Assessing Forecast Uncertainty: An Information Bayesian Approach

Abstract

Regardless of the field, forecasts are widely used and yet assessments of the embedded uncertainty—the magnitude of the downside and upside risks of the prediction itself—are often missing. Particularly in policy-making and investment, accounting for these risks around baseline predictions is of outstanding importance for making better and more informed decisions. This paper introduces a procedure to assess risks associated with a random phenomenon. The methodology assigns probability distributions to baseline-projections of an economic or social random variable—for example gross domestic product growth, inflation, population growth, poverty headcount, and so forth—combining ex-post and ex-ante market information. The generated asymmetric density forecasts use information derived from surveys on expectations and implied statistics of predictive models. The methodology also decomposes the variance and skewness of the predictive distribution accounting for the shares of selected risk factors. The procedure relies on a Bayesian information-theoretical approach, which allows the inclusion of judgment and forecaster expertise. For reliability purposes and transparency, the paper also evaluates the constructed density forecasts assigning a score. The continuous ranked probability score is used to assess the prediction accuracy of elicited density forecasts. The selected score incentivizes the forecaster to provide its true and best predictive distribution. An empirical application to forecast world gross domestic product growth is used to test the Bayesian entropy methodology. Predictive variance and skewness of world gross domestic product growth are associated with ex-ante information of four risk factors: term spreads, absolute deviations of headline inflation targets, energy prices, and the Standard and Poor's 500 index prices. The Bayesian entropy technique is benchmarked with naive-generated density forecasts that utilize information from historical forecast errors. The results show that the Bayesian density forecasts outperform the naive-generated benchmark predictions, illustrating the value added of the introduced methodology.