The GDP Accounting Identity & Causality
The fallacy here is essentially the same as the fallacy of protectionists that notes that imports are a negative factor in GDP statistics and therefore concludes that limiting imports would boost GDP. The fallacy lies in thinking that a change in one of the components of the right side of the GDP accounting identity ( Y= C+I+G+X-IM, with Y being GDP, C being consumer spending, I being investments, G being government spending, X being exports and IM being imports) will necessarily cause an equal change in the left side of it.
But that need not be the case at all as it could just as well cause an opposite change in one of the other components in the right side of the equation. The theory that higher imports enables higher domestic demand and exports is just as consistent with the GDP accounting identity as the theory that higher imports causes a reduction in GDP. Similarly, the theory that lower government spending enables higher private demand and a lower trade deficit is just as consistent with the GDP accounting identity as the theory that lower government spending causes a reduction in GDP.
We have different theories about whether a decrease in government spending will increase private sector GDP (private domestic demand and net exports) or whether it will reduce GDP or a combination of the two , but there is nothing in the GDP accounting identity that proves that lower government spending will reduce GDP.
But what about the fact that GDP and government spending were both downwardly revised? Doesn't that prove that lower government spending lowers GDP? No, it doesn't because this revision reflected an epistemological and not an ontological change. The revision reflected that more information about a past event was available, it wasn't that one revision necessarily caused the other.