Application of a modified CES production function model based on improved firefly algorithm

Maolin Cheng; Mingyin Xiang

doi:10.3934/jimo.2019018

Article Contents

2020, Volume 16, Issue 4: 1571-1584. Doi: 10.3934/jimo.2019018

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Application of a modified CES production function model based on improved firefly algorithm

Maolin Cheng^1, , and
Mingyin Xiang^2,

1.
School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, China
2.
School of Mathematics and Statistics, Huangshan University, Huangshan, 245041, China

^* Corresponding author: Maolin Cheng
^* Corresponding author: Maolin Cheng

Received: May 31, 2018

Revised: August 31, 2018

Early access: March 2019

Published: May 2020

The first author is supported by NSF grant 11401418

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Abstract

The conventional CES production function model fails to consider the influences of policy factors on economic growth in different stages. This paper proposes a modified model of the CES production function. Regarding model parameter estimation, the paper proposes a modern intelligent algorithm, the firefly algorithm (FA). The paper improves conventional FA to enhance the convergence rate and precision. To overcome the shortcomings of the conventional method in model application, the paper presents a new method of calculating the contribution rates of factors influencing economic growth and provides examples.

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Mathematics Subject Classification: Primary: 62P20, 91B62; Secondary: 68Q25.

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Table 1. Data on Chinese economic growth

Period	Year	$Y$	$L$	$K$	$E$
Period of the 9$^{th}$ five-year plan	1996	71176.6	68950	22913.5	135192
	1997	78973.0	69820	24941.1	135909
	1998	84402.3	70637	28406.2	136184
	1999	89677.1	71394	29854.7	140569
	2000	99214.6	72085	32917.7	145531
Period of the 10$^{th}$ five-year plan	2001	109655.2	72797	37213.5	150406
	2002	120332.7	73280	43499.9	159431
	2003	135822.8	73736	55566.6	183792
	2004	159878.3	74264	70477.4	213456
	2005	183217.5	74647	88773.6	235997
Period of the 11$^{th}$ five-year plan	2006	211923.5	74978	109998.2	258676
	2007	249529.9	75321	137239.0	280508
	2008	316228.8	75564	172828.4	291448
	2009	343464.7	75828	224598.8	306647
	2010	401512.8	76105	251683.8	324939
Period of the 12$^{th}$ five-year plan	2011	473104.0	76420	311485.1	348002
	2012	519470.1	76704	374694.7	361732
	2013	568845.0	76977	447074.0	375252
	2014	636462.7	77253	512760.7	426000
	2015	676780.0	77451	562000.0	430000
Period of the 13$^{th}$ five-year plan	2016	744127.0	77603	606466.0	436000
	2017	827122.0	77640	641238.0	449000

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Table 2. Comparison of results of three algorithms

Algorithm	Improved PSO	Conventional firefly algorithm	Improved firefly algorithm
$A$	0.7638	0.8268	0.7500
$\sigma $	0.0518	0.0700	0.0572
$\delta_{1} $	0.6612	0.6460	0.6502
$\delta_{2} $	0.3229	0.3827	0.3297
$\delta_{3} $	0.1852	0.1712	0.1834
$\alpha_{1} $	0.5352	0.5080	0.5184
$\alpha_{2} $	0.7295	0.6825	0.7164
$\alpha_{3} $	0.1683	0.2149	0.1986
$\alpha_{4} $	0.3224	0.3464	0.3223
$\alpha_{5} $	0.1511	0.1970	0.1538
$\beta_{1} $	0.1431	0.1878	0.1565
$\beta_{2} $	0.1072	0.1228	0.1170
$\beta_{3} $	0.1971	0.1916	0.2027
$\beta_{4} $	0.2472	0.2645	0.2498
$\beta_{5} $	0.2183	0.1981	0.2239
$\gamma_{1} $	0.1102	0.0988	0.1137
$\gamma_{2} $	0.0710	0.1352	0.0901
$\gamma_{3} $	0.1006	0.1478	0.1002
$\gamma_{4} $	0.0478	0.0375	0.0482
$\gamma_{5} $	0.1205	0.1945	0.1306
$\rho $	1.5457	1.4934	1.5310
$\mu $	1.2312	1.1995	1.2203
Iteration number	142	774	22
Objective function $RSS$	2.4602e$+$09	2.8225e$+$09	1.2426e$+$09
Model's coefficient of determination, $R^{2}$	0.9980	0.9977	0.9990

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