The Fed's reaction to the great recession was "far from perfect," and it should have provided more stimulus, Federal Reserve Bank of New York President and Chief Executive Officer William C. Dudley said Tuesday.

"Comparing actual growth to the growth projections by FOMC participants in the Summary of Economic Projections shows that we were consistently too optimistic about growth over the 2009-2012 period," Dudley told the Japan Society, according to prepared text of his speech, released by the Fed. "As a result, with the benefit of hindsight, we did not provide enough stimulus."

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