Monetary policy consists of adjusting interest rates. Plus QE is a new form of monetary policy, the supposed effect being similar to cutting interest rates. That is, interest rate cuts are supposed to increase investment spending, while the effect of QE is similar.
However, there’s one whapping great flaw in all that, which is that there is no reason suppose that the optimum mix of investment and consumption spending changes as between when an economy is in recession and normal times. And assuming that optimum mix does not change, then stimulus should aim to boost consumption spending, with employers being left to decide for themselves whether to spend more on investment as a result of any increase in consumption spending.
In view of that major flaw in monetary policy, there remains one possible saving grace for monetary policy, which is that it might act more quickly than fiscal stimulus. But the evidence seems to be that the lags in the case of monetary and fiscal stimulus are about the same.
Conclusion: monetary policy is nonsense.