if you use MZM (money zero maturity) as your measure of money. That is what Pedro Teles and Ruilin Zhou show in their paper, A Stable Money Demand: Looking for the Right Monetary Aggregate.
The [money demand] relationship... holds very well until the mid-1980s but not well at all after that. This could be because the demand for money is not a stable relationship after all... Another conclusion, which is our view, is that the measure of money is not a stable measure. In particular, we argue that technological innovation and changes in regulatory practices in the past two decades have made other monetary aggregates as liquid as M1, so that the measure of money should be adjusted accordingly. We show that once a more appropriate measure of money is taken into consideration, the stability of money demand is recovered.As noted above, the authors find MZM to be the appropriate measure of money. MZM is defined as M2 minus small denomination time deposits plus institutional money market mutual funds. The main idea behind MZM is that it is an aggregate measure of money that includes all forms of money that can be immediately turned into purchasing power--there are no time restrictions on the money balances. In making the case for MZM the authors go through the list of reasons for the instability of demand for M1 and M2:
...[A] series of sweeping regulatory reforms and technological developments [since the early 1980s]in the banking sector have significantly changed the way banks operate and the way people use banking services and conduct transactions. First, the Depository Institutions Deregulation and Monetary Control Act of 1980 abolished most of the interest rate ceilings that had been imposed on deposit accounts since the Banking Act of 1933 and authorized nationwide negotiable orders of withdrawal accounts (NOWs), which are interest-bearing checking accounts classified in M1. Furthermore, the Garn–St Germain Depository Institutions Act of 1982 authorized money market deposit accounts (MMDAs), interest-bearing savings accounts that can be used for transactions with some restrictions. MMDAs are classified in M2. These two major banking reforms blurred the traditional distinction between the monetary aggregates M1 and M2 in their transactions and savings roles. Second, the rapid development of electronic payments technology and, in particular, the growing use of credit cards and the automated clearinghouse (ACH) as means of payment, reinforced the effect of the banking reforms in slowing down the growth of M1. Both credit cards and ACH transactions can be settled with MMDAs and, therefore, with M2 rather than M1. Third, the widespread adoption of retail sweep programs (discussed in detail later) by depository institutions since 1994, which reclassify checking account deposits as saving deposits overnight, reduced the balances that were classified in M1 by almost half.The authors then go on to empirically estimate a stable money demand function with MZM and show that there is no "case of the missing money" with this monetary aggregate. One interesting series of graphs they report plots the ratio of a monetary aggregate to GDP against the nominal interest rate. Some interesting inverse relationships emerge from these figures. I have reproduced the graphs below, but here have flipped the monetary aggregate to GDP ratio. See if you note any striking differences in this relationship based on the monetary aggregate used (click on graphs to enlarge):
These fundamental changes in the regulatory environment and the transactions technology justify the use of a different measure of money after 1980... We show that changing the monetary aggregate measure from M1 to MZM from 1980 onward preserves the long-run relationship between real money, the opportunity cost of money, and economic activity up to a constant factor.
I find it striking that GDP/MZM tracks the nominal interest rate series so much more closely than the other monetary aggregates beginning in the late 1970s. Let's say these results hold up going forward. A key implication would be that U.S. monetary policy could once again look at a monetary aggregate.
Update: John Carlson and Benjamin Keehn come to a similar conclusion here.