First, spending and pricing decisions are assumed to be based on long-term assessments of real income and real rates of return. Second, changes in monetary policy can only change real interest rates temporarily. Ultimately, the forces of productivity and thrift determine them, not changes in nominal magnitudes on the central bank balance sheet. Combining the two propositions implies that the Federal Reserve's interest rate policy, as long as it stays within the narrow range of experience, would not be expected to have a significant or long-lasting imprint on markets or activity.
I have expressed this view before. The difference is that I never tried to demonstrate it empirically. The point of the Reinhart and Reinhart paper is to demonstrate empirically that central bankers can only make a big difference if they make really big policy changes. I believe that there is a very large Fed attribution error--people attribute to monetary policy far too much power. This puts me at odds with Scott Sumner and John Taylor, among many others.
My approach to macro has always been "nominal shocks have real effects." As a result, I've never cared for the Keynesian view that inflation was caused by an overheating economy, and disinflation was caused by economic "slack." If that were true, then it would be the case that "real shocks have nominal effects." I.e. changes in real GDP affect inflation. And that just didn't seem right.
When we called it the Phillips Curve, there was the question of whether unemployment was the causal variable (the original interpretation) or inflation was the causal variable (the Friedman-Phelps interpretation).
When the Phillips Curve morphed into Aggregate Supply and Demand, this question was finessed. You do not ask whether price causes quantity or quantity causes price. You talk about supply shocks (a shift to the right lowers P and raises Q) or demand shocks (a shift to the right raises both P and Q).
In the current setting, it appears that economic activity is expanding and inflation is higher than it had been. One may choose to interpret this as resulting from the Fed's quantitative easing. However, I am not signing onto that one. I recall reading recently that QE 2 was basically canceled out by offsetting changes in Treasury funding operations. That is, as the Fed bought more long-term bonds, the Treasury issued more long-term bonds relative to short-term securities. So we are left with the channel that the Fed announced a higher intended path for nominal GDP, and this was self-fulfilling. Strikes me as a very difficult proposition to prove or disprove.