When did unsystematic monetary policy have an effect on inflation?

An important stylized fact to emerge from the VAR estimates is that exogenous monetary policy shocks (also labelled unsystematic monetary policy) have a delayed, persistent, hump shaped effect on inflation. I argue that this empirical pattern is fragile. In particular it disappears when one corrects for the effects of large shifts (breaks) in average inflation or examines periods without such shifts (such as the 1984-2004 period). An important consequence is that the hump shaped VAR estimated response of inflation is not appropriate to fit stylised models of the response of inflation around a stable steady state inflation level.