What a mind-bogglingly empty question! The money multiplier equals the ratio of the money supply (however defined) and the monetary base. It’s simply a ratio, there’s nothing to believe or disbelieve. It’s like asking if someone believes in the ratio of men to women. Or whether MV=PY.
So let’s start over. Do you believe the money multiplier is stable? Most economists would answer; “It depends.” Or how about; “Do you believe the money multiplier is useful?” Now we are beginning to get somewhere. For instance, do economists believe that an increase in the monetary base will cause the money supply to rise by an amount equal to the change in the base times the multiplier? It turns out that the answer is; “No in the short run, but yes in the long run.”
What we actually need to do is start with the concept called “the neutrality of money,” which underlies almost all of macroeconomics, and has done so for hundreds of years. This says that an increase in the monetary base will not affect any real aggregates, and hence all nominal aggregates will rise in proportion. This suggests there are “multipliers” for every conceivable nominal aggregate, from nominal spending on toasters, to nominal spending on Brazilian waxes, to NGDP. The “multiplier” for NGDP has a special name; “base velocity.” But it actually has nothing to do with the velocity of money (the vast majority of money expenditures are not for final goods and services), and should be called the “NGDP multiplier.”
So according to the neutrality of money, a 10% rise in the base will increase all nominal aggregates by 10% in the long run. Since M1 and M2 are nominal aggregates, they are affected just like nominal toaster expenditures and nominal Brazilian wax expenditures. (I keep mentioning the latter in a pathetic attempt to show that I am a hip 56 year old keeping up with new industries that didn’t exist when I was 20 years old.)
Of course wages and prices are sticky in the short run, so a 10% rise in the base does not have a proportional effect on most nominal aggregates in the short run. The neutrality of money (and the money multiplier) are long run propositions. However some economists believe the money multiplier is relatively stable when interest rates are positive, even in the short run. This is because the multiplier has two behavioral components; the reserve ratio and the currency/deposit ratio. Many economists think that during normal times (when interest rates are positive), banks hold very little in the way of excess reserves. Hence the reserve ratio is stable, and equal to the required reserve ratio. They also believe the currency/deposit ratio is relatively stable in the short run.
This leads to the question of whether the money multiplier is useful. I don’t think it is, but let me try to explain why others disagree. They think a 10% rise in the base (when interest rates are positive) will result in a roughly 10% rise in M2, even in the short run. I have doubts, but I’m willing to accept that claim. Then they claim that changes in M2 have an important causal impact on NGDP—M2 is an important part of the monetary transmission mechanism. That’s the part I reject. I think future expected NGDP, plus asset prices, are the key transmission mechanisms. And future expected NGDP is driven by future expected changes in the supply and demand for base money. I don’t see anything special about M2.
All economists believe the money multiplier becomes highly unstable at zero rates, mostly because, well . . . because it does become highly unstable at zero rates. Yes, sometimes economists actually do believe what they see with their own eyes. I should add that if IOR is permanent, which seems increasingly likely, the money multiplier may become highly unstable at positive interest rates as well. Money will still be neutral in the long run, but the usefulness of the money multiplier (which I doubt even without IOR) will become even smaller. It will be as unimportant as the toaster multiplier, or the . . . Brazilian wax industry multiplier.