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

Abstract

Fan charts were pioneered by the Bank of England and Riksbank and provide a visually appealing means to convey the uncertainty surrounding a forecast. This paper describes a method for parameterising fan charts around GDP growth forecasts by which the degree of uncertainty is based on past forecast errors, but the skew is derived from a probit modelbased assessment of the probability of a future downturn. The probit-based fan charts clearly out-perform the Bank of England and Riksbank approaches when applied to forecasts made immediately preceding the Global Financial Crisis. These examples also highlight 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 because forecasters are generally poor at predicting downturns, which leads to bias and skew in the pattern of forecast errors. Thus, the Riksbank fan chart is neither an accurate representation of past forecast errors, nor is it a reflection of the risk assessment underlying 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 have correctly foreseen the nature of future risks, the quantitative translation of these risks into the fan chart skew has been too timid. Perhaps one reason for this is that the fan chart prediction intervals based on historical forecast errors already appear quite wide so that inflating them by adding skew may appear embarrassing (at least ex ante). The approach advocated in this paper addresses these weaknesses by recognising that forecast errors are not symmetrical: firstly, this leads to more compressed prediction intervals 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 downward skew clearly supports a more bold approach when there is a risk of a downturn. A weakness of the probit model-based approach is that it will not predict atypical downturns. For example, 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 be more severe if risk factors describing a typical business-financial cycle are also high.