The Application of Fractional Calculus in Chinese Economic Growth Models

Hao Ming,Michal Fečkan,Jinrong Wang

doi:10.3390/math7080665

Abstract

In this paper, we apply Caputo-type fractional order calculus to simulate China’s gross domestic product (GDP) growth based on R software, which is a free software environment for statistical computing and graphics. Moreover, we compare the results for the fractional model with the integer order model. In addition, we show the importance of variables according to the BIC criterion. The study shows that Caputo fractional order calculus can produce a better model and perform more accurately in predicting the GDP values from 2012–2016.

Highlights

As one of the most important macroeconomic statistics indicators, gross domestic product (GDP) is an effective tool for people to understand and grasp the macroeconomic operation of a country; it is an important basis for formulating economic policies
Fractional calculus is widely used to construct economic models; it incorporates the effects of memory in evolutionary processes; experimental results show that the fractional order model is superior to integer order model, such as [4,5,6,7,8,9,10,11,12,13]
We used R software and the least squares method to obtain the coefficient estimation in the integer order and Caputo fractional order models

Summary

Introduction

As one of the most important macroeconomic statistics indicators, GDP is an effective tool for people to understand and grasp the macroeconomic operation of a country; it is an important basis for formulating economic policies. There are still some shortcomings in using classical calculus to model real data. Luo et al [14] improved the fractional EGM model in [5] and adopted different computational methods to simulate GDP via MATLAB, SPSS, and R software. We adopt the idea in [14] to apply Caputo fractional order EGM and integer order to study China’s GDP growth, as well as the minimum mean-squared-error (MSE) to estimate the parameters in the model. In order to compare the fitting effect between the integer order and the fractional order model, we establish the minimum absolute error coefficient, determination, and the BIC index. Summarizing, based on fractional calculus, this paper conducts modeling of China’s economic growth. Real data are used for modeling and showing the advantage of fractional calculus. The purpose of the two methods is the same, but the case analysis is often more complex and difficult than simulation, so a simulation is not used in this paper

Models Description

Parameter Estimation

Conclusions