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More precisely:

Are there any implied bounds for the ratio M0/FRBS with

MB= the monetary base

and

FRBS=Federal Reserve Balance Sheet?

https://www.federalreserve.gov/monetarypolicy/bst_recenttrends.htm

https://tradingeconomics.com/united-states/money-supply-m0

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The two series are linked by an accounting identity, which is why they tend to move together closely. There’s no theoretical limit to how much larger assets can be than the monetary base, though. If you look at the two tables in the H.4.1 Release, you’ll see that the first table is basically the Fed’s assets (what you refer to as its “balance sheet,” but in reality one side of the balance sheet). The second table effectively shows the other side of the balance sheet, its liabilities. Two lines in the second table add up to the monetary base: “currency in circulation,” and “Reserve balances with Federal Reserve Banks.” The sum of all the other lines in the second table is the gap between the two series. These other balances serve a number of different purposes, and as of the moment I am answering this, the biggest contributor is something known as the Treasury General Account, which you can basically think of as the Treasury’s own checking account held directly at the Fed.

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