Fractional derivatives for economic growth modelling of the group of twenty: Application to prediction

Abstract

This paper studies the economic growth of the countries in the Group of Twenty (G20) in the period 1970-2018. It presents dynamic models for the world's most important national economies, including for the first time several economies which are not highly developed. Additional care has been devoted to the number of years needed for an accurate short-term prediction of future outputs. Integer order and fractional order differential equation models were obtained from the data. Their output is the gross domestic product (GDP) of a G20 country. Models are multi-input; GDP is found from all or some of the following variables: country's land area, arable land, population, school attendance, gross capital formation (GCF), exports of goods and services, general government final consumption expenditure (GGFCE), and broad money (M3). Results confirm the better performance of fractional models. This has been established employing several summary statistics. Fractional models do not require increasing the number of parameters, neither do they sacrifice the ability to predict GDP evolution in the short-term. It was found that data over 15 years allows building a model with a satisfactory prediction of the evolution of the GDP.