Studies on code documentation productivity gains/losses

Question

After much searching, I have failed to answer a basic question pertaining to an assumed known in the software development world:

WHAT IS KNOWN:

Enforcing a strict policy on adequate code documentation (be it Doxygen tags, Javadoc, or simply an abundance of comments) adds over-head to the time required to develop code.

BUT:

Having thorough documentation (or even an API) brings with it productivity gains (one assumes) in new and seasoned developers when they are adding features, or fixing bugs down the road.

THE QUESTION:

Is the added development time required to guarantee such documentation offset by the gains in productivity down-the-road (in a strictly economical sense)?

I am looking for case studies, or answers that can bring with them objective evidence supporting the conclusions that are drawn.

Thanks in advance!