In this paper, I revisit an old question in the analysis of monetary policy that was first studied by Rogoff (1985) - should central banks pursue objectives that differ systematically from social welfare? I investigate how the answer to this question is affected by the degree of transparency that characterizes monetary policy. When the policy regime is one of discretion and the central bank is opaque, changes in the policy instrument have informational effects that distort the central bank's incentives and generate policy biases. Directing the central bank to place more weight on inflation stabilization, i.e., to implement a less flexible inflation targeting policy, can offset this distortion and lead to lower social loss. In contrast, the objectives of a transparent central bank should coincide with those of society. However, outcomes under transparency may be dominated by those produced by an opaque and conservative (i.e., less flexible) central bank.