There is a growing literature on what exactly the Quantitative Easing has achieved. As we are going see, there is an agreement that QE has led to both higher output and higher inflation, however, there is less agreement on the magnitude and persistence of these effects.
Probably, the earliest studies were carried on the case of Japan; see the survey on empirical studies by Ugai. Quite interestingly, the largest effects were identified for the channel related to the expected short-term interest rates.
The paper by Kapetanios et al. (“Assessing the economy-wide effects of quantitative easing”) discussed the effects of QE run by the Bank of England. The paper focused mostly on the short term interest rate channel, although the authors acknowledged that this might have been a limitation. The methodology consisted in using three different VAR models: a large Bayesian VAR, a time-varying VAR as well as a change-point structural VAR. On average, they found a peak effect on output around 1.5% and a peak effect on inflation of about 1.25%.
A more innovative paper in terms of methodology is the one by Pesaran and Smith. Their study proposed an ex-post evaluation of the effects of Quantitative Easing based on outcomes conditioned on the ex-post variables (which are, at the same time, both invariant to policy and also determinants of outcomes). It also suggested a possible test for ex-post policy ineffectiveness. In terms of magnitudes, they found a peak effect on GDP of about 1%, however they also found that this effect quickly dissipates in about 9 to 12 months.
As we could see, usually the quantitative approach has been based on time series like VARs. An exception to this is the study by Falagiarda who used a DSGE model to evaluate the QE effects. The model has two important features that help capture the portfolio rebalancing channel: imperfect asset substitutability and a feedback from the term structure to the economy. His findings indicate a peak effect on long term rates of about 60 points, a peak effect on GDP around 1% and on inflation about 0.40%. As the author underlines, his work me be extended by including the credit channel of the QE.
The topic of the effects of QE is surely not a closed subject. Probably more evidences will be uncovered in time. A question probably not answered yet is whether these effects of quantitative easing outweigh the costs and potential risks.