1. "Economists define "money" as an asset that is used to pay for transactions. Thus, for example, we don't include your credit card in any measure of the money supply, because it's not an asset. Having a credit card doesn't make you rich-- I hope I'm not the first person to tell you that. We likewise don't count holdings of stock equity, because you can only use your stock wealth to buy your groceries if you first convert it into another asset. The quantity of money in circulation would be of economic interest insofar as it bears a stable relation to the dollar value of transactions that get undertaken."
2. "there is the now-no-longer-published M3. This added to M2 a number of liquid assets used by large institutions or wealthy investors, such as institutional money market funds, time deposits in excess of $100,000 with penalty for early withdrawal, repurchase liabilities of depository institutions, and dollar-denominated accounts held by someone with a U.S. address at certain foreign banks or foreign branches of U.S. banks.
I have to confess that in a quarter century of teaching and research, I never had any occasion to make use of M3. It always seemed to me that this unambiguously failed the definition of an asset that is used to pay for transactions. If you're going to include such assets in your concept of "money", why stop there? Don't you want to include T-bills as well, and if them, why not Treasury bonds? You have to stop somewhere, and I always stopped with M1 or M2.
In addition, a primary reason for focusing on the money supply for policy purposes is that it's a magnitude controlled by the government. The physical dollar bills are of course printed by the government, and a bank that issues checking accounts must hold credits that could be used to obtain physical dollars (known as Federal Reserve deposits) in a certain proportion to the value of the outstanding checkable deposits. However, it is unclear how the government is supposed to control the M3 components. Balances at foreign banks, for example, are clearly outside the control of the U.S. government." I agree with Dr. Hamilton's assessment...