I commonly hear that when the Fed conducts open market operations, it is directly increasing the money supply by exchanging newly created electronic money for US treasuries. But in the case where the Fed is buying the treasury from an institution that has an account at the fed, this seems incorrect, since the Fed would only be issuing newly created central bank reserves, which are not included in M1 or M2. (In fact, if the Fed went on to retire the treasuries it bought, it seems like the whole process could make M2 decrease since M2 includes treasuries.) Isn't this correct?
And if so, is there some way to find out if these M2-neutral OMOs are a majority of OMOs, or half, or a small minority etc.?
Footnote: As I understand things, the Fed only buys treasuries from primary dealers, and I have been able to find some lists of these, but I have a harder time finding lists of institutions with accounts at the Fed, and a near impossible time discerning precisely which accounts are credited when the Fed buys treasuries.
Footnote 2: I have included the modifier directly in order to head off any confusion about whether, via a multiplier model, an increase in the central bank reserves of a commercial bank has some effect on the amount of money the bank will subsequently loan out to the public. I don't subscribe to the multiplier model, so I want to isolate the question of whether the OMO's themselves have a direct and immediate effect on the M1 or M2 money supply.