People have been estimating the effects of QE in interest rates and GDP but I believe that is missing the point a little. BIS and Rogoff research indicates that delevering continues for on avg 7 years after a financial crisis, to me the biggest effect QE will have will be on the money supply and inflation measures. Assuming 40% of the money base printed turns into broader monetary aggregates(as it did in the QE1 program), this would ensure the money supply didnt collapse during these '7 lean years' and deflation is countered
But for some reason the Fed doesn't talk in that way, they keep referring to 'supporting economic growth' as a result people estimate effects on rates and GDP, they conclude the QE will be of little use since the effects will be small. Well, the effects would been large if they didnt do it and M2 collapsed. So even if rates go down by 10bps and GDP up by 0.2% its still worthwhile to do it in order to prevent debt deflation