We're already seeing the effects of minimum wage rises
That, at some point, high minimum wages cause job losses is both obvious and generally held to be true. The question, always, is when? And the truth of the matter is that we’re already seeing those losses at current levels of the UK minimum wage:
Young people and part time workers are bearing the brunt of the UK jobs slowdown,
The minimum wage is, obviously, enough, most bringing upon those with low wages. Who get lower wages than others? The young and part timers. So, who would we see losing out from a minimum wage that is “too high”? The young and part time workers.
From the ONS:
The number of part-time workers fell by 164,000 to 8.54 million in Quarter 3 2019, while the number of full-time workers increased by 106,000 to 24.21 million.
It’s not the same people either:
The decline in part-time workers was driven by women (down 106,000 in the quarter) and the increase in full-time employment by men (up by 93,000 in the quarter).
Thus, if we’re seeing the young and part time losing out to the older and full time then what might we conclude? That the minimum wage is already too high.