We know part of the precise impact:
We know the $80 billion per year the Fed has been turning over to the Treasury would have otherwise remained in the economy.
U.K.’s Quantitative Easing Has Worked, BOE’s Bean Writes in FT
May 3 (Bloomberg) — Studies of the Federal Reserve’s large-scale asset purchases provide corroboration that quantitative easing has been effective, Bank of England Deputy Governor Charlie Bean writes in the Financial Times.
The precise impact of QE is uncertain and it’s “plausible that the effectiveness of the policy depends on the state of the economy,” Bean writes.