# American Institute of Mathematical Sciences

## The relationship between China's industrial space agglomeration process and environmental damage

 1 College of Accounting and Finance, Jiangxi University of Engineering, Xinyu 338000, China 2 School of Electronic Commerce, Jiangxi University of Engineering, Xinyu 338000, China 3 Development Planning Office, Lishui University, Lishui 323000, China

*Corresponding author: Guangju Chen

Received  May 2019 Revised  May 2019 Published  February 2020

On the basis of introducing the agglomeration function, the Copeland and Taylor models were used to establish a general linear model for the influence of industrial agglomeration on environmental quality; following, the difference in such influence at the different marketization levels is further distinguished and the linear model is expanded to the non-linear threshold model. On this basis, the panel data of 30 China's provinces and municipalities during the period of 2000–2009, as well as the threshold regression method proposed by Hansen were adopted to test the influence of industrial agglomeration on environmental pollution, where the marketization level is used as the threshold variable. Additionally, the sensitivity analysis is conducted for other industrial pollutants, and the results show the one that the model setting and test result in this paper are stable and reliable. Compared with the former literatures, the paper answers not only the question how industrial agglomeration affects environmental quality, but also introduces the threshold variable of level and further answers the question "what the conditions in which industrial agglomeration may are improve environment", which provides the rational reference for the formulation of related policy.

Citation: Shurong Yan, Dehua Liu, Hongli Huang, Weihong Li, Lina Wang, Manwen Tian, Guangju Chen. The relationship between China's industrial space agglomeration process and environmental damage. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020274
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##### References:
 [1] L. Brandt, J. Biesebroeck and Y. Zhang, Creative accounting or creative destruction? firm-level productivity growth in chinese manufacturing, Journal of Development Economics, 97 (2012), 339-351.   Google Scholar [2] T. Caraballo, M. Herrera-Cobos and P. Marín-Rubio, An iterative method for non-autonomous nonlocal reaction-diffusion equations, Applied Mathematics and Nonlinear Sciences, 2 (2017), 73-82.  doi: 10.21042/AMNS.2017.1.00006.  Google Scholar [3] A. Ciccone and R. E. Hall, Productivity and the density of economic activity, American Economic Review, 86 (1996), 54-70.  doi: 10.3386/w4313.  Google Scholar [4] P.-P. Combes, G. Duranton, L. Gobillon, D. Puga and S. Roux, The productivity advantages of large cities: Distinguishing agglomeration from firm selection, Social Science Electronic Publishing, 80 (2012), 2543-2594.  doi: 10.3982/ECTA8442.  Google Scholar [5] B. Copeland and M. Taylor, North-south trade and the environment, The Quarterly Journal of Economics, 109 (1994), 755-787.   Google Scholar [6] W. Gao and W. Wang, A tight neighborhood union condition on fractional (g, f, n ', m)-critical deleted graphs, Colloquium Mathematicum, 149 (2017), 291-298.  doi: 10.4064/cm6959-8-2016.  Google Scholar [7] W. Gao and W. F. Wang, The fifth geometric-arithmetic index of bridge graph and carbon nanocones, Journal of Difference Equations and Applications, 23 (2017), 100-109.  doi: 10.1080/10236198.2016.1197214.  Google Scholar [8] M. García-Planas and T. Klymchuk, Perturbation analysis of a matrix differential equation $\dot{x} = abx$, Applied Mathematics and Nonlinear Sciences, 3 (2018), 97-103.  doi: 10.21042/AMNS.2018.1.00007.  Google Scholar [9] G. M. Grossman and A. B. Krueger, Environmental impacts of a north american free trade agreement, Social Science Electronic Publishing, 8 (1991), 223-250.  doi: 10.3386/w3914.  Google Scholar [10] B. E. Hansen, Threshold effects in non-dynamic panels: Estimation, testing, and inference, Journal of Econometrics, 93 (1999), 345-368.  doi: 10.1016/S0304-4076(99)00025-1.  Google Scholar [11] V. Henderson, The urbanization process and economic growth: The so-what question, Journal of Economic Growth, 8 (2003), 47-71.   Google Scholar [12] M. Hosny and M. Raafat, On generalization of rough multiset via multiset ideals, Journal of Intelligent and Fuzzy Systems, 33 (2017), 1249-1261.  doi: 10.3233/JIFS-17102.  Google Scholar [13] W. Huang, X. Tao, S. Li, W. Huang, X. Tao and S. Li, Pricing formulae for european options under the fractional vasicek interest rate model, Acta Mathematica Sinica, 55 (2012), 219-230.   Google Scholar [14] B. S. Javorcik, Does foreign direct investment increase the productivity of domestic firms? in search of spillovers through backward linkages, American Economic Review, 94 (2004), 605-627.  doi: 10.1257/0002828041464605.  Google Scholar [15] J. Jin and W. Mi, An aimms-based decision-making model for optimizing the intelligent stowage of export containers in a single bay, Discrete and Continuous Dynamical Systems Series S, 12 (2019), 1101-1115.   Google Scholar [16] P. Krugman, Multinational enterprise: The old and the new in history and theory, North American Review of Economics and Finance, 1 (1990), 267-280.  doi: 10.1016/1042-752X(90)90020-G.  Google Scholar [17] F. A. A. M. D. Leeuw, N. Moussiopoulos, P. Sahm and A. Bartonova, Urban air quality in larger conurbations in the european union, Environmental Modelling and Software, 16 (2001), 399-414.  doi: 10.1016/S1364-8152(01)00007-X.  Google Scholar [18] J. Levinsohn and A. Petrin, Estimating production functions using inputs to control for unobservables, Review of Economic Studies, 70 (2003), 317-342.  doi: 10.3386/w7819.  Google Scholar [19] M. J. Melitz and G. I. P. Ottaviano, Market size, trade, and productivity, Review of Economic Studies, 75 (2005), 295-316.  doi: 10.1111/j.1467-937X.2007.00463.x.  Google Scholar [20] G. S. Olley and A. Pakes, The dynamics of productivity in the telecommunications equipment industry, Econometrica, 64 (1996), 1263-1297.  doi: 10.3386/w3977.  Google Scholar [21] G. I. P. Ottaviano and D. Pinelli, Market potential and productivity: Evidence from finnish regions, Regional Science and Urban Economics, 36 (2006), 636-657.  doi: 10.1016/j.regsciurbeco.2006.06.005.  Google Scholar [22] S. Redding and A. Venables, Economic geography and international inequality, Journal of International Economics, 62 (2004), 53-82.  doi: 10.1016/j.jinteco.2003.07.001.  Google Scholar
Sensitivity Analysis Results
 Explanatory variable SO$_{2}$ gas water $al(ma\le \gamma _1 )$ 0.5601***(3.67) 0.8297***(6.04) 1.1063***(9.07) $al(\gamma _1\gamma _2 )$ $-0.4312**(-2.81)$ 0.4048***(4.02) 0.7876***(7.56) $1ncurb$ 0.0753***(2.51) 0.0602(1.29) 0.0401**(2.15) $1nopen$ 0.1967***(3.54) 0.1298**(2.04) $-0.1038(-1.38)$ $1nrd$ $-0.0021(-0.03)$ $-0.0582(-0.80)$ $0.0601(-1.46)$ $1nk$ 0.1017**(2.87) 0.8802***(18.04) 0.0503(1.15) Constant term 3.0769***(13.01) 0.1201(0.34) 1.5025***(6.73) 1$^{st}$ threshold valve $3.051[3.050, 3.050]$ $6.298[6.501, 6.802]$ $4.480[4.084, 4.536]$ 2$^{nd}$ threshold valve $4.731[4.160, 4.587]$ $8.186[3.145, 8.397]$ $8.053[7.698, 8.403]$ Note: the value in the round brackets is the statistical magnitude $t$ corresponded by all coefficients, **, **, * represents respectively the one passed the significance test at the level of 1%, 5% and 10%; the value in the middle brackets shows the confidence interval (95% of threshold values).
 Explanatory variable SO$_{2}$ gas water $al(ma\le \gamma _1 )$ 0.5601***(3.67) 0.8297***(6.04) 1.1063***(9.07) $al(\gamma _1\gamma _2 )$ $-0.4312**(-2.81)$ 0.4048***(4.02) 0.7876***(7.56) $1ncurb$ 0.0753***(2.51) 0.0602(1.29) 0.0401**(2.15) $1nopen$ 0.1967***(3.54) 0.1298**(2.04) $-0.1038(-1.38)$ $1nrd$ $-0.0021(-0.03)$ $-0.0582(-0.80)$ $0.0601(-1.46)$ $1nk$ 0.1017**(2.87) 0.8802***(18.04) 0.0503(1.15) Constant term 3.0769***(13.01) 0.1201(0.34) 1.5025***(6.73) 1$^{st}$ threshold valve $3.051[3.050, 3.050]$ $6.298[6.501, 6.802]$ $4.480[4.084, 4.536]$ 2$^{nd}$ threshold valve $4.731[4.160, 4.587]$ $8.186[3.145, 8.397]$ $8.053[7.698, 8.403]$ Note: the value in the round brackets is the statistical magnitude $t$ corresponded by all coefficients, **, **, * represents respectively the one passed the significance test at the level of 1%, 5% and 10%; the value in the middle brackets shows the confidence interval (95% of threshold values).
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