It's mildly interesting to check the CPI-deflated series and one indexed to average wages.
The blue and red lines track the nominal and CPI-adjusted minimum wages on the left hand axis; the yellow line traces the adult minimum wage as a percentage of the average wage on the right hand axis. In 1996, the minimum wage was 40.6% of the average wage. That increased to 50.4% of the average by 2008 and has held steady there since then.
NZ youths in their first 200-hours of work are now eligible for a new-entrant's wage that's 80% of the adult minimum wage: $11. That's 40.3% of the average wage (not the median, the average) for a new 16 year old worker with no experience.
Australia allows a youth minimum wage of $7.55 for 16 year olds.
Maybe there are reasons in the behavioural economics literature for nominal wage rigidity. But government does seem to like to turn that into real wage rigidity for the bottom of the wage distribution.
If National can't countenance holding the minimum wage steady when inflation is below 1%...