There is a good chance it is custom, but even then there could be some typeface which looks similar? 
I disagree about Caslon, because it seems to me only the A and C have any sort of Caslon similarity -- the other letters are much more like a classic Roman titling type. (My copy of the FontBook is not handy, or I might suggest a few similar ones.)
FWIW, AMICA is listed as a client of Font Bureau, although this typeface doesn't resemble any FB styles I have seen.
Thank you both for your input.
From what I was able to find online, there are several Amica magazines; one of which is German:
http://www.madonnatribe.com/images_covers/amica_2000.JPG
Probably FontBureau worked with them? The mast looks like Agenda to me.
This looks to me like a reduced-weight Cheltenham Oldstyle. I believe Font Bureau did something like that for the New York Times Magazine, but I don't know if this is the same one.
Mark is right - it looks very much like the NYT mag's redesign of Cheltenham, which is not (as far as I know) commercially available.
http://www.typophile.com/forums/messages/83/25489.html
Went out and bought the magazine today. Here is a scan from one of the pages. I am almost sure now it is the custom work by FontBureau Mike and Mark mentioned. It is a beautiful and exquisite face in my opinion.
The other FontBureau typefaces used in the magazine: FB Agenda Light and FB Agenda Regular (for captions and short paragraphs), FB Giza Seven Five (from what I can tell) for some of the titles.
Can anyone provide a scan of the NY Times version of the font?

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