This paper studies the implications of parameter estimation uncertainty on the central banker behaviour. It first describes the optimal monetary policy rule obtained by the linear quadratic stochastic control approach. The treatment of parameter estimation uncertainty is covered by the introduction of the full variance-covariance matrix of the parameter estimates in the optimal control theory. It then examines how this rule ought to be modified according to the preferences of the monetary authorities when there is uncertainty about the estimation of the persistence and/or transmission parameters. Our application to the euro area shows that (i) the conservatism principle is found relevant only when the central banker has an inflation and output stabilization objective, (ii) introducing an interest rate smoothing objective makes the central banker more aggressive, (ii) with conventional values for the weights of the loss function, there are few differences between the parameters of the rule under certainty-equivalence and those under uncertainty.