This paper contributes to the recent literature that studies the quantitative implications of the imperfect information about potential output for the conduct of monetary policy. By means of Bayesian techniques, a small New Keynesian model is estimated taking explicitly account of the imperfect information problem. The estimation of the structural parameters and of the monetary authorities.objectives is key in assessing the quantitative relevance of the imperfect information problem and in evaluating the robustness of previous exercises based on calibration. Finally, the model allows us to analyse the usefulness of unit labor costs as monetary policy indicator.