  Systematically biased forecasts are typically interpreted as evidence of
forecasters' irrationality and/or asymmetric loss. In this paper we propose an
alternative explanation: when forecasts inform economic policy decisions, and
the resulting actions affect the realization of the forecast target itself,
forecasts may be optimally biased even under quadratic loss. The result arises
in environments in which the forecaster is uncertain about the decision maker's
reaction to the forecast, which is presumably the case in most applications. We
illustrate the empirical relevance of our theory by reviewing some stylized
properties of Green Book inflation forecasts and relating them to the
predictions from our model. Our results point out that the presence of policy
feedback poses a challenge to traditional tests of forecast rationality.
