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A small forward-looking model of the euro-area economy is used to investigate the implications of incomplete information about potential output for the conduct of monetary policy. Three results emerge. First, under optimal monetary policy, output gap uncertainty leads to persistent deviations between the actual and the perceived output gap in response to supply and cost-push shocks. Second, in first-difference form, a simple policy rule such as the Taylor rule continues to perform relatively well as long as the output gap is optimally estimated. Third, incomplete information implies that it is optimal to appoint a more “hawkish” central bank.