Both are eloquent enough to speak for themselves, but Bainbridge makes more of a positive argument, while Drum is just making a passing dismissive crack. Drum favors raising the minimum wage at least "a buck or two." Bainbridge favors indexing it:
First, the minimum wage debate is not really a debate about how much money the working poor make. Instead, it is mainly a debate about how much working teenagers and twenty-somethings in their first job ought to make. The federal Bureau of Labor Statistics reports that (in 2002):
Minimum wage workers tend to be young. About half of workers earning $5.15 or less were under age 25, and slightly more than one-fourth were age 16-19.
Among workers over 25, only two percent - 2%! - earned the minimum wage. Sympathy for the working poor thus ought not to be a driver of minimum wage debates.
Second, setting aside the debate of whether an increase in the minimum wage affects the supply of jobs for teenagers (wages go up, employers hire fewer workers), an increase in the minimum wage increases the demand by teenagers for work:
Minimum wages increase the probability that teenagers leave school to become employed or work more hours, and increase the probability that they leave school and become non-enrolled and non-employed. Minimum wages also increase the probability that lower-wage employed teenagers become non-enrolled and non-employed.
In other words, because teenagers tend to apply too high a discount rate to the higher future income associated with higher educational attainment, they systematically underestimate the present value of the future deferred income associated with staying in school. As a result, when deciding between work and a present paycheck versus school and deferral of income, they will tend to err towards the former. Increasing the minimum wage simply makes the choice of work even more attractive.
This analysis has two implications for minimum wage policy. First, a differential lower minimum wage for those who have not completed a high school degree probably would result in a lower dropout rate. Second, the minimum wage ought to be indexed, so that it grows no faster than inflation, so as to not further bias the choice between work and school.