Calibrating GDP fan charts using probit models with a comparison to the approaches of the Bank of England and Riksbank

Fan charts were pioneered by the Bank of England and Riksbank and provide a visuallyappealing means to convey the uncertainty surrounding a forecast. This paper describes amethod for parameterising fan charts around GDP growth forecasts by which the degree ofuncertainty is based on past forecast errors, but the skew is derived from a probit modelbasedassessment of the probability of a future downturn. The probit-based fan chartsclearly out-perform the Bank of England and Riksbank approaches when applied toforecasts made immediately preceding the Global Financial Crisis. These examples alsohighlight weaknesses with the Bank of England and Riksbank approaches. The Riksbank approach implicitly assumes that forecast errors are normally distributed, but over a long track record this is unlikely to be the case becauseforecasters are generally poor at predicting downturns, which leads to bias and skewin the pattern of forecast errors. Thus, the Riksbank fan chart is neither an accuraterepresentation of past forecast errors, nor is it a reflection of the risk assessmentunderlying the forecast. The Bank of England approach relies heavily on the judgment of the members of the Monetary Policy Committee to assess risks. However, even when they havecorrectly foreseen the nature of future risks, the quantitative translation of theserisks into the fan chart skew has been too timid. Perhaps one reason for this is thatthe fan chart prediction intervals based on historical forecast errors already appearquite wide so that inflating them by adding skew may appear embarrassing (at leastex ante).The approach advocated in this paper addresses these weaknesses by recognising thatforecast errors are not symmetrical: firstly, this leads to more compressed predictionintervals in the upper part of the fan chart (representing the possibility of under-prediction);and secondly, using the large forecast errors from past downturns to calibrate downwardskew clearly supports a more bold approach when there is a risk of a downturn. A weaknessof the probit model-based approach is that it will not predict atypical downturns. Forexample, in the current conjuncture it would not pick up risks associated with a ‘no deal’Brexit or a global trade war. However, a downturn triggered by atypical events may bemore severe if risk factors describing a typical business-financial cycle are also high.