Realistically, there isn’t much of a difference between these. Since you have asked, I am digging in to try to come up with something, and I do have something, but I would be very careful about trying to read much into the inclusion or absence of “as” in this kind of construction. It really doesn’t make much difference and a native English speaker likely won’t think twice about it—which means they may well not have considered any distinction you are drawing from it.
But I’ll discuss what I can.
The house price is guided by the base rate determined by the central bank.
Here, “determined by the central bank” modifies “rate,” that is, the thing the central bank determines is this base rate. How that “guides” the house price is not discussed, just that somehow the central bank’s base rate is a factor in the house price (probably an important one, if not the most important or even only one).
The house price is guided by the base rate as determined by the central bank.
Here, “as determined by the central bank” could be a little more ambiguous. It might not be modifying “rate,” it might be modifying “guided by the base rate” as a whole—that is, it’s possible that the central bank is in charge of determining the relationship between house price and the base rate. It’s even possible (though unlikely, and poorly worded if this is the case) that the base rate isn’t something the central bank sets. Those possibilities don’t really occur without “as” here, since the “determined by the central bank” is directly attached to “rate” and it has to be modifying that.