Testing for the usefulness of forecasts

Ashley (Journal of Forecasting 1983; 2(3): 211–223) proposes a criterion (known as Ashley's index) to judge whether the external macroeconomic variables are well forecast to serve as explanatory variables in forecasting models, which is crucial for policy makers. In this article, we try to extend Ashley's work by providing three testing procedures, including a ratio-based test, a difference-based test, and the Bayesian approach. The Bayesian approach has the advantage of allowing the flexibility of adapting all possible information content within a decision-making environment such as the change of variable's definition due to the evolving system of national accounts. We demonstrate the proposed methods by applying six macroeconomic forecasts in the Survey of Professional Forecasters. Researchers or practitioners can thus formally test whether the external information is helpful.