Using a New Keynesian model subject to misspecifications, we examine the accountability issue in a framework of delegation where government and private agents are uncertain about the central bank's preference for model robustness. We show that, in the benchmark case of full transparency, the optimal inflation targeting weight (or penalty) is decreasing with the preference for robustness. Departing from the benchmark equilibrium, the central bank has then incentive to be less transparent in order to reduce the optimal inflation targeting weight and thus to become more independent vis-à-vis the government. We also find that greater opacity will increase the sensibility of inflation and model misspecification to the inflation shock but will decrease that of output-gap. Since macroeconomic volatility could be increased or decreased under more opacity, there could exist in some cases a trade-off between the level and the variability of inflation (and output gap). Persistent inflation shocks could be associated with a higher inflation targeting weight as well as a higher sensibility of inflation and output gap to the inflation shock but a lower sensibility of model misspecification.