Uncertainty, information, and disagreement of economic forecasters

Maximum entropy distributions with quantile information

“…In general, these options provide two different forecast models. For example, the ME model consistent with the arithmetic pools of moments is in the same family as the individual ME models, but is not the mixture of the individual ME models ( Shoja & Soofi, 2017 ). However, the ME model (27) produces the same model for the two options when probabilities are elicited from multiple experts using fixed interval method.…”

“… Rich and Tracy (2010) used the discrete entropy of the probabilities H ( P α ) ≥ 0, but did not use any information divergence for disagreement. Shoja and Soofi (2017) proposed an information framework for measuring uncertainty and disagreement. This framework requires a set of individual forecast distributions, specifying weights for their arithmetic pooling, and measures of uncertainty and divergence.…”

“…These authors used the discrete entropy, H ( P α ), and the ME models based on the variance of the midpoints to illustrate their proposed framework. Lahiri and Wang (2019) avoided using discrete entropy and applied the information framework of Shoja and Soofi (2017) using the entropies of beta and triangular distributions fitted to the histograms of forecasters’ subjective probabilities and their average; they estimated bounds for the unbounded intervals according to the fit. The use of fitted parametric distributions, such as the normal and beta, induces non-elicited information, so does the use of their variance.…”

“…We use the ME model (27) to measure uncertainty, disagreement and information of economic forecasters within the framework of Shoja and Soofi (2017) . The subjective probabilities of each forecaster provide an ME model .…”

“…These probabilities are used to produce economic outlook reports for policy makers. The research area of measuring the uncertainty and disagreement of economic forecasters is primarily based on using these probabilities for developing other aspects of forecast distribution of variables such as the growth of Gross Domestic Product (GDP); Lahiri and Wang (2019) and Shoja and Soofi (2017) provide reviews and latest developments on this topic. In operations and business decision problems a quantile appears as the solution to the minimum risk (expected loss) under the asymmetric linear loss function such as the newsvendor problem, where the optimal order quantity that maximizes the profit is a quantile of the demand distribution ( Snyder and Shen, 2011 ).…”