Applied Mathematics and Nonlinear Sciences (Aop) (Aop) 1–17

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Applied Mathematics and Nonlinear Sciences (aop) (aop) 1–17

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A comprehensive evaluation of county economies in the Beijing-Tianjin-Hebei Re- gion based on entropy TOPSIS analysis

Lu Sen, Zhang Yang, Zhang Caihong†, Wu Chengliang

Beijing Forestry University, Beijing 100083, P.R. China

Submission Info Communicated by Juan Luis García Guirao Received February 7th 2021 Accepted March 25th 2021 Available online May 25th 2021

Abstract Although the economy of a county that is linked to surrounding towns and rural areas constitutes a multiple basic economic unit within China’s national economy, it usually exhibits independent characteristics and functions. Consequently, a county’s economy plays a critical role in the overall economic development of a country’s national economy. We created an evaluation index system based on entropy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to carry out a comprehensive evaluation of county economy across the entire Beijing-Tianjin-Hebei region. We found serious imbalances in the development of these counties, with county economies within Beijing and Tianjin being more advanced than those in Hebei Province. Furthermore, there were marked differences between county economies within prefecture- level cities of Hebei Province. The developmental level of counties in cities like Langfang, Tangshan and Chengde was relatively high. Conversely, the level of development of counties in Hengshui, Baoding, Xingtai and Handan was lower. Moreover, there were imbalances among cities in relation to county economic development, especially in Langfang, with smaller differences being found in Hengshui and Qinhuangdao. We analysed and identiﬁed the factors inﬂuencing differences between counties before providing recommendations.

Keywords: county economy, Beijing-Tianjin-Hebei region, entropy method, TOPSIS

1 Introduction

The strategic location of the Beijing-Tianjin-Hebei region of China is of particular importance. The eastern portion of this region is located adjacent to the Bohai Sea, while the western portion is linked to the interior and the northern part borders the old industrial base in the northeast. Efforts to promote coordinated development of the region primarily aim to resolve the challenges facing Beijing’s urban regions. Other aims have included easing core non-capital functions to adjust and optimise the region’s urban layout and industrial structure [23], expanding the region’s environmental capacity, and promoting the sharing of public services [11,23]. At the end of 2015, the total permanent population of the Beijing-Tianjin-Hebei region was approximately 111 million, of

†Email address: [email protected]

ISSN 2444-8656 doi:10.2478/amns.2021.2.00014 Open Access. © 2021 Sen et al., published by Sciendo. This work is licensed under the Creative Commons Attribution alone 4.0 License. 2 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17 which the urban and rural populations, respectively, accounted for 67.48 million and 43.44 million. According to data published in the National Bureau of Statistics of China of 2016, the region’s gross domestic product (GDP) reached 6.94 trillion yuan, with machinery manufacturing, digital information technology, raw materials, logistics, and transportation constituting its main industries. Most of the country’s major high-tech industries and industrial bases are located in this region, with its three component sub-regions–Beijing, Tianjin, and Hebei- evidencing differences in their industrial structures, as depicted in Figure1. In 2015, the value of the output of Beijing’s primary industry accounted for <1% of the local GDP, and that of Tianjin accounted for 1.26%, while the output of Hebei Province was more than one-tenth of the GDP, at 11.54%. As Figure1 shows, the proportion of Beijing’s secondary industry was just under 20% in 2015, while Tianjin’s and Hebei’s secondary industries accounted for =∼50% of the GDP. Remarkably, the value of the output of Beijing’s tertiary industry accounted for the highest proportion of this sub-region’s total industry, at 79.65%, while the proportions of tertiary industry in Tianjin and Hebei Province in relation to the total industries in these sub-regions were 52.16% and 40.19%, respectively. Figure1 reveals that whereas tertiary industry was Beijing’s main industry type, Tianjin’s main industry types comprised a combination of secondary and tertiary industries. The primary industry in Hebei Province was more productive than the primary industries in Beijing and Tianjin, and the proportion of the other two industries accounted for =∼90%. The land area of the Beijing-Tianjin-Hebei region accounts for 2.3% of China’s total land area and supports 8% of the country’s entire population. Moreover, this land area contributes to 10.12% of the total value of China’s economy.

Fig. 1 The proportions of the industries in the sub-regions of Beijing, Tianjin and Hebei Province in 2015.

Consequent to signiﬁcant internal disparities existing within the overall economic development structure of the Beijing-Tianjin-Hebei region, a number of issues need to be solved. These issues relate to the fast pace of population growth in Beijing, limited resources and environmental carrying capacities and their deterioration, marked differences in development within the region, inappropriate functional layouts and imbalanced urban and rural structures. Each city and county within the region exhibits a polarised state of development, and there are notable disparities between the levels of economic development and ecological environment in every region. Given its mediating role between urban and rural economic development, a county is a fundamental unit of the national economy and it is therefore inﬂuenced by the state of economic development characterising the nation as a whole and by urban and rural development strategies. Promoting coordinated development between counties in this region is perceptibly advantageous. Consequently, the question of how to coordinate the relationship between regional economic development and social development has been widely discussed within academic circles and within local governments. Evaluation of county economies by entropy TOPSIS analysis 3

2 Literature review

Following the implementation of the reform and opening-up policy in the 1980s, China’s economy has grown rapidly. However, there has been a concurrent increase in gaps and disparities between regions, with the eastern, southern, and northeastern regions being more developed than the western region. In the 1990s, most discussions on regional economic differences occurred at the national level and focused on East-West, North- South, and coastal areas-inland differences [37]. Foreign scholars have used state-of-the-art research methods to investigate regional economic differences within China, and their studies provide useful references for domestic scholars. Rozelle’s decomposition of the Gini coefficient for the period 1984–1989 indicated that economic disparities between the eastern coastal provinces were rapidly expanding, mainly because of advancing rural industrialisation [16]. In 2002, county economies became national strategies aimed at economic reform, gradually evolving into a key research topic within the disciplines of Economics and Economic Geography. According to a clear administrative system, China has a total of 1,470 counties – excluding county-level cities and autonomous counties – comprising one component of the Chinese national economy. The total area of all of the counties exceeds 90% of China’s entire territory (excluding the marine area), and more than 70% of the total population resides in counties, contributing more than 50% of the total GDP. Therefore, ensuring healthy economic development of counties is critical for sustaining efficient development of the country as a whole [7]. Development of county economies entails availing of the economic advantages of individual counties and carrying out appropriate planning [25]. Existing studies about county economies mainly focused on eastern coastal areas and central regions: Henan Province [31], Hubei Province [29], and Anhui Province [27]. Studies that focused on western regions included those that concentrated their effort on the following regions: Shanxi Province [40], Gansu Province [6], Inner Mongolia [27] and the Xinjiang Autonomous Region [7]. There were a few studies on county economies in southwestern provinces such as Yunnan and Guangxi [3]. Foreign scholars have conducted some research on county-level differences within China. For example, Lyons, Long and Ng, selected the county as the unit of analysis in their study on internal economic differences within Fujian and Jiangsu Provinces. Their results indicated that economic differences between these provinces were expanding [10]. Moreover, in recent years, the Beijing-Tianjin-Hebei region has become a popular target for research because of the emphasis on coordinated development and strategic planning in this region. However, most of the existing research has focused on the provincial or municipal scale, there being a dearth of studies undertaken at the county level. An exception is Cui et al., who evaluated the industrial economies of counties in Hebei Province [1, 17]. Currently, two types of research methods were used in evaluations of the economic development of counties: the single index evaluation method and the comprehensive index evaluation method. Single index evaluation methods included the Gini coefficient, the coefficient of variation, the Theil index ( [13, 34]), the standard deviation method, the separation ratio method, the weighted coefficient of variation, the Wolfson index and the Cui Wang index [15,27]. Comprehensive index evaluation methods include the principal factor analysis, the analytic hierarchy process [7], the Delphi method [33], the catastrophe progression method [32], Grey relational analysis [5] and clustering analysis [12]. Wang observed that although data collection on GDP indicators was easy to implement and enabled continuous vertical comparison, this method only revealed the sum of the value of a variety of products and services during a particular time period and did not fully represent the level of comprehensive development within a region [22]. Xie also noted the limitations of using only GDP to evaluate county-level economic development and construction, arguing that this would lead to blind pursuit of GDP growth while ignoring other important indicators. Usage of exclusively GDP would be detrimental to the transformation of the mode of development, according to Xie et al. [28]. Among the comprehensive index methods, the analytic hierarchy process and Delphi methods are used frequently. However, weighting indicators used in these two methods are subjective, since they are lacking in objectivity. Although factor analysis can extract the main indicators from a number of indicators quickly, the downside of this process is insufficient information and the requirement of a greater number of indicators, as well 4 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17 as a greater amount of information loss [2]. The catastrophe progression method, which combines the analytic hierarchy process and the fuzzy evaluation method, entails a mix of qualitative and quantitative indicators that are based on the relative importance of the index. Specialists are not required for the weighting of indicators, since weights are obtained automatically according to potential functions. However, because of a defect in the potential function, the number of indicators cannot exceed four. Thus, this method is evidently not appropriate for evaluating an index system [19, 21]. In general, Grey relational analysis and clustering analysis are based on AHP or factor analysis, either of which are post-analysis methods [8]. The level of independence of these two analytical methods is too poor and too subjective to facilitate determination of the objective weight of the index. Based on the latest research results, the entropy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method will be used in this study. Through deployment of this method, the present study aims to objectively evaluate levels of social and economic development in 118 counties located in Beijing, Tianjin and Hebei Province, during the period 2001-2015.

3 Methodology

3.1 Detail of study area

The Beijing-Tianjin-Hebei region encompasses two municipalities (Beijing and Tianjin) and one province (Hebei), covering a total area of 216,000 square kilometres. By the end of 2014, there were 14 municipal districts and 2 counties located in Beijing and 13 municipal districts and 3 counties located in Tianjin. The administrative division of Hebei Province is more complex, with 11 prefecture-level cities, 39 municipal districts, 20 county- level cities, 107 counties and 6 autonomous counties. There are 118 counties (including autonomous counties but excluding county-level cities) within the entire region. These counties collectively generate 8,452.95 billion yuan or 12.77% of the region’s total GDP. GDP per capita varies signiﬁcantly across these counties. For example, whereas GDP per capita for Quyang in Baoding is as low as 11,200 yuan, that of Tianjin Ninghe County is over 10 times higher at 127,500 yuan. Qinaxian County has the highest GDP per capita (106,500 yuan) within Hebei Province. An examination of values of GDP per capita both at the provincial level and between provinces revealed signiﬁcant disparities and imbalances in the levels of economic development characterising these provinces. Based on available data, a comparative study will be carried out on counties within this region, including Yanqing, Miyun, Ninghe, Jinghai, Ji and 113 counties within Hebei Province. Although some of the counties have renamed as districts, the administrative area remains unchanged.

3.2 Indicator system and data source

Consequent to the diversity and complexity of factors used to evaluate county economies, different but sim- ilar selections of factors have featured in various studies. In a county-level evaluation of coordination efforts relating to socioeconomic development and the environment in Hunan, Xiongying constructed an economic subsystem based on two criteria layers: economic scale and the economic structure. Specific indicators used for this study were GDP per capita, the GDP growth rate, local government revenues per capita, the proportion of non-agricultural industry to the GDP, the proportion of the total investment of fixed assets to the GDP and the proportion of government revenue to the GDP. The social subsystems included the following four criteria layers for population-related indicators: quality of life, science and education, culture and health and infrastructure. Specific indicators used for this study were population density, the natural population growth rate, per capita farmers’ net income, per capita disposable income of urban residents, Engel’s coefficient, number of secondary school teachers per million residents, per capita comprehensive energy consumption, per capita post and telecommunications and business income [30]. In a comprehensive evaluation of county economies in the city of Chongqing, Du Ting used three criteria layers: economic strength, investment consumption and the level of individual wealth. The following 13 indicators were selected for this study: GDP per capita, GDP density, local government budgetary revenues per capita, the output values of secondary and tertiary industries, the proportion Evaluation of county economies by entropy TOPSIS analysis 5 of the non-agricultural population, per capita total retail sales of consumer goods, per capita total investment in fixed assets, the agricultural commodity rate, the loan balance per capita, per capita savings of urban and rural residents, wages and per capita net farmers’ income [3]. Furthermore, in a study aimed at evaluating the regional economy of Jiangsu Province, Ou developed three dimensions of regional economic development: social development and the development of resources and the environment. A total of 15 indicators were selected for evaluating regional development in this study. Regional development includes two criteria layers: the economic level and the economic structure. The indicators for the economic level included GDP per capita, local government revenues per capita, total investment assets per capita, GDP density, the per capita industrial output value and other indicators. The economic structure comprised five components: the social structure, population development, infrastructures, education relating to science and technology, and quality of life. The main indicators were the proportion of employment within secondary and tertiary industries, the natural population growth rate, population growth, passenger volume per capita, per capita road length, per capita electricity consumption, per capita educational expenditure, and per capita income [18]. In a study of coordinated regional development that combined the economy and ecological environment with the tourism industry, regional economic subsystems were divided into the following three criteria layers: the total size of the economy, the economic structure, and social and economic development. A total of 12 indicators were applied: GDP, GDP per capita, local government revenues, total retail sales of consumer goods, the proportion of tertiary industry to the GDP, unem- ployment within the urban population, per capita disposable income of urban residents, per capita road area and other indicators [38].

Table 1 A comprehensive system for evaluating county-level social and economic development. Target Criteria Index Indicators layer Attributes layer layer code Per capita GDP/yuan X1 + Economic Scale Per capita local government revenue/yuan X2 + The proportion of total investment X + in ﬁxed assets to GDP /% 3 Economic The proportion of government revenue to GDP /% X4 + The proportion of total retail sales of Economic X + consumer goods to GDP/% 5 Structure The proportion of secondary and tertiary industry X + output value to GDP /% 6 The proportion of output value of primary X + industry to GDP /% 7 The proportion of industrial output X + above designated size to GDP /% 8 Population density /(per/km^2) X9 − Living Standards Per capita net income of rural residents /yuan X10 + The average wage of workers /yuan X11 + Society Number of full - time teachers in general X + secondary schools /per 12 Infrastructures Number of beds in hospital and health institutions /bed X13 + Highway mileage/Km X14 + Rural electricity consumption/ ten thousand /KW.h X15 −

An index system should be scientific and systematic. Therefore, the selection of indexes should entail equal consideration of scientific validity and regional specificity. Based on the studies mentioned in the foregoing 6 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17 paragraph, 15 indicators that strongly influenced county economies according to the criteria of economic and social development were selected. Table1 shows the index system that was developed for conducting a comprehensive evaluation of county economies. GDP per capita objectively reflected the level of regional development. Local government revenues reflected regional economic performance and the performance capacity of local governments. The proportion of local government revenue to the GDP indicator enabled economic development assessed from the perspective of government finances, which reflected the strength of the government’s revenue growth. The total investment in fixed assets referred to the amount of money invested in construction and the purchase of fixed assets and was an indicator of monetary performance. Specifically, it provided a comprehensive index of the scale, speed, proportion and direction of fixed asset investments. The total retail sales of consumer goods were an indicator of the material wealth and cultural life of the population during a particular period, thereby reflecting realisation of purchasing power in relation to social commodities. The proportions of the three types of industry in relation to the GDP reflected the extent of coordinated development of the industrial structure. Per capita economic scale referred to the overall size of per capita processing, making the results more accurate. The average wages of workers and the per capita net income of rural residents reflected the level of regional economic development and the living standards of residents. Population density indicated population sizes within the region. Education and health care were critically associated with livelihoods. The number of teachers was considered reflective of the basic educational level within a county. To a certain degree, the number of hospital beds could be considered reflective of basic medical conditions within a county. The final indicator, highway mileage, reflected the degree of traffic convenience, which is an important aspect of public infrastructure within a county. The data for this study were selected for the period 2001-2015 from the Beijing and Tianjin Statistical Yearbooks, the Hebei Economic Yearbook, the Beijing Regional Statistical Yearbook, the China County Statis- tical Yearbook and the Chinese Regional Economic Statistical Yearbook The interpolation method was used to compensate for some missing items.

3.3 Research methods: entropy TOPSIS

In this study, the entropy TOPSIS method was the primary method that was used to identify differences in levels of comprehensive economic development of counties located within the Beijing-Tianjin-Hebei region. This method is an improved version of the traditional TOPSIS evaluation method. The weight of the evaluation index was first determined using the entropy method; the TOPSIS method, entailing the approximation ideal technique, was subsequently used to rank the evaluation objects [3]. The entropy method is based on information acquired using each evaluation index that objectively determines its weight as the entropy of the weight. This method not only objectively reflects the importance of an index within the index system but also reveals the weight of the index over time; this advantage is particularly appropriate for evaluations of county economies. The TOPSIS method aims at defining the best and worst solution distance for the problem requiring a decision. The final step entails calculation of the relative progress of each scheme and the ideal solution. The application of the TOPSIS method is important for determining the weights of indexes, while the information entropy method enables elimination of the impacts of subjective factors. The main calculation steps of the entropy TOPSIS method are described below [3, 35, 36, 38, 41]. Assuming that the evaluation object has m, and each evaluation object entails evaluation index n, an evaluation matrix is displayed as follows: X = (x ) (1) i j m×n Standardised processing: Xi j − minXi j Positive indicators: yi j = (2) maxXi j − minXi j

maxXi j − Xi j Negative indicators: yi j = (3) maxXi j − minXi j Evaluation of county economies by entropy TOPSIS analysis 7 where the maximum and minimum values of the evaluation sample values are maxi j and mini j of the j-th index, respectively. Since the entropy calculation applies the natural logarithm, the index value must be positive. Thus:

ui j = yi j + d (4) where d has a positive value, resulting in yi j being slightly above zero. This leads to the creation of a standardised matrix:

U = (ui j)m×n Calculating the weight of each index: The ﬁrst step entails obtaining pi j, which is the proportion of the index of the i-th sample under item j.

ui j pi j = m (5) ∑ ui j i=1

Next, the entropy of the j-th indicator will be calculated as follows:

m e j = −k × ∑ pi j × ln(pi j) (6) i=1

1 In the above formula, the constant k is related to the number m of the indicator system. If k = lnm at a particular point in time, then 0 ≤ e ≤ 1. The following equation is used to calculate the utility value of the indicator:

d j = 1 − e j (7)

The larger the value of d j for the index, the greater its weight will be. The ﬁrst j index weight is obtained as follows: d j w j = n (8) ∑ d j j=1

n where w j ∈ [0,1] and ∑ j=1 w j = 1. Calculating the weighting matrix:

R = (ri j)m×n , ri j = w j × ui j (i = 1,2,...m; j = 1,2,...n) (9)

+ − The following equation is used to obtain the best solution (S j ) and the worst solution (S j ), as follows:

+ − S j = max(r1 j,r2 j,...rn j),S j = min(r1 j,r2 j,...rn j) (10)

The following equation is used to calculate the Euclidean distance between the schemes and the optimal and worst solutions: s n 2 s n 2 + + − − Sepi = ∑ S j − ri j ,Sepi = ∑ S j − ri j (11) j=1 j=1 Finally, the comprehensive evaluation scores are calculated as follows:

− Sepi Ci = + − (12) Sepi + Sepi 8 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17

4 Results

The evaluation matrix for assessing the economies of 118 counties formed using the index system is shown in Table1. For the period 2001-2015, the entropy weight of each index was calculated using Eqs (1)-(8). These results are displayed in Table2. Applying equations (9)-(12), the Euclidean distance of the 118th county and + − the best solution (Sepi ) and worst solution (Sepi ) were calculated to obtain the order of the best solution. The scores were sorted and the ranking dynamics were calculated based on changes in ranking over a period of 15 years (Table3).

Table 2 The best solution, worst solution, entropy, and weight of each index. + − + − Index 2001S j 2001S j 2001e j 2001w j 2015S j 2015S j 2015e j 2015w j X1 0.0033 0.0000 0.9530 0.1002 0.00644 0.0000 0.9238 0.1240 X2 0.0029 0.0000 0.9630 0.0790 0.01308 0.0000 0.8880 0.1821 X3 0.0013 0.0000 0.9753 0.0527 0.00108 0.0000 0.9706 0.0479 X4 0.0009 0.0000 0.9837 0.0348 0.00648 0.0000 0.9232 0.1250 X5 0.0009 0.0000 0.9817 0.0390 0.00030 0.0000 0.9884 0.0188 X6 0.0010 0.0000 0.9738 0.0560 0.00036 0.0000 0.9843 0.0255 X7 0.0009 0.0000 0.9759 0.0515 0.00110 0.0000 0.9679 0.0522 X8 0.0061 0.0000 0.9468 0.1136 0.00156 0.0000 0.9657 0.0558 X9 0.0007 0.0000 0.9774 0.0483 0.00047 0.0000 0.9792 0.0338 X10 0.0011 0.0000 0.9725 0.0586 0.00175 0.0000 0.9561 0.0714 X11 0.0017 0.0000 0.9733 0.0570 0.00187 0.0000 0.9618 0.0621 X12 0.0019 0.0000 0.9664 0.0717 0.00224 0.0000 0.9587 0.0672 X13 0.0039 0.0000 0.9522 0.1020 0.00136 0.0000 0.9658 0.0556 X14 0.0038 0.0000 0.9414 0.1249 0.00166 0.0000 0.9568 0.0703 X15 0.0001 0.0000 0.9950 0.0107 0.00008 0.0000 0.9948 0.0084 − Note: The results were rounded off to four decimal places. S j = 0.0000 did not indicate a value of zero, because when the value was close to the minimum value, this resulted in a small number of ﬁnal weighted total values.

4.1 Analysis of the weight of the comprehensive evaluation index of county economies

Table2 shows that the difference between the best and worst solutions in the index layer was large. This indicated that a higher degree of variation corresponded to a lower entropy. A lower entropy value indicated that a greater amount of useful information for decision making provided by the indicator corresponded to a greater weight of the indicator. If the entropy of the index is greater, then the entropy will be lower. For the index weight, three indicators of entropy, namely GDP per capita, local government revenues per capita and the proportion of government revenue to the GDP exceeded 0.1. The weights of the following indicators exceeded 0.01 but remained below 0.1:the proportion of total investments in fixed assets to the GDP, the proportion of total retail sales of consumer goods to the GDP, the proportion of the output values of secondary and tertiary industries to the GDP, the proportion of primary industry to the GDP, the proportion of industrial output above a designated size to the GDP, the population density, the net income of rural residents per capita, the average wage of workers, the number of full-time teachers in general secondary schools, the number of beds in hospitals and healthcare institutions and highway mileage. Based on the weight values of these indicators, it was ascertained that the economic scale and economic structure in the regional socioeconomic competitiveness accounted for the largest weight. Followed by people’s living standards and infrastructure, the smaller weight–which also showed that the main force of economic competitiveness of the county was the total economy and economic structure as well as industrial distribution–was the primary potential factor of regional economic development, and infrastructure Evaluation of county economies by entropy TOPSIS analysis 9 was the inevitable product of county economic development. During the period 2001–2015, the weight of X2 increased from 0.0790 to 0.1821, while the weight of X4 increased from 0.0348 to 0.1250. The increases in entropy of these two indicators were the greatest among all of the indicators. These results indicate that the status of local government revenues is gradually rising and assuming prominence within the region’s economic development. This will constitute an important foundation for regional economic development. During the period 2001–2015, the entropy weight of the GDP per capita indicator (X1) was >0.1, indicating that the region’s economic strength associated with socioeconomic development has remained a priority. The living standards of the population are subject to constraints relating to the economic scale and structure, which are consistent with the actual situation. Of the assessed indicators, there was a marked reduction in the weight of highway mileage (X14) from 0.1249 to 0.0743 during the period 2001–20155; an explanation for this fact can be obtained from an examination of China’s actual development trajectory during this period. In 2001, China’s economy was still underdeveloped, and county economies were lagging behind. At that time, a developed transportation network was the first prerequisite for developing the regional economy. Therefore, the weight of highway mileage in 2001 was greater than that of other indicators. By 2015, China’s overall level of economic development had advanced considerably compared to the level in 2001, and most of the regional transport network is now highly developed, especially in the Beijing-Tianjin-Hebei region. Consequently, in 2015, the highway mileage indicator was not a decisive factor affecting the region’s economic development. In addition, the proportion of industrial outputs above a designated size in relation to the GDP also dropped from 0.1136 to 0.0558, and industrial economic benefits have weakened.

4.2 Comprehensive evaluation of county economies

Based on the analysis of entropy weight, the TOPSIS method was applied to calculate the comprehensive socioeconomic scores (Ci) of counties in the Beijing-Tianjin-Hebei region. The relevant results are available in Table3. Optimal results reﬂected on an increased distance between the county and the best solution and a reduced distance between the county and the worst solution. The results indicated imbalanced socioeconomic development of counties in Beijing, Tianjin and Hebei and growing disparities within the region.

Table 3 Scores and ranking of the 118 counties in the Beijing-Tianjin-Hebei region.

Ranking Ranking Ranking Ranking Ranking Ranking County C in County C in County C in i change i change i change 2015 2015 2015 Dachang 0.7409 1 12 Mengcun 0.1558 41 65 Zanhuang 0.1135 81 -17 Miyun 0.6916 2 0 Chicheng 0.1557 42 42 Lincheng 0.1134 82 -13 Jinghai 0.6577 3 -2 Xushui 0.1549 43 -23 Mancheng 0.1129 83 -43 Ninghe 0.6414 4 0 Gucheng 0.1513 44 34 Julu 0.1125 84 18 Xianghe 0.5856 5 18 Anping 0.1509 45 8 Nanhe 0.1125 85 33 Gu’an 0.4356 6 54 Qing 0.1478 46 -13 Cheng’an 0.1125 86 14 Yanqing 0.4279 7 -4 Yuanshi 0.1461 47 5 Ren 0.1123 87 29 Ji 0.3569 8 -3 Weichang 0.1415 48 -29 Yangyuan 0.1116 88 16 Qianxi 0.3276 9 13 Dongguang 0.1413 49 24 Pingxiang 0.1113 89 19 Kuancheng 0.3244 10 45 Cang 0.1412 50 -34 Nanpi 0.1084 90 7 Huailai 0.2884 11 71 Gaoyang 0.1401 51 11 Yi 0.1077 91 -53 Luan 0.2798 12 25 Huyuan 0.1395 52 55 Quzhou 0.1058 92 11 Chongli 0.2763 13 92 Longhua 0.1383 53 12 Linzhang 0.1052 93 -8 Suning 0.2697 14 54 Zhulu 0.1379 54 9 Wuqiao 0.1047 94 -1 Zhengding 0.2582 15 -6 Yu 0.1369 55 -14 Guantao 0.1039 95 -7 Luanping 0.2361 16 67 Dacheng 0.1362 56 10 Qingyuan 0.1033 96 -57 10 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17

Leting 0.2308 17 -9 Ningjin 0.1360 57 -51 Anxin 0.1030 97 -46 Luancheng 0.2252 18 11 Xuanhua 0.1345 58 19 Xingtang 0.1018 98 -55 Chengde 0.2165 19 -9 Qinglong 0.1336 59 -12 Longyao 0.1014 99 -50 Luannan 0.2096 20 4 Rongcheng 0.1332 60 19 Linxi 0.1008 100 -24 She 0.2094 21 -6 Shenze 0.1326 61 -3 Dingxing 0.1004 101 -42 Piangshan 0.1930 22 -10 Yanshan 0.1315 62 51 Wuqiang 0.0987 102 -12 Zhangbei 0.1926 23 66 Xian 0.1307 63 32 Raoyang 0.0973 103 -11 Ci 0.1923 24 32 Zhao 0.1298 64 -39 Jize 0.0972 104 -8 Pingquan 0.1920 25 1 Qinghe 0.1295 65 -54 Quayng 0.0969 105 -18 Yutian 0.1901 26 -8 Jing 0.1289 66 -24 Qiu 0.0955 106 -49 Fengning 0.1848 27 8 Kangbao 0.1287 67 44 Li 0.0953 107 -73 Laiyuan 0.1816 28 26 Haixing 0.1276 68 33 Fucheng 0.0909 108 -10 Changli 0.1814 29 -2 Huaian 0.1270 69 43 Tang 0.0900 109 -18 Xinglong 0.1810 30 -16 Lulong 0.1257 70 -9 Shunping 0.0879 110 -66 Handan 0.1760 31 19 Zaoqiang 0.1240 71 -64 Linshou 0.0867 111 -44 Funing 0.1733 32 -11 Fuping 0.1237 72 -42 Guangping 0.0865 112 -64 Xingtai 0.1708 33 -16 Feixiang 0.1213 73 36 Wangdu 0.0861 113 -19 Jingxing 0.1708 34 -6 Xiong 0.1206 74 6 Boye 0.0845 114 -4 Yongqing 0.1674 35 35 Wuyi 0.1205 75 -1 Shangyi 0.0828 115 0 Wanquan 0.1621 36 39 Damin 0.1203 76 5 Xinhe 0.0788 116 -2 Gaoyi 0.1595 37 -5 Neiqiu 0.1199 77 -5 Baixiang 0.0771 117 -18 Wen’an 0.1580 38 -7 Wei 0.1178 78 8 Guangzong 0.0655 118 -1 laishui 0.1566 39 6 Wei 0.1175 79 -8 Yongnian 0.1559 40 6 Wuji 0.1167 80 -44 Note: The results are rounded off to four decimal places, and the names of all of the counties are abbreviated. 4.2.1 More advanced county development in Beijing and Tianjin than in Hebei Province In 2015, Dachang Hui Autonomous County in the city of Langfang had the highest comprehensive evaluation score (0.7409), which was approximately ten times higher than the lowest score (0.0655) assigned to Guangzong County in the city of Xingtai. The coefficient of variation of the comprehensive evaluation score increased from 38.55% in 2001 to 71.3% in 2015, with growing disparities between counties becoming evident. Whereas the maximum value of the comprehensive evaluation score for county economies increased during the study period (2001-2015), the minimum value conversely decreased. This result indicated that the overall level of socioeconomic development of counties in the Beijing-Tianjin-Hebei region has been rising. The top-scoring counties in 2015 ranked according to the level of their economic development were, in descending order: Dachang Hui Autonomous County, Miyun, Jinghai, Ninghe, Xianghe, Gu’an, Yanqing, Jixian, Qianxi and Kuancheng Manchu Autonomous County. Among these ten highest-ranked counties, five were located in Bei- jing and Tianjin, with these counties evidencing higher levels of economic development compared with counties in Hebei Province. As Table 4 shows, the comprehensive scores of counties in Beijing and Tianjin were >0.3, with those of Miyun, Ninghe and Jinghai being >0.6. In Hebei Province, Dachang Hui Autonomous County ranked first among all 118 counties, at 0.7409, followed by Xianghe (0.5856) and Gu’an (0.4356). The scores of Qianxi and Kuancheng Manchu Autonomous County were both >0.3, whereas those of other counties were <0.3. County economic development was not good in the cities of Zhangjiakou, Baoding, Cangzhou, Hengshui, Xingtai and Handan, and an aggregation effect was evident. 4.2.2 Imbalances in the pace of county-level development A comparison of the 118 counties in the Beijing-Tianjin-Hebei region revealed that the 10 counties with the fastest pace of growth were Chongli, Huailai, Luanping, Zhangbei, Mengcun Hui Autonomous County, Guyuan, Gu’an, Suning, Yanshan and Kuancheng Manchu Autonomous County. Their rankings, based on their Evaluation of county economies by entropy TOPSIS analysis 11 comprehensive scores, rose by 92, 71, 67, 66, 65, 55, 54, 54, 51 and 45, respectively. The counties exhibiting the most rapid development were mainly located in the cities of Zhangjiakou, Langfang and Cangzhou. The 10 counties with the slowest growth were Lixian, Shunping, Qingyuan, Xingtang, Qinghe, Yixian, Ningjin and Longyao, which were mainly located in the cities of Baoding and Xingtai. Their rankings, based on their comprehensive scores, decreased to 66, 64, 64, 57, 55, 54, 53, 51 and 50, respectively. An examination of dynamic changes in the rankings based on the 2 years’ comprehensive scores revealed that the ranks of only three counties remained unchanged. These counties were Miyun, Ninghe and Shangyi. Of these counties, Miyun and Ninghe maintained their ranks within the top ten counties, Shangyi maintained its low ranking among all of the counties, 52 counties were ranked up and 63 counties was ranked down. This result indicates that development was not synchronous and that there were significant differences within the region. 4.2.3 Significant differences in the comprehensive development of counties located within cities Figure2 shows evident differences in levels of development within the 13 cities in the Beijing-Tianjin- Hebei region. Cities that showed the most significant differences in their internal development were Langfang, Zhangjiakou and Shijiazhuang, with the following composite index coefficients of variation: 63.18%, 36.28% and 32.25%, respectively. A slight increase in differences between the five counties in the Beijing-Tianjin subregion was observed in 2015, when compared with differences found in 2001. Internal differences between counties were greatest in Langfang, where Gu’an and Dachang Hui Autonomous County were significantly more developed than other counties in this city. Internal disparities between counties in Shijiazhuang and Zhangjiakou have widened at a more rapid pace, whereas they have increased only slightly in Chengde, Handan, Baoding and Tangshan compared with disparities evident in 2001. Internal differences in the cities of Qinhuangdao and Cangzhou have remained almost unchanged, whereas gaps within Hengshui and Xingtai have shown a decreasing trend.

Fig. 2 Composite index coefﬁcients of variation for cities in the Beijing-Tianjin-Hebei region.

4.2.4 An analysis of overall differences in the Beijing-Tianjin-Hebei Region As shown in Table4, the 118 counties in the Beijing-Tianjin-Hebei region were assigned to three categories based on their comprehensive scores in 2015. The following ten counties were grouped under the ﬁrst category: Dachang Hui Autonomous County, Miyun, Jinghai, Ninghe, Xianghe, Gu’an, Yanqing, Jixian, Qianxi and Kuancheng Man Autonomous County. Overall, these counties were economically strong, representing the highest tier of counties in the Beijing-Tianjin-Hebei region. Five out of the ten counties were located in Beijing and Tianjin, with four further counties in their vicinity. All of these counties were economically vibrant. The level of industrial competitiveness is the most important indicator of economic competitiveness and of the characteristic industries of counties that have played an integral role in their development. Counties can only sustain their competitive advantages when supporting factors relating to production are enhanced within an enduring development process. The region’s GDP per 12 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17

Table 4 An analysis of overall differences in the Bejing-Tianjin-Hebei region. Category County Evaluation 0.3 ≤ Ci Dachang Hui Autonomous County, Miyun, Jinghai, The higher overall county Ninghe, Xianghe, Gu’an, Yanqing, Jixian, Qianxi, economic development level Kuancheng Manchu Autonomous County

0.15 < Ci ≤ 0.3 Huailai, Luanxian, Chongli, Suning, Zhengding, The middle overall county Luanping, Laoting, Luancheng, Chengde and so on economic development level

Ci ≤ 0.15 Qingxian, Yuanshi, Weichang Meng&Man Au- The lower overall county tonomous County, Dongguang, Cangxian, Gaoyang, economic development level Huyuan, Longhua, Zhulu, Yuxian and so on capita directly reflects the overall level of economic development of its counties. As shown in Figure3, the average GDP per capita for counties assigned to the first category was 66,991 yuan, whereas these figures for counties belonging to the two other categories were 34,857 yuan and 21,155 yuan, respectively. The average value of the first type of area was significantly higher than that of the other two types of areas. Changes in the values of local per capita revenues and differences within the region were aligned, with higher per capita local revenues corresponding to more economically developed counties. The per capita revenue for counties belonging to the first category was 6,639 yuan, whereas this value for counties belonging to the third category was significantly lower at 1,000 yuan. Figure4 shows that the proportion of financial revenue to the GDP was positively related to the degree of regional development. A stronger growth point of government revenue corresponded to a higher economic level at the scale of the county. In the areas of investment and consumption, there were no significant differences in total investments in fixed assets for the three sub-regions. A higher level of economic development in a county corresponded to a higher proportion of total retail sales of social consumer goods to the GDP, indicating the greater driving strength of residents’ consumption.

Note: The data presented in the ﬁgure comprises mean values for the three categories.

Fig. 3 A comparison of the scale of per capita county economies relating to the three categories.

Huailai, Luanxian and 35 other counties characterised by middle-level economic development belong to the second category. These counties evidenced relatively high GDPs, and, overall, their economies were strong. Their levels of economic development were constrained by factors such as population, industrial structure and constraints relating to financial investments. Generally, the populations of these counties were significantly larger than other counties. These large populations were incommensurate with existing levels of urbanisation in these counties, which inevitably impacted negatively on their economic development. Figure5 shows that counties where primary industry was developed and secondary industry was underdeveloped were usually relatively backward in terms of economic development. Secondary and tertiary industrial development evidently played an important role in the economic development of counties. However, there were no significant differences Evaluation of county economies by entropy TOPSIS analysis 13

Note: The data presented in the ﬁgure comprises mean values for the three categories.

Fig. 4 A comparison of investment and consumption in counties across the three categories. in average levels of the proportion of industrial outputs above the designated size to the GDP among counties belonging to the three categories. At the microscale, there were signiﬁcant differences between counties in the sub-regions. Counties with developed industrial economies tended to evidence a higher overall level of development. These counties included Jinghai in Tianjin and Qianxi in the city of Tangshan. Therefore, although the total economic outputs of these counties had reached a certain scale, there were still gaps in relation to counties belonging to the ﬁrst category.

Note: The data presented in the ﬁgure comprises mean values for the three categories.

Fig. 5 A comparison of the industrial structures of counties across the three categories.

The third category included Qingxian, Yuanshi and 73 other counties. The level of industrialisation in these counties was lower compared to those counties in other categories, and traditional agriculture still accounted for a large proportion of the GDP. Consequently, the industrial structure required optimisation in these counties, since they have low potential for economic development and comprise relatively poorer areas within the Beijing- Tianjin-Hebei region. Figure6 shows that the population distribution within these counties was concentrated, and per capita net incomes of rural residents and average wages of workers were lower than they were in counties belonging to the ﬁrst two categories. Education and health care also require improvement in these counties. Figure7 shows that educational and medical indicators declined in counties across all three categories. An examination of rural residents’ electricity consumption revealed that the developed counties tended to consume more resources than other counties. 14 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17

Note: The data presented in the ﬁgure comprises mean values for the three categories.

Fig. 6 A comparison of life quality of county populations across the three categories.

Note: The data presented in the ﬁgure comprises mean values for the three categories.

Fig. 7 A comparison of infrastructure for counties across the three categories.

5 Discussion and Conclusions

There were significant differences in levels of economic development of counties located in the Beijing- Tianjin area and in Hebei Province. The overall level of economic development of counties in Hebei Province lagged behind that of counties in the Beijing-Tianjin subregion. The development of counties within cities in Hebei Province was also imbalanced, and the economic levels of these counties were either high or low. Ad- jacent counties also affected each other’s economic development. Thus, when formulating policies to promote the economic development of counties located in the Beijing-Tianjin-Hebei region, governments should fully consider interrelated influences of counties and design mechanisms to foster collaborative development as well as labour division and cooperation at the level of prefecture-level cities. In some areas, significant differences between counties may promote region-specific functional divisions of county economies, and the strategies developed should therefore be consistent with local conditions. At the same time, policymakers should strive to balance differences between theory and reality. For example, industrialisation has had a significant effect on the economic growth of some counties in Zhangjiakou Chengde. Many counties within this region contain prohib- ited and restricted areas associated with ecological conservation. Thus, industrial development projects should be scientific to achieve the joint objectives of economic development and ecological conservation. Specific recommendations pertaining to the "13th five-year plan" period for counties in the Beijing-Tianjin-Hebei region are the following. The industrial structure requires adjustment. Secondary and tertiary industries are predominant in counties located in Beijing and Tianjin, and the proportion of primary industry is very small. By contrast, most counties located in Hebei Province are still traditional agricultural areas, and an inappropriate structure relating to the layout of their industries and leading to an industrial agglomeration effect is not apparent, making optimal upgradation difficult to implement. More specifically, counties in the cities of Qinhuangdao and Tangshan are the most industrially advanced in the country. They exhibit high levels of industrial agglomeration and Evaluation of county economies by entropy TOPSIS analysis 15 superior urban infrastructure as well as intensive industrial towns. Those “dual-core" and “multi-core" counties should continue to promote industrial development and since they are attracting a growing influx of people, the inflow of people into these counties results in population concentration and a benign circle. Levels of industrial development are comparably lower in the cities of Baoding, Shijiazhuang, Cangzhou and Hengshui than they are in Qinhuangdao and Tangshan, which feature scattered industrial layouts. Generally, only some counties and very few towns have reached the scale of concentration required for promoting the industrialisation of urbanisation. Therefore, these counties should actively connect with labour-intensive industries in the eastern cities of Hebei Province, changing functions and providing guidance to the latter on how to develop more efficient county and town clusters, absorb surplus rural labour, and accelerate the pace and scale of the land management process. Populations are smaller and there is more land and poor natural conditions in the cities of Chengde and Zhangjiakou. Production in their counties is limited by poor public infrastructure and natural conditions and by the low level of industrialisation. Consequently, absorption of labour in these counties is difficult to achieve. Thus, the developmental focus should be on the central counties, and production factors sourced from adjacent counties should accelerate infrastructure construction and adjust the industrial structure. Another recommendation is to increase food subsidies. Given the steadily declining role of grain production in the development of county economies, the government should consider providing more financial subsidies to Baoding, Xingtai, Handan, Hengshui and Cangzhou to compensate for opportunity costs in food producing areas. In addition, active efforts to design and implement an inter-provincial grain compensation mechanism are required to ensure the fulfilment of grain production targets, thereby increasing farmers’ incomes. All levels of governments that are experiencing financial constraints should develop preferential tax policies to attract non- government investments. Counties located near Beijing should avail of opportunities relating to the construction of the capital’s green circular economy, modernise traditional agricultural methods, improve production effi- ciency and realise an increase in green production and financial revenues to reduce opportunity costs of grain production in agricultural counties. Attention should focus on talented individuals and innovative technologies. The “Science and technology beneficial to county; science and education beneficial to agriculture" policy is well established, but few counties have succeeded in effectively implementing it. A major factor affecting economic disparities among counties in the Beijing-Tianjin-Hebei region entails differences in human capital. A key factor accounting for low levels of economic development is a lack of talent. It is therefore necessary to explore human resources and the rational use of talent to promote regional development. Increasing investments in education would ensure that the entire public education system within counties is fully covered. In addition, the provision of rural vocational and technical education for rural residents is a feasible option for enhancing the skills of the majority of farmers and consequently the quality of human accomplishments. In this study, the entropy TOPSIS method was used for a comprehensive evaluation of levels of socioeconomic development in counties located in the Beijing-Tianjin-Hebei region, during the period 2001-2015. The following are the two main conclusions from this study. The entropy TOPSIS method is based on information theory. Accordingly, the amount of information provided by information entropy was used to calculate the corresponding weights of the indicators used in the study. These results were then combined with the multi-objective decision-making TOPSIS method and a comprehensive evaluation of each county’s level of economic development was conducted. This method effectively avoided the subjective factor influencing the assigned weight and entailing a sophisticated projection process. The study results indicated that the weight of each indicator was not a fixed value; rather, it changed according to the degree of socioeconomic development. This was illustrated in the indicator for highway mileage, which had a greater weight in 2001 than in 2015. Consequently, a more rational approach would be to use the entropy weighting method synthetically to evaluate individual years. In an evaluation using the same index system and conducted in the same area, not only will the difference between the subjective and objective evaluation methods be evident, but the difference between objective evaluation methods will also differ. Although the entropy TOP- SIS method, unlike factor analysis, does not lead to loss of data, its validity is closely related to the index system 16 Sen et al. Applied Mathematics and Nonlinear Sciences (aop)1–17

used for an evaluation. Thus, the rationality of the index system directly determines the evaluation outcome. If an indicator within the constructed system is not particularly important, then this indicator may result in an overly high entropy value when there are significant differences in the study area. Consequently, the weight of other important indicators would be reduced, leading to results that are inconsistent with the actual situation. However, because of the use of different statistical analysis methods in this study, the evaluation results relating to the economic development of counties in the Beijing-Tianjin-Hebei region based on TOPSIS analysis differed slightly, whereas the general results were basically in agreement with those of other researchers, which was more or less consistent with the actual situation. Therefore, the analysis and evaluation results were considered appropriate. The overall finding of the study was that a lack of coordinated development of regional economies in the Beijing-Tianjin-Hebei region has led to significant differences that are especially important for achieving independent county development. Inefficient allocation of resources and a relatively slow pace of economic development of the entire region have led to an unobvious regional economic integration development trend.

Acknowledgements

This work was funded by the National Natural Science Foundation of China (Grant No. 71573019).

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