The U.S. unemployment rate, rather than the inflation rate, will likely be "key" to the Federal Reserve's eventual return to normalized interest rates, but a lower top-line joblessness number will not automatically begin that tightening process, a senior Federal Reserve official said Monday.

New York Federal Reserve Bank President William Dudley, answering questions following a short speech at Queens College, said "it's very likely that a 6.5% unemployment rate is going to be key."

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