I think that's overstated: we can't just look at how much more the youth unemployment rate rose than the adult unemployment rate; we have to look at how much more it rose than we would have expected it to rise given the increase in the adult unemployment rate. We expect youth unemployment to be worse hit in a recession than adult unemployment; this time, it's been rather worse than in prior recessions. I've pegged it at around 10-12k more kids unemployed than we'd expect given the prior worst performance of youth unemployment. The method's described here; results here. It remains possible that something else happened that threw a great big wedge between the adult and youth unemployment rates, but you'd need something that happened about the same time as the change in minimum wage legislation and that has persisted from 2008 to present and that has a plausible theoretical reason for causing the effect and is big enough to have done the job.
On the other side, the New Zealand Herald columnist Tapu Misa says minimum wage critics are falsely painting Labour as folks ignorant of economic reality, citing Card & Krueger and Hyslop & Stillman as evidence against disemployment effects of minimum wages. But the American studies over an era where minimum wages were about a third of average wages just don't carry over well to New Zealand, where the minimum wage is half the average. And the Hyslop and Stillman paper, while very nice, spanned a period during which ability to fog a mirror was sufficient to get a job in New Zealand; increases in the youth minimum wage over that period were unlikely to be binding.
It's a bit ironic that Misa writes:
Since the global financial crisis, I've wondered if even economists understand what Thomas Carlyle called "the Dismal Science".As all economists know, or ought to know, Carlyle called economics the Dismal Science because economists like JS Mill opposed slavery; Carlyle thought that slavery was necessary to turn blacks from subhumans to being fully human. Economists were dismal for wishing to deny blacks the beneficent lash, in contrast to the gay science of poetry that recognized blacks' inferiority. And the minimum wage was introduced by early twentieth century progressives deliberately to disemploy blacks and women, rendering them unemployable.
Those wishing to ally with Carlyle in deeming economics as dismal ought consult the work in which he coined the term: his "Occasional Discourse on the Negro Question", or the US version entitled "Occasional Discourse on the Nigger Question". And their research on the economics of minimum wages really ought to go beyond literature reviews from the Council of Trade Unions.