Minimum wage is complicated

According to a simple economic analysis, minimum wage should decrease employment.

At equilibrium, the wage level is set such that the supply of workers is equal to the demand for workers.  If we artificially set wages higher, then the supply of workers increases (as more people are willing to work) and the demand for workers decreases (as fewer employers are willing to hire).  The level of employment is set by the supply or demand, whichever is lower.  Thus a minimum wage should create a demand-limited market with fewer people employed.

Personally, I would support increasing the minimum wage whether or not it reduces employment.  In light of the gross wealth inequality in the US, I am in favor of transferring as much wealth to unskilled workers as possible.  Thus, I do not actually want to maximize employment, I want to maximize the product of wages and employment.  Even though a higher minimum wage might hurt some people by costing them their jobs, there is a net gain in wealth to the class of unskilled workers.

One thing that annoys me about (other) people who advocate increasing minimum wage is that they never seem to discuss the argument that it decreases employment. Do they believe that decreased employment is an acceptable cost, or do they believe that the simple economic argument is incorrect?  If the latter, why is it incorrect?  Silence is just about the least satisfying rebuttal.

But the other day I heard an interesting argument.  Minimum wage workers currently have their income supplemented by welfare.  This allows employers to skimp on wages, essentially benefiting from welfare.  A minimum wage should be implemented such that employers can no longer do this.

Intriguing, but does it actually work as an explanation?

I wanted to do some simple mathematical analysis, like I did with monopolies and monopsonies, but I immediately ran into problems.  For one thing, a simple analysis of welfare suggested that it should actually increase wages, not decrease them (perhaps I'll show this in a different post).  For another, a quick bit of research revealed that nobody understands how minimum wage affects employment.

Apparently, it's one of the hottest questions in economic research.  A few major meta-analyses show that there is no link between state-level minimum wage and unemployment, and that net positive results are due to publication bias.  However, there might be a link for federal minimum wage.  Economists have proposed all sorts of explanations but few of them I can understand, and none of them have consensus.  One thing's for sure, the simple economic analysis is inadequate.

Lesson learned: I was wrong.  I had a little bit of knowledge of economics, but this is a case where a little knowledge is actively harmful.  I believed that I could apply simple economic analysis when I couldn't.  People who argue that minimum wage does not increase unemployment, but fail to supply any reason for this are in fact taking the correct position.  So far as we can tell, minimum wage does not necessarily increase unemployment, and so far as we can tell, no one knows why.