in order to follow the process that leads to economic prosperity very closely: correct, but the object is too long (the process that leads to economic prosperity) and, as a result, you lose track of what the adverb (very closely) refers to.

in order to follow very closely the process that leads to economic prosperity: put the adverb between the verb and the object. Some people highly disapprove of this (I don't like it myself).

in order to very closely follow the process that leads to economic prosperity: Split the infitive. Some people would rather you stabbed them in the back.

Rephrase:
in order to keep a close watch on the process that leads to economic prosperity (My preference)
or: keep tabs on
monitor


--------------------------------------------------
Note added at 5 hrs 2 mins (2005-10-10 18:09:28 GMT)
--------------------------------------------------

Lakasa, I was concentrating too much on the syntactic aspect (what does one do with the adverb in a case like this) that I failed to read the whole sentence properly.
"To follow ... closely" normally means "to keep a close watch on something", but this is not what they mean to say here, as Kenneth and Brie have already pointed out.
What these people do is to study every step of the process. And another problem crops up here: Normally the (implied) subject of the infinitive (after "in order to") should be the same as the subject of "are analysed" (i.e factors etc.).
So my adjective+noun version would be:
...are analysed in order / so as to allow for a careful study / close examination of the process that leads to economic prosperity.
And I'm sure there are other ways of rephrasing this, but I'm sticking to the syntactic principles here.