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The $M_1$ component of the money supply is given by the sum of the value of money held by the public+the demand deposits in the country + other deposits(money of other government institutions held by the central bank + deposits of international organisations+ deposits from other central banks), however, I'm not sure why we include the deposits of other country's banks if we exclude what the central government deposits in the central bank.

Could someone help?

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M1 is supposed measure all money outside the Treasury, Fed and depository institutions (FRED).

Foreign central banks are not part of Fed, they are not part of the Treasury and modern central banks are not depository institutions either.

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