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In this paper, a mathematical model based on the one-parameter Mittag-Lefflerfunction is proposed to be used for the first time to describe the relationbetween unemployment rate and inflation rate, also known as the Phillips curve.The Phillips curve is in the literature often represented by anexponential-like shape. On the other hand, Phillips in his fundamental paperused a power function in the model definition. Considering that the ordinary aswell as generalised Mittag-Leffler function behaves between a purelyexponential function and a power function it is natural to implement it in thedefinition of the model used to describe the relation between the datarepresenting the Phillips curve. For the modelling purposes the data of twodifferent European economies, France and Switzerland, were used and an"out-of-sample" forecast was done to compare the performance of theMittag-Leffler model to the performance of the power-type and exponential-typemodel. The results demonstrate that the ability of the Mittag-Leffler functionto fit data that manifest signs of stretched exponentials, oscillations or evendamped oscillations can be of use when describing economic relations andphenomenons, such as the Phillips curve.

The Mittag-Leffler Fitting of the Phillips Curve