I am confused between option (B) and (D). I have no reason to eliminate the choice (B).

For rest of the choices.

This sentence has a structure something like this X, Y, Z where X, Y and Z are phrases and Y act a as filler in the sentence that provides the extra information. So, in such cases, if we remove the filler phrase then also sentence should make the complete sense.

A) If we look at choice (A) and remove the filler phrase then sentence seems to be awkward and incomplete.
Modified A: The science of economics who

(C) and (E) are make the sentence more complex and awkward. Hence they can be rule out.

Only choice (B) and (D) makes the first sentence as the modifier. But I am not able to find the reason to rule out the choice (B), which actually seems more prominent to me.

Let me know in either case, whether it makes some sense.

IMO D

'is' is necessary here to complete the sentence. If we read the sentence with ans choice B, it is not a complete sentence.

IMO D

The science of economics, which for four decades was dominated by Keynesians, (who at first stressed the government’s role in stimulating the economy, but who were ultimately led away from solutions based on government intervention)

The part under bracket is modifying Keynesians, the sentence needs another clause. Hence B incorrect

The science of economics, which for four decades was dominated by Keynesians,...............

you need to complete the sentence.

The Q.statement has a longgggg modifier modifying the Object-noun "Keynesians" and a main noun " The science of economics", So we need a MAIN VERB here.....

So down to D and E.

In E, the modifier "for four decades" is misplaced.Meaning -the science for four decades is one and later two.
so, this modifier should be placed after the object (apposition) of the main noun "The science of eco".i.e, one

Hence D.