The Mittag-Leffler Fitting of the Phillips Curve

TL;DR

This paper introduces a novel mathematical model using the Mittag-Leffler function to describe the Phillips curve, demonstrating improved data fitting for economic relations involving oscillations and stretched exponential behaviors.

Contribution

The paper is the first to apply the one-parameter Mittag-Leffler function to model the Phillips curve, offering a flexible alternative to traditional exponential and power models.

Findings

Mittag-Leffler model fits data with oscillations better.

Model outperforms power and exponential models in out-of-sample tests.

Applicable to economic data exhibiting complex behaviors.

Abstract

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