There is no single "correct" measure of the money supply. Instead there are several measures, classified along a continuum between narrow and broad monetary aggregates. Narrow measures include only the most liquid assets, the ones most easily used to spend (for example, currency and checkable deposits). Broader measures add less liquid types of assets (certificates of deposit, etc.). The continuum corresponds to the way that different types of money are more or less controlled by monetary policy. Narrow measures include those more directly affected and controlled by monetary policy, whereas broader measures are less closely related to monetary policy actions.
The different types of money are typically classified as "M"s. Around the world, they range from M0 (the narrowest) to M3 (broadest), but which of the measures is actually the focus of policy formulation depends on a country's central bank.
M2 is one of the aggregates by which the Federal Reserve measures the money supply . It is a broader classification of money than M1 and a key economic indicator used to forecast inflation. M2 consists of all the liquid components of M1 plus near-monies. Near monies are relatively liquid financial assets that may be readily converted into M1 money. More specifically, near monies include savings deposits, small time deposits (less than $100,000) that become readily available at maturity, and money market mutual funds.
Federal Reserve
Historically, the Federal Reserve has measured the money supply using the aggregates of M1, M2, and M3. The M2 aggregate includes M1 plus near-monies.
Imagine that Laura writes a check for $1,000 and brings it to the bank to start a money market account. This would cause M1 to decrease by $1,000, but M2 to stay the same. This is because M2 includes the money market account in addition to all the money counted in M1.