I'm not from the US and was born after Greenspan took up the position but I thought Paul Volcker was a pretty well known name during his tenure?

I'm probably a fair bit younger. I came to know the phrase, then (of) him, through the flash animation of the Happatai/Yatta song on Albino Black Sheep in the early 2000s (and these days on youtube if you search 'irrational exuberance yatta'; mildly nsfw in a few spots). Never bothered to dig into its meaning, though.

He said it in 1996.

A very Economist answer to Ryan's question. So basically, no.