I noticed the ballast, on my AEL HPS NEMA, has a QR code style barcode on it, like you see on a lot of things these days that people scan with their smart phones. But it was made in 2007 and I didn't know they had those back then. Was it for some inventory at the factory or something?

I just googled them and QR codes were invented in 1994 by one of Toyota's subsidiaries to help track parts quickly . In fact the "QR" stands for "Quick Response" So, to answer your question, Yes, the QR code was more than likely used by AEL to help locate and track parts .

Could you post a pic?

Toyota?/That's funny.

Yes. It allowed them to track every, even the cheapest parts in a very cheap manner (because the reading was automated and very quick, at any angle, so posed no costly production bottleneck), so could be done at even the smallest manufacturing steps. And that tracking allowed them to address deffective batches of any components way before these poisoned larger subsequent production, or even prevented a slipped part from that deffective batch to poison the folliwing production as well.
All that rigorous tracking was one of the biggest contributors making Toyota enjoying the reputation as the most reliable brands the following two decades.

Unfortunately this led the upper management to cut corners further, plus the competition used that as well improving their reliability too, so the quality became back more equal later on...

Barcodes were used much earlier than Toyota:

Barcodes yes, but these required positioning of the code with the reader device or scanning it manually, which was rather complicated with many parts. The QR code system invented by Toyota (or better to say their subsidiary) solved these issues, plus (maybe the main reason) the bar code has very limited data capacity (for given sticker size and printer/engraver/scanner resolution, so the bits just run out quickly, so can be used only for fewer bigger assemblies. The QR data capacity is way greater, so allow direct writing of many logistic data, so the system does not need any background database to decode the required information (e.g. the part number, the date and time stamps, logged exact conditions of some manufacturing steps,...).

All derived from the original bar codes.

...all derived from the Morse telegraph...

Could you post a pic?

I put a picture of it now in the gallery here. If you open it bigger, it easier to see the QR code.