I have been very critical of any measure of the quantity of money that includes assets that do not serve as media of exchange. In particular, I have never thought that time deposits should count as part of the quantity of money. The arbitrary dividing line of $100,000 (between small and large time deposits) has always made M2 an absurd measure of the quantity of money. Unfortunately, the development of sweep accounts has made reported values of M1 nearly worthless. Probably the least bad option is to include all savings accounts in a measure of the quantity of money. MZM includes currency, checkable deposits, savings accounts, and money market mutual funds. The dollar value of each item is summed up.
Unfortunately, it doesn't include other overnight financial assets, especially repurchase agreements, but also other commercial paper. The Fed used to include overnight repurchase agreements as part of M3, but they were bundled with term repurchase agreements. Worse, the Fed stopped reporting M3. (As far as I can tell, there are no good measures of the volume of overnight commercial paper, though the Fed does report yields on various maturities of commercial paper.)
With modern communication and payments technology, any overnight financial asset can serve as media of exchange. When they are tied to a checkable deposit with a sweep agreement, these are funds in checkable deposits, just as are the funds reported as being in savings accounts. (In my view, sweep accounts amount to a fraudulent effort to evade reserve requirements. On the other hand, I think reserve requirements are an unjust tax, with the burden suffered by small depositors.)
I have also long rejected the inclusion of Treasury bills in any measure of the quantity of money. The Fed had a measure of the money supply it called "L," that included T-bills. The problem with T-bills is that they have a market price that adjusts based on supply and demand. While the core characteristic of money is that it serves as media of exchange, that its price is fixed in terms of the unit of account is also very important.
But as the yields on T-bills approach zero, I must admit that those who argue that T-bills approach a perfect substitute for base money become more persuasive. As I have argued many times, the zero-nominal bound on other financial assets is intimately related to monetary disequilibrium. Further, there is good reason to doubt the effectiveness of open market operations using financial assets with very low yields. But does that mean that those T-bills still held by households and firms are effectively money?
The Divisia approach provides a solution to all of these problems. While I don't think it is a perfect solution, perfection is usually not a real option. But the real reason why I find it very interesting is the charts below. It is really a surprise that nominal GDP is so far below the trend of the great Moderation?
The make up of the different measures is here. The difference between M4 and M4nt is T-bills. The divisia measures show that T-bills are providing substantial monetary services. (They are now a better, if not perfect, substitute for money.) The difference between M4nt and M3 is commercial paper. Commercial paper isn't providing much in the way of monetary services now.
I support a target rule for nominal GDP. I am skeptical regarding instrument rules--formulas that tie a policy interest rate like the fed funds rate or base money to a goal of monetary policy. However, it is certainly looking like getting the divisia M4 measure of the money supply back up to trend would be a sensible intermediate goal for the Fed. (For that matter, returning them to their previous peak might be helpful.)