Discrete Dynamics in Nature and Society

Volume 2019, Article ID 1570364, 10 pages

https://doi.org/10.1155/2019/1570364

## Measuring and Fitting the Relationship between Socioeconomic Development and Environmental Pollution: A Case of Beijing–Tianjin–Hebei Region, China

Department of Economics and Management, North China Electric Power University, Baoding 071003, China

Correspondence should be addressed to Ming Meng; moc.621@mmupecn

Received 22 March 2019; Revised 29 April 2019; Accepted 9 May 2019; Published 2 June 2019

Academic Editor: Francisco R. Villatoro

Copyright © 2019 Ming Meng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The Beijing–Tianjin–Hebei (BTH) region is a top urban agglomeration of China but has the problem of severe environmental pollution. Most of the current researches on the sustainable development of this region only concentrate on the environmental pollution itself and ignore its relationship to the socioeconomic development. In this research, an entropy-based coupling model, a polynomial equation with partial least squares algorithm, and socioeconomic and environmental data in 2006–2015 were used to measure and fit the above relationship. Empirical analysis led to the following conclusions. Beijing, Tianjin, and Hebei presented similar socioeconomic development modes but different environmental pollution modes. The social economy of the BTH region has been developing at the expense of environmental pollution, but the environmental cost has been decreasing year by year. At present, the BTH region has huge potential to improve its environment. Increasing the investment in the treatment of industrial pollution in Tianjin and mitigating the soot (dust) emissions in Tianjin and Hebei are the major environmental policy directions. Controlling the development of smelting and pressing of ferrous metals and other building material sectors in Hebei is the major economic policy direction.

#### 1. Introduction

The Beijing–Tianjin–Hebei (BTH) region is one of the most dynamic but seriously polluted urban agglomerations in China [1, 2]. The aim of this research is to measure the coupling relationship between socioeconomic development and environmental pollution in the BTH region, fit the changing trend of this relationship, and offer policy implications to guide the sustainable development of this region.

The BTH region is located in the heart of China’s Bohai Rim. It covers about 2.26% of China’s territory (217.16 thousand km^{2}) and is inhabited by almost 8.09% of the population of China (112.47 million people) [3–5]. At present, the BTH, Pearl River Delta, and Yangze River Delta are China’s top three urban agglomerations. The three regions produce approximately 10.20%, 10.91%, and 20.62% of China’s GDP and contributed 11.26%, 14.45%, and 26.41% to GDP growth, respectively [1]. However, unlike the latter two regions, the BTH region faces serious environmental pollution. On 22 July 2018, a report released by China’s Ministry of Ecology and Environment shows that one-fourth of the most polluted cities in China are located in the BTH region and nearly all cities in this region do not meet the air quality standards recommended by the World Health Organization [2, 6]. Environmental pollution not only has led to the deterioration of living conditions in the BTH region but also threatens the economic development [7]. China will face the risk of losing this important economic growth engine if the effects of environmental pollution are not mitigated.

Although the environmental and economic issues of the BTH region have gained the attention of researchers, most studies focus on three areas as follows. Impacts of environment pollution: Zhang et al. [8] used city-level panel data to explore the influence of urban pollution on labor supply. Their research results indicated that the above impact is nonlinear, and the extent of impact is affected by income level. Zhu et al. [9] adopted Lagrange Multiplier test and Spatial Durbin Model to investigate the relationship between foreign direct investment and sulfur dioxide (SO_{2}) emissions in the BTH region. They confirmed the existence of the causality of the above two variables. Cause and countermeasure of environment pollution: A positive Matrix Factorization research conducted by Gao et al. found that PM2.5 pollution in the BTH region was dominated by vehicle and combustion emissions, including coal burning and biomass combustion, and soil and construction dust emissions [10]. Wang et al. [11] evaluated the impacts of thermal power plants on air quality in the BTH region. These emissions contributed 38%, 23%, 23%, 24%, and 24% of CO_{2}, SO_{2}, NO_{2}, PM2.5, and PM10, respectively. Based on studies on pollution sources, Wang and Zhao [12] proposed a Joint Prevention and Control of Atmospheric Pollution program to control PM2.5 and PM10 in the BTH region. Adjustment directions for development policies to mitigate environment pollution: Zhang et al. [13] proposed a vulnerability assessment method of atmospheric environment associated with human impact to identify and prioritize the undesirable environmental changes. Decision makers can make appropriate development policies based on the vulnerable results. Fang et al. [14] applied Gini coefficient and Technique for Order Preference by Similarity to an Ideal Solution to measure the performance of collaborative development in the BTH region. They proposed that optimizing investment structures and establishing an ecological compensation mechanism contribute to smooth collaborative development. These studies offer useful suggestions to guide economic development and/or pollution mitigation, but fail to draw policy implications based on descriptions of the general relationship between economy and environment in terms of coupling degree and driving factor. The goals of this research are measuring and fitting the coupling relationship between socioeconomy and environment in the BTH region. Based on the empirical results, some policy implications are offered to prompt the sustainable development.

In 1955, Kuznets [15] proposed a hypothesis that the relationship between various indicators of income inequality and economic development presents an inverted -shaped curve. In the early 1990s, this inverted -shaped curve was used by Grossman and Krueger [16, 17] to fit the relationship between economic growth and environmental pollution. It was later named Environmental Kuznets Curve (EKC) by Panayotou [18]. In the next two decades, the EKC analysis was widely used in many countries and regions [19, 20]. However, when used in these studies, the EKC has two limitations. For one thing, the EKC needs only one indicator to reflect economic growth and one indicator to measure environmental pollution. However, both economic growth and environmental pollution are very complex, and it is difficult to select one indicator to represent each of them. For example, the economic development of China manifests not only as scale expansion but also as structure upgrade. Obviously, both aspects have impacts on environmental pollution, and using one indicator (e.g., GDP output) in EKC analysis is hence improper. For another, as a developing country, China also has unstable economic and environmental policies. Thus, EKC presents different shapes in China for different indicators and time spans. Some studies supported the inverted shape [21–23], but others recommended different figures [24, 25]. The best fitting equation for the EKC in China is difficult to ascertain, especially in the short term.

In this research, a multi-indicator system and an entropy weight evaluation method were used to evaluate the socioeconomic development and environmental pollution levels. Derived from the entropy information theory, this method ascertains the weight of an indicator is based on its information scale. This idea can ensure that the obtained weights have the maximum differentiation ability to the evaluation objects [26]. It is especially suitable for the situations that the importance of the evaluation indicator is close, just as the evaluation issue of this research. To precisely fit the relationship between the above two levels, a coupling coordination degree model and a polynomial equation that has the ability to fit a variety of trends were used. Furthermore, the partial least squares (PLS) algorithm was used to estimate the parameters of the multivariate equation. Compared with the traditional ordinary least squares (OLS) algorithm, the PLS can obtain more stable parameters using small samples.

The remainder of this paper is organized as follows. Section 2 illustrates the methodology and data used in this research. Section 3 lists the modelling results, and Section 4 discusses them. Section 5 concludes the research and offers policy implications.

#### 2. Methods and Data

##### 2.1. Coupling Coordination Degree Model

To measure the coupling coordination degree of the socioeconomic development and environmental pollution, the scores of the above two indicators should be calculated first by the entropy weight evaluation method. The modelling process of the entropy weight evaluation method is introduced as follows.

Supposing indicators are used to evaluate objects, and is the static of the th indicator in the th object, the preprocessing step to the indicator statistics is

The algorithm of (1) can eliminate the impacts of the static units to the evaluation results. Based on the pre-processing results, the information entropy of the th indicator is a measure of its chaos situation, calculated by

Obviously, . The more information th indicator has, the larger is. Based on the information entropy, the evaluation weight of the th indicator is obtained by

Then, the evaluation result (score) of the th object is

Supposing and are evaluation scores of socioeconomic development and environmental pollution, respectively, the coupling coordination degree is as follows [27]:where and ; *α* and *β* denote the contributions of socio-economic development and environmental pollution to the comprehensive system, respectively.

The difference of and identifies the lagging factor. For example, implies that socioeconomic development is ahead of environment pollution.

##### 2.2. Polynomial Fitting Equation

The polynomial equation is written as follows:where refers to time; is explained variable; and – are regression parameters.

The Weierstrass approximation theorem has proven that any continuous function can be uniformly approximated by (6) [28].

The specific form (number of independent variables) of (6) is determined by the following akaike information criterion (*AIC*) and schwarz criterion (*SC*).where is the sample number used for parameter estimation;* RSS* is the residual sum of squares.

The above two criteria have similar function. The lower their values are, the better the equation is.

Considering the equation structure of (6), the multicollinearity phenomenon may well exist between the explanatory items. Moreover, the smaller sample size can increase the multicollinearity extent [29]. If the traditional OLS algorithm is used to estimate the parameters of (6), unstable estimations are obtained. The following PLS algorithm can obtain stable regression parameters in the abovementioned environment [30].

Let and the following preprocessing process is essential:

The first component can be extracted by the following:where and .

Let and be the residual vector (matrix) of and explained by , respectively, and replace and with and in (12); the second component () is then extracted. Using a similar algorithm, more components can also be obtained.

The number of extracted components must be proper because too many components will introduce stochastic information into the final equation. In general, as the first component () represents the most important quantity relationship between the explained and the explanatory variables, it should be directly introduced into the final equation. Beginning with the second component (), the importance of extracted components should be tested one by one. Reserving or abandoning a component is decided by the following cross efficiency indicator [31].

When testing the importance of the component, a fitting equation using the first components and -1 samples (the sample is excluded) is estimated, and the fitting result of this equation to the sample is written as . Moreover, a fitting equation using the first -1 components and all samples is also estimated, and the fitting result of this equation to the sample is written as . Using the two abovementioned fitting results, the cross efficiency of the exponent is measured by

In (13), a small implies that the first components have contained the useful information and a large means the first -1 components are not sufficient. According to the statistic experience, for the exponent, implies that the importance of this component is notable and it should be reserved. Otherwise, it should be abandoned. As the importance of variables decreases one by one and if the component is abandoned, there is no need to test the importance of the next component (abandoned directly). However, if the component is reserved, the importance of the next component should be tested until the first abandoned component appears. As the process of component extraction is efficient in gathering useful information, the number of reserved components usually does not exceed three.

Supposing components are reserved, an equation between and the components can be obtained by the OLS algorithm, as follows:

Using the inverse calculation of the preprocessing and component extracting processes, the linear regression equation of to can be obtained from (14).

##### 2.3. Data Selection

In this research, we selected five indicators to evaluate the socioeconomic development and environmental pollution levels, respectively, as shown in Table 1. These indicators cover most aspects of socioeconomic development and environmental pollution. To facilitate the follow-up analysis, a code was assigned to each indicator.