Master of None, Just to be clear, I am not one of those monetarists who argues that you should expect to find a correlation between current movements in M, however defined, and future movements in AD. Indeed if you did find this sort of correlation, it would suggest extraordinary incompetence on the part of the Fed. If they are inflation targeting, there should be no correlation between M and P. And yet M would still be causing P.
These studies don't seem to incorporate recent advances in monetary theory, such as the Woodford model where current movements of AD are caused by changes in the future expected path of monetary policy. It's almost impossible to pick that up with Granger causality.
I agree with the logic of Scott's point, but I might interpet it differently than he does. I would file this one under "Good macroeconomic knowledge is hard to come by."