There's a guy in Oslo (Pål Kristian Eriksen) who's just finished/gotten
his doctorate in typological linguistics. His dissertation is on "to
be": which languages have a separate word for it, which languages don't,
and why.

Unfortunately, his uni the University of Oslo isn't too fond of the
riffraff (that is: anyone not at the university of Oslo) paving on their
precious dissertations[*] so I don't know if there exists an electronic
copy at all (it's only 2006 after all, gotta wait another century).
Therefore I'll provide a summary of the published summary, in English

Basically: languages which inflect the verb itself for present and
preterite/past, will also have a verb for "to be". Examples include most
IE-languages. Languages which use some other way to show time, don't
have a verb for "to be". Examples include Chinese. The reason why "to
be" is needed is because you can't add a particle/word meaning "not"
directly to a noun used as a predicate, you need a buffer-word of some
sort, hence "to be".

I haven't managed to get hold of the dissertation itself so beware of
the above being a summary of a summary of no doubt a summary.

[*] <rant>In general, publicizing things beyond the minimum necessary to
get a PhD seems to be beyond the pale, or maybe there are too few
journals? The n hundreth higher education reform might change things but
I don't think the old prof.s really want to have to write something once
a year that may be read by potential riffraff... or is it just that the
human(e) arts or as they are called here, humaniora, are supposed to
publish long and rarely instead of short and often?</rant>