Ok, you can open up a really big debate on what is rational and what is not. At least one can settle down at a very basic textbook distinction between adaptive (naive and extrapolative) on the one hand and rational expectations on the other. In our models, inflation expectations are typically assumed to be rational in this sense, hence, no systematic error is undertaken.
However, if I take a look at the "data" (i always wanted to say that), this assumption seems to be hasty. The graphic shows inflation de facto, hence the ex-post measured and published hcpi from the ecb (red with asterisk) and expectations on inflation taken from the survey of professional forecasters of the ecb (green with dots). And there are two things to mention:
First: before 2007, inflation was always underestimated. It seems like, observers always had confidence in the ecb to bring down inflation below but close to 2% (in the near future), but in reality this never happened.
Second: After 2007, inflation seems to be rather adaptive than rational. Of course, there is a nearly simultaneous behaviour of both lines but, the green line is the 4 quarter ahead expectation! Hence, take 2008q4, the first dot after the peak. Expectations go down, but these expectations are only evaluated at 2008q4, these are the expectations for 2009q4. In this light, they seem to be a little bit to late. So expectations do adopt the real values just to late to be labeled anything like rational, but rather adaptive.
