Interpretation of point forecasts with unkown directive.

Following recent suggestions in the literature, we interpret point forecasts as functionals (i.e., point summaries) of predictive distributions. We consider the situation of unknown directives, and estimate the functional, which might vary over time as a function of certain state variables, using the generalized method of moments. Focusing on two classes of state-dependent functionals, quantiles and expectiles, we show that our estimators are identifiable, consistent, and asymptotically normal. We construct specification and rationality tests for forecasts, and propose a novel approach to combine point forecasts. In a data example, we show that the gross domestic product (GDP) Greenbook forecasts of the U.S. Federal Reserve can be interpreted as an evolving quantile that depends on the current growth rate. Based on these findings, we construct an improved GDP mean forecast. Using simulated data, we demonstrate that our rationality test is better calibrated and more powerful than existing approaches.