So a lot of bank commercials who mention that they are FDIC insured by saying " ‘Bank name’ member FDIC" as a standalone sentence. What kind of grammar is that? Shouldn’t it be "…is a member of FDIC?
Meh. I evaluate TV ad language like I do for signage. I mean, it’s not really grammatical to just say “No smoking” but hey, that’s the way we do it. But if it’s time that the bank is trying to save, couldn’t they say “First National Bank, FDIC member” instead?
Well, it is grammatical to say “No smoking” (find a grammar expert who would claim otherwise), but what the bank is saying is “First National Bank, Member FDIC.” If you listen, you can hear a pause that indicates the comma.
It’s not a sentence, but it doesn’t have to be. It’s the equivalent of signing your name on a painting.
FWIW, back when I was writing copy for bank advertisements, if I tried to change so much as a single word in those boilerplate sections, my clients (more than just one bank) would send it back with big red lines through it.
There probably isn’t a rule about it per se, just a tradition of “if we say it exactly this way, we know we won’t have a problem with it.”
I always interpreted the pause as a colon, as in “Member: FDIC.” Of course, it’s all just verbal shorthand. And since advertising costs money, a few fractions of a second matter. Saying “Member FDIC” takes a fraction of a second less time to say “[We are a] member [of the] FDIC.”
The FDIC approves of this particular grammatical atrocity.
By this, do you mean signing your name on painting you painted, or signing your name on just any painting you happen to come across? 
This post brought to you by: Švejk, member SDMB
Ads no time big word go fast.
I think they call this telegraphic style. Back in the day a lot of people used to send telegrams because they were cheaper than long distance calls–a lot cheaper. The telegraph companies charged by the word, so it behooved you to omit words of low information value. If you cabled
ARRIVING SAT UNION STATION 3PM
it was just as clear for the present purpose as
I WILL BE ARRIVING ON SATURDAY, THREE O CLOCK PM, AT UNION STATION.
You also see this sort of thing in military communications, as in
LCDR PF QUEEG USN CO CAINE REPORT IN PERSON REPEAT IN PERSON CINCPAC
(Leutenant commander P.F. QUEEG, COMMANDING OFFICER OF THE USS CAINE (Etc.).
I didn’t think there’d be so straightforward of an answer, but I guess this works.
Thanks.
Why would this be a grammatical atrocity? There is no one English language. There are dozens or hundreds of languages depending on context. The rules of formal written English apply to situations in which formal written English is proper.
The rules of signage, advertising, slang, argot are their own and in their own contexts are exactly are proper - and strict - as those of formal written English.
Can you back up that atrocity accusation with some actual grammatical authority?
I was being facetiousifical.
Customer: You a member FDIC?
Teller: 'Course I 'member FDIC. You 'member LS/MFT?