Abstract
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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- 1.
Sections 6.1 and 6.2 of this chapter are based on Clements, M.P. (2014), Probability Distributions or Point Predictions? Survey Forecasts of US Output Growth and Inflation, International Journal of Forecasting, 30(1), 99–117. Material from this article is used with the permission of Elsevier. The remainder of Chap. 6 is based on Clements, M.P., (2011), An empirical investigation of the effects of rounding on the SPF probabilities of decline and output growth histograms, Journal of Money, Credit and Banking, 43(1), 207–220. Material from this article is used with the permission of John Wiley and Sons.
- 2.
García and Manzanares (2007) find that the growth and inflation forecasts of the European Central Bank’s Survey of Professional Forecasters follow a similar pattern, and Boero et al. (2008) find that the same is generally true of the Bank of England Survey of External Forecasters, especially for the output growth forecasts. Clements (2009) also looks at the consistency of the ‘probabilities of decline’ elicited by the SPF and its output growth histograms.
- 3.
More generally, the lower bound sums the probabilities of all the histogram intervals whose upper limits are less than 1.7, while the upper bound includes in this sum the probability attached to the histogram interval containing the 1.7 value.
- 4.
That is, the percentage of pairs of forecasts for which the upper bound on the probability of decline (p U) calculated allowing for rounding is below the lower bound on the histogram probability, l.
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Clements, M.P. (2019). Consistency of the Point Forecasts and Probability Distributions. In: Macroeconomic Survey Expectations. Palgrave Texts in Econometrics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-97223-7_6
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