This one has me stumped. A didone, but the Q is atypical of the style.

Some version of Century that was never digitized?

None of the search engines kicks out a match....

VHS tape boxes. I used to have a huge number of these, including this brand. Looks like a photo compressed font. There are normal width substitutes that might pass for _HQ_, such as Century Oldstyle http://www.myfonts.com/fonts/mti/century-os-mt/ but I didn't spot anything that world work perfectly as a digital substitute for the compressed text _HQ HIGH QUALITY TAPE_. The closest I was able to find out of the box is Georg Trump's Mauritius Medium Condensed as digitized by Canada Type
http://www.myfonts.com/fonts/canadatype/mauritius/
An alternative, Monotype Clarendon® Condensed

http://www.fonts.com/font/monotype/monotype-clarendon/condensed
Don

edited:
You can get a lot closer by taking a bold weight of a font with similar letterforms and compressing the width to perhaps 85%
This one is News 706 Bold http://www.myfonts.com/fonts/bitstream/news-706/
If you want to get a pretty good match you could edit the tail on Q and anything else that you think is out of place.
A runner up is Harriet Text Bold

http://www.myfonts.com/fonts/okay-type/harriet/ Same comments on editing.
Some fonts have a weight heavier than bold, which might give a better match for weight when the width is compressed to perhaps 85%
This one is Ingeborg Heavy.
http://www.myfonts.com/fonts/typejockeys/ingeborg/ Same comments on editing.
Don

Wow, thanks for all the info, Don! I particularly like News 706 Bold and Ingeborg Heavy at 85%. I'll try experimenting with those and the others and, perhaps, drawing it from scratch as an alternative.