This short blog by TONY ROSS-HELLAUER does a nice job of distinguishing between (i) “open pre-review” and (ii) “open final version commenting”, both of which are, unfortunately, lumped under the category of “post-publication peer review.” The blog includes references.  To read more, click here.

As an aside, TRN notes that the journal Economics E-Journal allows both.  It publishes submissions as working papers, with open review.  Then, after a paper is accepted, it allows post-publication comment.