Americans are calling for an increase in the minimum wage and the airwaves and internet are filled with commentators claiming increasing the minimum wage won't have any unemployment effects, or any ill effects at all.
The problem with studies which claim there's no immediate employment effect is that they don't or can't examine other reactions to price controls. Employers could respond by cutting worker hours or hiring less (which would play out over the course of several years). They could raise prices, effectively reducing the wages of their customers. They could cut wages or raises from higher-paid workers which could hurt the underlying functionality of the business as these employees work less hard or quit. Indeed, many studies point to a real and negative unemployment effect to the minimum wage.
We know legally fixing prices make a mess of things. Pegging gas prices artificially low back in the 1970s created huge lines and massive shortages. Capping bread prices caused Washington's army to starve at Valley Forge. FDR and Hoover encouraged high prices during the Depression (on the theory that it would increase wages and employment), which helped transformed the 1930s into America's worst economic crisis in history.
Wages are prices for labor. Proponents of increasing the minimum wage are so willing to overturn over two centuries of economic thought, yet have no explanation why this particular price control won't have well-documented unintended consequences. The demand curve slopes down.