If I re-run things allowing for the four different regimes, I get the following.
|Period||Coefficient||Constant||Implied Youth unemployment rate if adult rate is 4.75%|
|No youth minimum wage at all||1.98||4.54||14%|
|60% of adult rate||1||11.3||16%|
|18-19 year olds are adults, higher youth rate||1.05||10.6||16%|
|All on adult rate||4.46||2.12||23%|
So when there was no youth rate at all, youth unemployment largely tracked as a small multiple of the adult rate; the youth rate pushed it to a level shift that tracked the adult unemployment rate; and, the current regime has youth unemployment at a much larger multiple of the adult rate.
Stephen also sends me data on the youth minimum wage as effective percentage of the average hourly rate; afraid I'm not going to have time to play much with that one. Down that route lies a replication and extension of Hyslop and Stillman which would make for a fine honours project, but for which I certainly don't have the time now!