On paper it seems like high minimum wages would likely lead to worse working conditions that partially offset the gains of a minimum wage, are economically inefficient, and seem really bad from a liberal perspective.
This is one of my biggest worries about minimum wages. I'm interested in understanding what is known about that kind of phenomenon and how proponents of minimum wages feel about it---is the difference between me and other people that I find the theoretical case more convincing, or is it that other people have empirical evidence that makes them less concerned? Is this kind of argument less persuasive to people who have real experience in low-wage jobs, and if so what do they see that makes it seem so much less persuasive? Are there big differences between the views of low-wage workers vs low-wage employers?
Suppose I'm paying a market-clearing wage of $10/hour. The desire to attract and retain my employees is likely to be a big part of why I pay $10/hour instead of $9/hour. It may also be a big part of how I pick other parameters of the job---if I offer jobs that give more skills, are more flexible, or are more pleasant, then I'm more likely to attract and retain employees at a lower wage.
The economically efficient outcome is to spend $1 making working conditions better iff employees would be willing to spend $1 for that improvement. Fortunately, this is roughly what a selfish employer would do, since they could spend $1 either to increase wages by $1 or to improve working conditions, and they are incentivized to do whichever potential employees prefer.
(A priori I'd expect workplaces to have inefficiently bad working conditions because changing jobs is hard and it's easier for potential hires to monitor wages than working conditions, which seems super important but doesn't seem to change the bottom line here.)
If we introduce a $15/hour minimum wage, the selfish motive for not exploiting workers seems to be gone or greatly reduced. If I could legally lower wages by $1 then I would do so, and by the same token if I could find some other way to save $1 by making the job crappier then I'd do that too (even if it would impose $2 of costs on my employees). We'll try to make that illegal, but the law can't cover everything and there is a huge surface area---I can reduce flexibility, pressure people into working harder or longer, invest less in workplace pleasantness, work at worse hours, etc.
This dynamic, where employers are incentivized to exploit workers with the law as worker's only protection, seems very bad. This is one reason that a large minimum wage increase sounds like a really bad idea relative to a tax credit, even if we ignored possible employment effects (which seem real but modest) and efficiency considerations (which seem decisive but not a huge deal in the scheme of things).
One reason this effect might be smaller is if the parameters of low-wage jobs are mostly being determined by goodwill of employers rather than by economic incentives. This isn't my impression of the common view on the left (which seems to basically consider corporate employers evil), but I could imagine it making a huge difference to the appeal of minimum wages.
I think the most satisfying way to study this would be looking at working conditions for jobs that have been at the minimum wage for a long time vs those that have been somewhat above the minimum wage. But it would also seem extremely valuable just to get survey data about how employers have responded or anticipate responding to minimum wage changes. I'm not aware of empirical work along those lines but it seems like it must exist and I'm just failing to find it.
My sense is that minimum wage proponents don't believe very much in the market as a protection against exploitation in low-wage jobs, and I'm also interested in other empirical evidence (or anecdote) that bears on that. The theoretical case seems quite good, and behavior seems to match the theory in high-wage work. People often cite ways in which low-wage jobs suck, but it would be super interesting to get even anecdotal evidence of the form "Improving working conditions would only increase costs by $1/hour but it would be worth $2/hour to employees."
(The flip side of this is that a UBI would also increase low-wage worker's willingness to pay for workplace improvements and so lead pretty directly to better working conditions. It would also decrease the supply of low-wage work and so tend to improve both wages + working conditions. So the same sorts of evidence also seem important for understanding whether a UBI would effectively achieve other goals on the left.)