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An important stylized fact to emerge from 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 examines periods without large shifts in the level of inflation (such as 1984-2005). An important consequence is that the hump-shaped VAR estimated response of inflation is not appropriate to fit stylized models of the response of inflation around a stable steady state inflation level.