I see more and more academic studies confirming that Federal Reserve QE policies were effective during the Great Recession. Here is the abstract of a 2018 paper by Eric Swanson:

I survey the literature on monetary policy at the zero lower bound (ZLB) and effective lower bound (ELB) to make three main points: First, the Federal Reserve’s forward guidance and large-scale asset purchases are effective monetary policy tools at the Z/ELB. Second, during the 2008–15 U.S. ZLB period, the Fed was not very constrained in its ability to influence medium- and longer-term interest rates and the economy. Third, the risks of the Fed being significantly constrained by the ELB in the future are typically greatly overstated. I conclude that the Federal Reserve is not very constrained by the lower bound on nominal interest rates.

And here’s the conclusion of a recent paper by Daniel Lewis:

Moreover, I find important macroeconomic effects. Both consumer and professional expectations respond to the shocks at the monthly frequency. Asset purchase shocks are especially impactful, raising expectations of both inflation and real GDP growth; this lends support to the expectations channel in explaining possible effects of unconventional policy shocks. Finally, the dynamic responses of both realized inflation and GDP growth display significant responses to asset purchase shocks, but not to Fed Funds or forward guidance shocks. Taken together, these results offer some of the first evidence on the macroeconomic effects of the Federal Reserve’s unconventional monetary policy broken down by policy dimension. They suggest that asset purchase policies in particular were effective with regard to a number of policy objectives.

This is not to say that “QE works”. That would be reasoning from a quantity change. For instance, QE often represents a defensive move after failed monetary policies, as the central bank meets a growing demand for liquidity that is itself caused by deflationary central bank policies. Rather, QE can work if utilized as part of a sensible monetary regime.

One goal of QE is to lower longer-term interest rates.  But a truly effective QE program might well raise long-term rates.