Consistency of the Point Forecasts and Probability Distributions
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The US SPF provides probability distributions (in the form of histograms), point forecasts, and probabilities of the event that output growth will be negative (output will decline) in upcoming quarters. Are these different types of forecasts consistent one with another? For example, can the point forecasts be interpreted as the means of the histograms? Although a histogram does not fully reveal the probability density function, a lower and upper bound on the mean value for that histogram can be calculated, without making any assumption about how the histogram relates to the underlying distribution. If the point prediction falls within the lower and upper limit, the point prediction is deemed to be consistent with being the mean. Similar bounds can be calculated for the mode and median. A possible explanation in terms of asymmetric loss is considered for the apparent inconsistencies that are found. The possible importance of reporting practice—the rounding of probabilities either to convey ambiguity or to simplify communication—is explored in terms of the comparison of the forecast probabilities of decline, and the implied histogram probabilities of this event.
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