If the Fed sterilizes the purchase of foreign assets,

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Sterilization refers to the process of offsetting the impact of a monetary action on the money supply. When the Fed purchases foreign assets, it increases its own assets. To sterilize this purchase, the Fed must sell an equal amount of domestic assets, such as government bonds, to decrease its asset holdings back to the previous level. This means that the composition of its assets changes, but its liabilities are unaffected.

If the Fed Sterilizes the Purchase of Foreign Assets