Monetary policy transmission lags create credibility problems for the inflationtargeting policy maker who acts under discretion. We show that if prices react to monetary policy with a longer lag than output, the welfare maximizing inflationtargeting policy implies no policy stabilization of cost-push shocks in the canonical New Keynesian model. The reason is simple: for the period monetary policy influences output, inflation is predetermined and the best discretionary policy is to stabilize the output gap fully. We find that money growth targeting comes close to replicating the welfare-maximizing policy under commitment if there are transmission lags. Keywords: discretionary and stabilization bias, monetary policy, transmission lags, inflation targeting, money targeting JEL classification numbers: E52, E58, E61