Does minimum wage impact employment?
The problem is (of course) that it doesn't always, and doesn't always immediately impact it. So there's some plausible deniability for the economics deniers out there to find edge cases and say, "see". But as soon as you look deeper than the surface, you find that it does suppress growth, or increase a decline, sometimes ahead of the law and sometimes well behind it but it happens, and it especially hits certain segments and groups of people harder than others (like teens, starting out, part time work, and so on). Let's dive into the evidence.
Logically and historically, “yes”, raising the minimum wage hurts employment. There are lots of studies or politicians that will tell you the opposite, and they have some weak data to support their point. But the real economists can poke holes in their studies and reasoning.
Some of the common mistakes in the bad studies include:
- Bad studies cherry pick and look at a hot economy and look at growth instead of growth rate. If the majority of the market was already paying more than the new base rate, and in a growth market (labor demand is high), then you might lose a few jobs, but there’s enough growth to bury those losses in noise. So what they often find is “labor grew at 4%/year after the minimum wage increase”, and claim “no impact". Sure, but it was growing at 8% before the minimum wage and in competing areas that didn’t have the that burden. Thus the politicos will claim “4% growth” despite the minimum wage, the economists see a 4% loss compared to competitive markets. And when that market cools later (as all markets do), how many jobs are shed, and how quickly? Studies show that burdened economies drop faster/further than non-burdened ones.
- Bad studies only look at trailing impact — but people react in advance. So imagine it’s June and a law passes that says, “minimum wage will go up to $100/hour next January” — junk studies only track job losses from January on -- but businesses and businessmen aren’t dumb. Some people layoff in advance, even more just stop hiring in advance. Those are losses in advance. Once the debate about raising minimum wage first starts, there are losses (assuming businessmen are paying attention to their business). The flawed studies compare a few months before enactment (after the job hiring has cooled) to afterwards, and see little difference. But if you start counting from before the debate to after, you see a completely different story (the truth).
- Your total work package is not just your hourly wage but your benefits, work rules, and so on -- so if you get a $1/hour increase, that's worth $160/month, but if you lose a benefit worth $320/month (time off, training, etc), that can easily offset the wage increase (and more). Good studies looked at total benefits and proved minimum wage increases were often offset (and then some). Bad studies ignore this factor, proving they're either not very smart/good, or they're intentionally deceptive.
- A new gimmick is to start phasing in minimum wage over years: cook the frog slowly, so it doesn't jump out of the pot. This proves that even the left knows that minimum wage hurts. Why would you phase a benefit in over time and delay all that help? Why stop at $15/hour? Why not $150/hour, tomorrow (all at once), and make everyone rich? The fact that they phase it is, in proof that they know it hurts an economy. The reason they phase it in, is to hide the impact they know they’ll have. If they did it quickly, the impact would be more obvious and remove plausible deniability.
- Minimum wage doesn't hit all groups equally -- it hits the bottom, starting out, or restarting the hardest. Think about it. You're an employer and you're making a choice -- you can hire person-A for $10/hour, they have 10 years of experience in a fast food restaurant making minimum wage, or you have person-B who is either a teenager, immigrant (with limited communication skills), new college graduate with no job experience, or an ex-convict. It's a risk to hire B over A -- so you'll always pick A if they're at the same price. On the other hand, if you can save 20% on person B (hire them at $8/hour), then you might give them a chance. Removing that price flexibility makes it harder to start out, restart, or relocate -- hurting the people at the bottom the most. And remember, delaying getting a job and getting work-experience by 5 or 10 years, has a ripple in lifetime earning potential. Minimum wage ruins lives.
Studies that looked at subgroups most likely to be hurt by raising minimum wage, show exactly what you expect: it hits some people more than others. Downward moves (or hiring suppression) often happened in advance of enactment (labor markets scare easily). And any logic shows that if you raise all the workers pay by an amount, then the goods/services they produce will have to go up by at least as much -- and then everything the worker buys goes up by at least that much, meaning a best case net zero effect for that worker (and a negative effect for everyone else that had savings that wasn’t inflation protected) -- and more realistically, since there are margins to cover at multiple stages, things will go up by more than just the cost of labor (they go up by the cost of labor + margin), meaning a net loss for even the workers that think they benefited.
- 98% of economists say that raising the minimum wage doesn't help GDP (the economy). That's more consensus than Global Warming. 
- Economists will even start petitions to try to teach their politicians to stop. But it doesn't stop them.
- Prager University Video on Minimum Wage: https://www.facebook.com/prageru/videos/998924830150373/?theater
- Other studies show that while sometimes only a few jobs are lost, benefits are lost to offset the differences in costs, which is worse for workers. (It means more of their income is taxable, so they came out behind). 
- I offer a ton of links at the bottom to explore if you doubt any of this. Though deniers are good at denying, no matter how much evidence is provided.
- 98% Concsensus (more than Global Warming):
- Income offset by benefit cuts: