The simple minimum wage example in a principles of microeconomics goes something like this: If the minimum price of labor (wage) is set above the existing equilibrium wage in the market for labor, the result will be a decrease in the quantity demanded for labor (hiring), and an increase in the quantity supplied of labor (more people want to work at higher wages). The result in a surplus of workers willing to work at the minimum wage (unemployment). If prices work properly to ration labor, then we would expect wages to fall, but because the price cannot fall below the minimum wage, the surplus of labor (unemployment) is persistent.
An ironic caveat to this simple analysis is that the expected unemployment occurs among the group of people at whom the minimum wage law is targeted--those willing and able to work at the minimum wage. That is, if the simple analysis of minimum wages hold, then minimum wage laws are likely to cause unemployment among the lowest wage workers.
Until now, the empirical evidence on whether minimum wages laws cause unemployment has been mixed at best. In most studies, the change in minimum wage has been small, and authors have had to rely on comparing labor markets in similar cities that border policy jurisdictions with different minimum wage laws (think difference in minimum wage laws for similar cities in New Jersey and Pennsylvania, both located near the state line). But with the recent move toward large and geographically disparate changes in minimum wage laws, it looks like we will be seeing more studies examining this question.
And here's one from Luca and Luca* of the Harvard Business School put out in the last month that seems to support the simple model prediction that minimum wage laws result in decreases in employment:
We study the impact of the minimum wage on firm exit in the restaurant industry, exploiting recent changes in the minimum wage at the city level. The evidence suggests that higher minimum wages increase overall exit rates for restaurants. However, lower quality restaurants, which are already closer to the margin of exit, are disproportionately impacted by increases to the minimum wage. Our point estimates suggest that a one dollar increase in the minimum wage leads to a 14 percent increase in the likelihood of exit for a 3.5-star restaurant (which is the median rating), but has no discernible impact for a 5-star restaurant (on a 1 to 5 star scale).
Seems to be consistent with what we would expect from simple economics.
*I wonder if they live on the second floor?