and depth that studies would require to demonstrate wage floor and employment effects is several magnitudes greater than any study has done.
What we do have is theory and models. We also have tons of data, but as with lots in economics, it's tangential and marginal. The value in economics comes mostly from engaging its concepts. Studies are great but they are hard as shit to conduct properly. Economics is a field of rigorous logic more than a field of experimentation, even though experimentation is great for it.
To conceptually see why the minimum wage negatively affects employment, all we have to do is conduct a simple thought experiment: make the minimum wage $1000 and evaluate what you think is going to happen. The sensible will say "prices will increase by that dollar amount and that's it". Which is true in a vacuum, and it shows that wages by themselves should not be expected to increase prosperity.
I'll try to get brief here on out (fat chance): the short of the effects of relatively small minimum wage increases do include price increases as an offset and a reduction in new hiring and higher structural unemployment. But I want to hit more deeply on how minimum wage harms the several different groups it tries to help. The two groups are the poor-poor and the "well-off" poor, so to speak.
The poor-poor are typically minorities with low skills. Think: large percentages of black or Hispanic. The well-off poor are typically white and educated. Think: liberal arts graduate baristas. The latter is the less egregiously affected group.
As was pointed out by Renton and Spoon, the most valuable tool any laborer has is the value employers find of their skills and their ability to negotiate. If a laborer produces $7 in value, he won't have a job if his skills only produce $6 in value. A minimum wage forces him out of the labor force and makes him perpetually dependent on the taxes taken from people in the labor force. Additionally, the most effective method for a low-skill laborer to increase his skills is on-the-job work. Not allowing low-skilled individuals to work for whatever they can get, no matter how low, is the poverty trap. Wage floor and barrier-to-entry regulations is a system of productive laborers being forced to subsidize maintenance of non-labor.
But what about for laborers with low-skill who still have their jobs even with increased wage floors? Well, guess what, their jobs just got worse. Take a laborer who creates $11/hr and is paid $9/hr. Bump his minimum wage up to $15/hr. Now he is losing money for his company and either has to get fired or increase productivity. So now instead of making 20 burgers/hr he makes 30. But wait, the sales don't call for 30 burgers/hr, so instead he has to do other stuff to justify his employment. Those 20 burgers he makes now must achieve specs better. No more leeway on tiny portion discrepancies. The managers install a new ridiculous measurement technique to keep costs down. He now has to keep the kitchen cleaner. The dishwasher's hours now have to be cut and the cook now is responsible for two jobs during non-peak hours. The fry cook no longer works in non-peak hours, so our protagonist now works grill and fry simultaneously from 1-4PM. Our protagonist making $15/hr now has three jobs when he previously had just one job. His stress is through the roof and he hates his fucking job now. He blows all his extra money on needless consumer goods to keep him from going insane. He wishes he could go back to a time when the government didn't force his employer to pay him more money than he wants to work for.
Enter: the well-off poor. He got his degree. He can think critically and he has a work ethic, but his skills are not terribly effective for well-paying business, and honestly he doesn't want to wear a button up shirt to work or sit in a cubicle. His productivity is double that of the low-skill employees in his sector. A minimum wage boost to $15 doesn't hurt him much since he was already pretty good at his job and his employer was already paying him accordingly. But now, all of a sudden, nobody named Jose or Tyrone seems to get hired anymore. Every new employee is another college educated hipster. He rooms with three of them. Together they make just enough to "live the dream" in the most vibrant city in the region.
Nevermind that this sounds to me like that "institutional racism" that the left-wing falsely blames the market for creating. Here we have a scenario that vastly subsidizes one group of people. The group that that isn't wealthy or terribly poor, but isn't that interested in using all their tools. Their education is subsidized, their culture is indirectly subsidized, and they're inadvertently locked into their income bracket. They're the only beneficiaries of minimum wage, at the cost of the poor non-majority groups and the productive business/labor classes. But the benefits they receive from the wage floor is the worst thing for them. They may not be stuck in a poverty trap, but they're certainly stuck in a trap of what one of my friends called "baristas who want to maintain the lifestyle one would normally only get if not a barista".
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