I would like to propose that the answer book is wrong.
In the example sentence ものか could only be used to express complete disbelief or rejection of the idea that the economy will improve.
ものか is used to flat out deny an idea as false.
And trying to follow that with 悪化する一方であった would be strange grammatically and in terms of meaning.
どころか is used to negate a statement in order to emphasize that the alternative is true.
Thus, どころか is correct because of the way it contrasts 回復 with 悪化 where ものか does not have that function.