WASHINGTON, Jan 3 (Reuters) - Economic data in the coming months will help the U.S. central bank build conviction that inflation is falling as expected, absent some unexpected shock, Richmond Federal Reserve President Thomas Barkin said on Wednesday.

"Is it settling as convincingly as the last six months would have suggested or not?" Barkin, speaking at an event in North Carolina, said of inflation that by some measures has been below the Fed's 2% target for about six months now. "With every month that goes on we will build more conviction about that or not." (Reporting by Howard Schneider; Editing by Paul Simao)