Inflation fan charts, monetary policy and skew normal distribution

Issues related to classification, interpretation and estimation of inflationary uncertainties are addressed in the context of their application for constructing probability forecasts of inflation. It is shown that confusions in defining uncertainties lead to potential misunderstandings of such forecasts. The principal source of such confusion is in ignoring the effect of feedback from the policy action undertaken on the basis of forecasts of inflation onto uncertainties. In order to resolve this problem a new class of skew normal distributions (weighted skew normal, WSN) have been proposed and its properties derived. It is shown that parameters of WSN distribution can be interpreted in relation to the monetary policy strength and symmetry. It has been fitted to empirical distributions of inflation multi-step forecast errors of inflation for 34 countries, alongside others distributions already existing in the literature. The estimation method applied is using the minimum distance criteria between the empirical and theoretical distributions. Results lead to some constructive conclusions regarding the strength and asymmetry of monetary policy and confirm the applicability of WSN to producing probabilistic forecasts of inflation.