Are internally consistent forecasts rational?

Economic forecasts, such as the Survey of Professional Forecasters (SPF), are revised multiple times before realization of the target. This paper studies the sources of forecast revisions. By decomposing the fixed-event forecast error into a rational component due to unanticipated future shocks and an irrational component due to measurement error in acquired information or forecasters' reactions, we derive the conditions under which fixed-event forecasts that contain an irrational forecast error can still possess the second moment properties of rational forecasts. We show that internal consistency of fixed-event forecasts depends on the magnitude of the rational and irrational components in the revisions. As such, fixed-event forecasts subject to irrational error may still be internally consistent, although they are not rational, as evidence in many empirical studies. We illustrate our methodology with the SPF inflation forecasts data. Our results show evidence of a sizeable and heterogeneous irrational forecast error component across forecast horizons and a high irrational-to-news ratio for most forecasters. This finding also provides insight into why forecast revision effort is not always fully compensated by revision reward.