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I think you have it backwards. Stability is the overall target, and the 2% target was chosen as a way to achieve that. See for example https://www.federalreserve.gov/faqs/money_12848.htm.

> The objectives as mandated by the Congress in the Federal Reserve Act are promoting (1) maximum employment, which means all Americans that want to work are gainfully employed, and (2) stable prices for the goods and services we all purchase.

> Following its meeting in January 2012, the FOMC issued a statement regarding its longer-run goals and monetary policy strategy. The FOMC noted in its statement that the Committee judges that inflation at the rate of 2 percent (as measured by the annual change in the price index for personal consumption expenditures, or PCE) is most consistent over the longer run with the Federal Reserve's statutory mandate.




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