Statistics New Zealand continues to prove itself the most fun stats agency in the world. Here's their infographic on the price of haircuts and the difficulties of quality-adjustment. And, here's their more detailed analysis.
I happily attend a barber (formerly of Manchester Street, now of Ferry Road) who gives me something close to the 1951 haircut for about $20. I am forbidden from attending any barber who would give me the 1981 haircut.
We'd also expect that non-traded, labour intensive goods like haircutting would outstrip the overall inflation index; productivity increases in haircutting have been smaller than those in other sectors, and the sector does have to compete for labour.