Again, Rational Expectations may not be very accurate. Nevertheless, Rational Expectations will be unbiased.
Clearly, we are making a distinction here between "accuracy" and "bias." An analogy may help to make the distinction more clear. The analogy is to target shooting. I find that most of my students do not have experience with target shooting, but, after all, the idea is a pretty simple one. The objective in target shooting is to get one's shots as near as possible to the center of the target. The objective is similar in economic forecasting. We want our forecasts to be as near as possible to what really happens.
The following figure illustrates accuracy and bias in rifle shooting.
Two candidates for the rifle team have fired trial rounds at this target. One candidate's hits are marked by the letter A and the other candidate's hits are marked by the letter B. As the coach, which candidate will you drop from the team and which will you keep?
Neither candidate is very accurate. Candidate A has the higher score. More to the point, if you were to average the five shots by candidate A, the average would be quite close to the center of the target. That means Candidate A's shooting has been approximately unbiased. By contrast, if you were to average candidate B's shots, the average would be far to the right and a little above the center of the target, where all of B's five shots are. B's shots are biased.
All the same, a rifle coach would keep candidate B on the team, and drop candidate A. The reason is that it is much easier to coach a target shooter to move the center of his shots to the center of the target than it is to coach a shooter to get the shots all together on any part of the target. That is, bias is much easier to correct than other forms of inaccuracy.
That's true also in economic forecasting.