Abstract
The environmental Kuznets curve (EKC) hypothesis is used to describe the relationship between economic development and environmental pollution. In this paper, an EKC-estimating method based on an improved nonlinear gray Bernoulli model (NGBM) is proposed from the perspective of gray system modeling. First, a non-equigap NGBM is established taking the GDP per capita and pollutant emission as the input and output of the gray system, respectively. Then, a particle swarm optimization algorithm is used to find the parameters in the nonlinear model. Finally, the EKC is validated by applying it to the per capita emission of wastewater, SO2, CO2, and soot in China. The results show that the new method proposed in this paper optimizes the exponent of the NGBM which allows it to describe the trends in the different morphological data very well, resulting in a higher fitting accuracy. China’s per capita emission of wastewater, SO2, CO2, and soot show trends corresponding to monotonically increasing, inverted U-shaped, S-shaped, and N-shaped changes, respectively.
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References
Al-Mulali U, Ozturk I (2016) The investigation of environmental Kuznets curve hypothesis in the advanced economies: the role of energy prices. Renew Sust Energ Rev 54:1622–1631. https://doi.org/10.1016/j.rser.2015.10.131
Alvarez-Herranz A, Balsalobre-Lorente D, Shahbaz M, Cantos JM (2017) Energy innovation and renewable energy consumption in the correction of air pollution levels. Energy Policy 105:386–397. https://doi.org/10.1016/j.enpol.2017.03.009
Apergis N (2016) Environmental Kuznets curves: new evidence on both panel and country-level CO2 emissions. Energy Econ 54:263–271. https://doi.org/10.1016/j.eneco.2015.12.007
Bilgili F, Koçak E, Bulut U (2016) The dynamic impact of renewable energy consumption on CO2 emissions: a revisited environmental Kuznets curve approach. Renew Sust Energ Rev 54:838–845. https://doi.org/10.1016/j.rser.2015.10.080
Bimonte S, Stabile A (2017) Land consumption and income in Italy: a case of inverted EKC. Ecol Econ 131:36–43. https://doi.org/10.1016/j.ecolecon.2016.08.016
Chang CJ, Li D, Chen CC, Chen CS (2014) A forecasting model for small non-equigap data sets considering data weights and occurrence possibilities. Comput Ind Eng 67(1):139–145. https://doi.org/10.1016/j.cie.2013.11.002
Chen CI (2008) Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos Solitons Fractals 37(1):278–287. https://doi.org/10.1016/j.chaos.2006.08.024
Chen CI, Chen HL, Chen SP (2008) Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM (1,1). Commun Nonlinear Sci Numer Simul 13(6):1194–1204. https://doi.org/10.1016/j.cnsns.2006.08.008
Chen CI, Hsin PH, Wu CS (2010) Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Syst Appl 37(12):7557–7562. https://doi.org/10.1016/j.eswa.2010.04.088
Chinadaily (2012) http://www.chinadaily.com.cn/dfpd/18da/2012-11/19/content_15941219.htm/, (accessed 18 Jan 2019)
Deng JL (1989) Introduction of grey system. J Grey Syst 1:1–24
Deng JL (1997) A novel GM(1,1) model for non-equigap series. J Grey Syst 9(2):111–116
Deng JL (2002) Basis of grey theory. Huazhong University of Science and Technology Press, Wuhan
Dinda S (2004) Environmental Kuznets curve hypothesis: a survey. Ecol Econ 49(4):431–455. https://doi.org/10.1016/j.ecolecon.2004.02.011
Ding S (2019) A novel discrete grey multivariable model and its application in forecasting the output value of China’s high-tech industries. Comput Ind Eng 127:749–760. https://doi.org/10.1016/j.cie.2018.11.016
Duarte R, Pinilla V, Serrano A (2013) Is there an environmental Kuznets curve for water use? A panel smooth transition regression approach. Econ Model 31(38):518–527. https://doi.org/10.1016/j.econmod.2012.12.010
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory, International Symposium on MICRO Machine and Human Science. IEEE 39-43. https://doi.org/10.1109/MHS.1995.494215
Giovanis E (2013) Environmental Kuznets curve: evidence from the British Household Panel Survey. Econ Model 30(1):602–611. https://doi.org/10.1016/j.econmod.2012.10.013
Grossman GM, Krueger AB (1991) Environmental impacts of a North American free trade agreement. Soc Sci Electron Publ 8(2):223–250. https://doi.org/10.3386/w3914
Gui S, Zhao LG, Zhang ZJ (2019) Does municipal solid waste generation in China support the environmental Kuznets curve? New evidence from spatial linkage analysis. Waste Manag 84:310–319. https://doi.org/10.1016/j.wasman.2018.12.006
Hashem-Nazari M, Esfahanipour A, Fatemi Ghomi SMT (2017) Non-equidistant “basic form”-focused grey Verhulst models (NBFGVMs) for ill-structured socio-economic forecasting problems. J Bus Econ Manag 18(4):676–694. https://doi.org/10.3846/16111699.2017.1337045
Hove S, Tursoy T (2019) An investigation of the environmental Kuznets curve in emerging economies. J Clean Prod 236:117628. https://doi.org/10.1016/j.jclepro.2019.117628
Hsin PH, Chen CI (2015) Application of game theory on parameter optimization of the novel two-stage Nash nonlinear grey Bernoulli model. Commun Nonlinear Sci Numer Simul 27(1–3):168–174. https://doi.org/10.1016/j.cnsns.2015.03.006
Hsu LC (2010) A genetic algorithm based nonlinear grey Bernoulli model for output forecasting in integrated circuit industry. Expert Syst Appl 37(6):4318–4323. https://doi.org/10.1016/j.eswa.2009.11.068
Kang YQ, Zhao T, Yang YY (2016) Environmental Kuznets curve for CO2 emissions in China: a spatial panel data approach. Ecol Indic 62:231–239. https://doi.org/10.1016/j.ecolind.2015.12.011
Kijima M, Nishide K, Ohyama A (2011) EKC-type transitions and environmental policy under pollutant uncertainty and cost irreversibility. J Econ Dyn Control 35(5):746–763. https://doi.org/10.1016/j.jedc.2011.01.005
Kuznets S (1995) Economic growth and income inequality. Am Econ Rev 45(1):1–28 https://www.jstor.org/stable/1811581. Accessed 20 Jan 2019
Lee CC, Chiu YB, Sun CH (2010) The environmental Kuznets curve hypothesis for water pollution: do regions matter? Energy Policy 38(1):12–23. https://doi.org/10.1016/j.enpol.2009.05.004
Lewis CD (1982) Industrial and business forecasting methods. Butterworth Scientific, London
Li DC, Chang CJ, Chen WC, Chen CC (2011) An extended grey forecasting model for omnidirectional forecasting considering data gap difference. Appl Math Model 35(10):5051–5058. https://doi.org/10.1016/j.apm.2011.04.006
Lin BQ, Omoju OE, Nwakeze NM, Okonkwo JU, Megbowon ET (2016) Is the environmental Kuznets curve hypothesis a sound basis for environmental policy in Africa? J Clean Prod 133:712–724. https://doi.org/10.1016/j.jclepro.2016.05.173
Moutinho V, Varum C, Madaleno M (2017) How economic growth affects emissions? An investigation of the environmental Kuznets curve in Portuguese and Spanish economic activity sectors. Energy Policy 106:326–344. https://doi.org/10.1016/j.enpol.2017.03.069
National Bureau of Statistics of China (2018) http://data.stats.gov.cn/easyquery.htm?cn=C01 (accessed 20 Jan 2019)
Özokcu S, Özdemir Ö (2017) Economic growth, energy, and environmental Kuznets curve. Renew Sust Energ Rev 72:639–647. https://doi.org/10.1016/j.rser.2017.01.059
Ozturk I, Al-Mulali U (2015) Investigating the validity of the environmental Kuznets curve hypothesis in Cambodia. Ecol Indic 57:324–330. https://doi.org/10.1016/j.ecolind.2015.05.018
Pablo-Romero MD, Jesús PJD (2016) Economic growth and energy consumption: the energy-environmental Kuznets curve for Latin America and the Caribbean. Renew Sust Energ Rev 60:1343–1350. https://doi.org/10.1016/j.rser.2016.03.029
Park S, Lee Y (2011) Regional model of EKC for air pollution: evidence from the Republic of Korea. Energy Policy 39(10):5840–5849. https://doi.org/10.1016/j.enpol.2011.06.028
Shafik N (1994) Economic Development and Environmental Quality: An Econometric Analysis. Oxford Economic Papers 46 (Supplement_1):757-773
Shi BZ (1993) Modeling of non-equigap GM(1,1). J Grey Syst 5(2):105–113
Shi Y, Eberhart R (1998) A modified particle swarm optimizer. Inst Electr Electron 9:69–73. https://doi.org/10.1109/ICEC.1998.699146
Tsai SB, Xue Y, Zhang J, Chen Q, Liu Y, Zhou J, Dong W (2017) Models for forecasting growth trends in renewable energy. Renew Sust Energ Rev 77:1169–1178 https://doi.org/10.1016/j.rser.2016.06.001
Wang ZX, Li Q (2019) Modelling the nonlinear relationship between CO2 emissions and economic growth using a PSO algorithm-based grey Verhulst model. J Clean Prod 207:214–224. https://doi.org/10.1016/j.jclepro.2018.10.010
Wang ZX, Dang YG, Liu SF (2009) Solution of GM (1, 1) power model and its properties. Syst Eng Electron 31:2380–2383
Wang ZX, Hipel KW, Wang Q, He SW (2011) An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China. Appl Math Model 35(12):5524–5532. https://doi.org/10.1016/j.apm.2011.05.022
Wang X, Qi L, Chen C, Tang J, Jiang M (2014) Grey system theory based prediction for topic trend on Internet. Eng Appl Artif Intell 29:191–200. https://doi.org/10.1016/j.engappai.2013.12.005
Wu L, Li N, Zhao T (2019) Using the seasonal FGM(1,1) model to predict the air quality indicators in Xingtai and Handan. Environ Sci Pollut Res 26:14683–14688. https://doi.org/10.1007/s11356-019-04715-z
Xu GQ, Liu ZY, Jiang ZH (2006) Decomposition model and empirical study of carbon emissions for China: 1995-2004. China Popul Resour Environ 16(6):158–161
Yan Y, Liu DW (2012) Construction accidents forecast based on nonlinear grey Bernoulli model. China Saf Sci J 22(4):43
Yang X, Lou F, Sun M, Wang RQ, Wang YT (2017) Study of the relationship between greenhouse gas emissions and the economic growth of Russia based on the environmental Kuznets curve. Appl Energy 193:162–173. https://doi.org/10.1016/j.apenergy.2017.02.034
Yang XY, Fang ZG, Yang YG, Mba D, Li XC (2019) A novel multi-information fusion grey model and its application in wear trend prediction of wind turbines. Appl Math Model 71:543–557. https://doi.org/10.1016/j.apm.2019.02.043
Zambrano-Monserrate MA, Silva-Zambrano CA, Davalos-Penafiel JL, Zambrano-Monserrate A, Ruano MA (2018) Testing environmental Kuznets curve hypothesis in Peru: the role of renewable electricity, petroleum and dry natural gas. Renew Sust Energ Rev 82:4170–4178. https://doi.org/10.1016/j.rser.2017.11.005
Zeng B, Li C (2016) Forecasting the natural gas demand in China using a self-adapting intelligent grey model. Energy 112:810–825. https://doi.org/10.1016/j.energy.2016.06.090
Zhang L, Zheng Y, Wang K, Zhang XL, Zheng YJ (2014) An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of hepatitis B in Xinjiang, China. Comput Biol Med 49(1):67–73. https://doi.org/10.1016/j.compbiomed.2014.02.008
Zhang Y, Gu A, Pan B (2017) Relationship between industrial water consumption and economic growth in China based on environmental Kuznets curve. Energy Procedia 105:3557–3564. https://doi.org/10.1016/j.egypro.2017.03.818
Zhou W, Pei LL (2019) The grey generalized Verhulst model and its application for forecasting Chinese pig price index. Soft Comput 5:1–14. https://doi.org/10.1007/s00500-019-04248-0
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The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.
Funding
This research is supported by the National Natural Science Foundation of China (Grant No. 71571157, 71971194, and 71801190).
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Li, Q., Wang, ZX. & Zhang, XY. An improved gray Bernoulli model for estimating the relationship between economic growth and pollution emissions. Environ Sci Pollut Res 27, 25638–25654 (2020). https://doi.org/10.1007/s11356-020-08951-6
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DOI: https://doi.org/10.1007/s11356-020-08951-6