Are there studies testing whether academia rewards researchers based on number of publications? I would like to know whether any scientific study has tested a hypothesis relating number of publications to career advancement.

It is often suggested that hiring and promotion decisions at research institutions are based heavily on the number of publications produced.  That is, one is more likely to get a tenure-track position and subsequently to get tenure if one has a larger number of publications (independent of quality).  One could also introduce an opposing argument that large numbers of publications are negatively correlated with quality of work and therefore negatively impact career advancement.  Are there any studies supporting either of these views?

Some remarks: I understand well that even if there is correlation it would not imply causation.  Also, I suspect that the relation between publication quantity and career advancement is very different between disciplines and between world regions.  I would be interested in studies that address the question globally or among some subset of academe.

I believe this question is different from Whether to publish one big paper or many smaller papers for a given research project?, since I am asking for general scientific studies rather than opinions.

I am aware that, for many reasons, reaching valid conclusions may be impossible.  I am interested in whether it has been attempted.
There's quite a bit of this sort of thing in economics. One early and now classic study, Katz 1973, performs a regression of salary on the number of books, articles, "excellent articles", and other variables associated with a faculty member, and finds what seems to me to be very low impact of publication on annual salary even in 1973 dollars: an article is worth $18 and an excellent article worth $102 in annual salary. 

A later study Diamond 1986, estimates the marginal value of a citation on lifetime salary: somewhere in the $50 to $1300 range (!!).  Note that is in economics where citations are somewhat stingy, back before people started gaming citation rates as much as they do today. 

Since there has been a huge volume of publications on the determinants of faculty salary within the economics literature. For some reason, this particular labor market has been of exceptional interest to academic economists.