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The definition of M2 money supply:

M2 is a measure of the money supply that includes cash, checking deposits, and easily convertible near money. M2 is a broader measure of the money supply that M1, which just include cash and checking deposits.

I was wondering if this money is what banks reports? Because they mention checking deposits. Are FEDs able to use this metric to keep track of money like coins and change which never make it to the banking sector such as informal employment like hiring illegals or babysitter. I would imagine there are a lot of business which are not able to or not reporting. So does officially reported M2 numbers get skewed?

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First remember that these are very broad factors and are not meant to be hyper-accurate.

money like coins and change which never make it to the banking sector such as informal employment like hiring illegals or babysitter.

This would be M1 money - cash in circulation. This is not "reported" but the fed know how much cash and coin has been printed and minted so (other that what has been destroyed) it has a decent knowledge of this amount.

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