Measurement for coordinated development of "four modernizations" and its efficiency of prefecture level cities or above in China

JingHu Pan， YanXing Hu

College of Geography and Environment Science， Northwest Normal University， Lanzhou， Gansu 730070， China

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Measurement for coordinated development of "four modernizations" and its efficiency of prefecture level cities or above in China

JingHu Pan*， YanXing Hu

College of Geography and Environment Science， Northwest Normal University， Lanzhou， Gansu 730070， China

ABSTRACT

The efficient and coordinated development of industrialization， urbanization， informatization and agricultural modernization（so called "Sihua Tongbu" in China， and hereinafter referred to as "four modernizations"） is not only a practical need but also an important strategic direction of integrating urban-rural development and regional development in recent China. This paper evaluated the comprehensive， coupling and coordinated developmental indices of "four modernizations" of China's 343 prefecture-level administrative units， and calculated their efficiency of "four modernizations" in 2001 and 2011. The efficiency evaluation index system was established. The efficiencies and their changing trend during the period 2001-2011 were investigated using the data envelopment analysis （DEA） model. Spatial-temporal pattern of the efficiency of China's prefecture-level units was explored by using exploratory spatial data analysis （ESDA）. Finally， the main influencing factors were revealed with the aid of geographically weighted regression （GWR） model. Results indicate that the comprehensive， coupling and coordinated developmental indices and efficiency of "four modernizations" of China's prefecture-level administrative units have obvious spatial differences and show diverse regional patterns. Overall， the efficiency is relatively low， and only few units with small urban populations and economic scale are in DEA efficiencies. The efficiency changing trends were decreasing during 2001-2011， with a transfer of high efficiency areas from inland to eastern coastal areas. The difference between urban and rural per capita investment in fixed assets boasts the greatest influence on the efficiency.

coordinated development； four modernizations； efficiency； influencing factor； geographically weighted regression model； China

1　Introduction

Since China adopted reform and opening-up policies in 1978， economic construction and social development has become the focal point of the government， bring along at the same time the issues of urbanization， industrialization， informatization and agricultural modernization for both scholars and administrators （Chen et al.， 2013； Fang et al.， 2013； Wang et al.， 2015）. The drawbacks of urban-rural division， land partition and man-land separation are increasingly exposed （Liu et al.， 2014）， the supply shortage of education， medical and pensions is increasingly exacerbated （Bai et al.， 2014）， and the "rural disease" due to rapid urbanization becomes increasingly worsening，which comprehensively lead to the difficulty of urban-rural coordinated development and sustainable development of rural areas （Liu et al.， 2015）. In 2012，the report of the 18th National Congress of the Communist Party of China （CPC） pushed for an im-portant strategic requirement and historic task of "the promotion of integrating informatization and industrialization， the positive interaction of industrialization and urbanization， and the coordination of urbanization and agricultural modernization to boost the synchronous development of industrialization， informatization， urbanization and agricultural modernization" （so called "Sihua Tongbu" in China， and hereinafter referred to as "four modernizations"）， which acted as the new guidance for the regional development in the new era （Li et al.， 2014）. Industrialization is the core substance of modernization and will support and stimulate its development， and is also an important transformation process from traditional agricultural society to modern industrial society. Urbanization， accompanying with industrialization， is a process of population flowing into urban areas in the period of boosting industrialization， or a period of second and tertiary industries gathering together in and around cities. Informatization is a modern social civilized developed period through the revolution of high technology and the spread of knowledge and information. Agricultural modernization is a period in which people use modern productive tools to change traditional agriculture，whose development is accompanied by the development of industrialization， urbanization and informatization. From the international perspective， currently，China has entered the middle stage of industrialization and urbanization development on the whole； informatization is going through the accelerated development and expansion stage， but agricultural modernization is lagging behind. For the uneven， uncoordinated and unsustainable development and other issues existing in China's current "four modernizations"，strategic guideline for the simultaneous developments of "four modernizations" with distinct era characteristics and Chinese characteristics has been proposed in the report to the 18th National Congress of the CPC. However， it is a complex and difficult task to solve the issues of coordinated development for "four modernizations"； it is the premise and necessary preparation for promoting comprehensive， coordinated， efficient and sustainable development of "four modernizations" to correctly understand their development connotation and mutual relationships. In addition， significant regional differences exist in the economic and social development of various regions in China， and imbalanced development is also prevalent even within one province. Since the Third Plenary Session of the 18th CPC Central Committee， China's economy has entered a period of new normal （so called "Xin Changtai" in Chinese）， and the changing economic development mode and the transformation of urban-rural development are imperative （Liu et al.， 2014）. In the critical period of the current economic transition of China， it has important theoretical and practical significance for achieving scientific， comprehensive and integrated understanding of the degree of synchronization for the regional "four modernizations" to carry out objective evaluations of the level of coordinated development and spatial-temporal differentiation of the regional "four modernizations".

Informatization was enhanced to the height of national development strategy for the first time in the report to the 18th National Congress of the CPC. The literature related to the studies of "four modernizations" published by scholars was scarce， but the interactive development of industrialization， urbanization and agricultural modernization in the "four modernizations" has been the focus of attention in academic circles. From the overall perspective， the study contents of existing "four modernizations" involved among others the connotation and mechanism， evolution locus of the concept， realization path， evaluation index system and the measurement of developmental level for "four modernizations" （Qian et al.， 2012）. However， few studies concentrated on China's coordinated development and efficient measurement of the "four modernizations". The study scale was mostly provincial， and nationwide comprehensive studies based on the prefectural level and county-level administrative units were scarce.

In addition， if "four modernizations" have had a higher or lower level of coordinated development， how about their investment level， and what are the cost to achieve a high or low level of coordination？ Namely，how about the efficiency of "four modernizations" coordinated development （FMCD）？ In response， one of the objectives of this study is therefore to contribute to knowledge surrounding the urban "four modernizations" coordinated development efficiency （FMCDE）in China. Efficiency is the ratio of the total value of all goods and services to the total resource factors and investment （for example， human， material and capital resources） at a specific production and technology level （Fang et al.， 2013）. A higher input-output efficiency means a more efficient allocation of resource factors， better management and more rational utilization. Much effort has previously been dedicated to developing simulation methods for measuring efficiency. In a relatively short period， data envelopment analysis （DEA） has grown into a powerful quantitative， analytical tool for evaluating performance， which has been successfully applied to a host of different types of entities engaged in a wide variety of activities in many contexts world-wide （Assafa and Matawieb，2010）. Input-output efficiency measurement and analysis are being taken seriously as a research method in relation to cities （Morais and Camanho， 2011）. Unfortunately， the efficiency of FMCD has received much less attention amongst the research community（Li et al.， 2014）. The FMCDE was a process includingfunds， resources and technical inputs， production，conversion and output. Based on this， FMCDE can be defined as the output effect of coordinated development generated by various resource factors of "four modernizations" within a specific time （such as a year）and under certain input conditions （labor， financial and material resources）， which was used to reflect the level of coordination for the regional "four modernizations"；higher FMCDE indicated that various factor allocations of the region was more reasonable， and the resources and factor input can achieve better effect. FMCD not only can grasp the utilization efficiency and existing problems of regional resource factors in a timely manner， but also can provide a scientific basis for adjusting and optimizing the allocation and utilization of various factors for the future regional "four modernizations"， and developing effective regional development policy to study the FMCDE and its spatial-temporal pattern. However， a case study combining the FMCDE has not been reported.

The development state of FMCD and FMCDE can be rated as an important perspective to identify and discuss regional problems （Ding et al.， 2013； Li et al.，2014）. This paper aims to investigate the spatial patterns and influencing factors of FMCD and its efficiency in China at prefecture level administrative units from both exploratory and analytical perspectives， and reveal the change tendency in recent 10 years， and corresponding implications for regional polices. Firstly， a comprehensive evaluation index system will be establish to evaluate comprehensive， coupling and coordinated development of "four modernizations". Secondly， this paper proposes an input-output efficiency evaluation indicator system of the efficiency，and a DEA method is used in order to evaluate the input-output efficiency of China's prefecture level cities， based upon data drawn from 2001 and 2011. ESDA， which explores temporal and spatial changes in the coordinated development and its efficiency from an exploratory perspective， is applied to form visual spatial patterns in China. Thirdly， we explore the spatial association of efficiency with several potential determinants to examine potential spatial variations in assumed relationships between these factors and the efficiency by using GWR model.

2　Material and methods

2.1Datasets

The socio-economic data needed in this study were mainly extracted from the China City Statistical Yearbook （National Bureau of Statistics of China，2002a， 2012a）， and the China Regional Economy Statistical Yearbook （National Bureau of Statistics of China， 2002b， 2012b）. Basic geographic information data comes from the Data Center for Resources and Environmental Sciences， Chinese Academy of Sciences （http://www.resdc.cn/）. We have collected the data of 343 prefecture-level administrative units which nearly covers all of China's prefecture-level units and thus have a strong representation. These units included prefecture， prefecture-level cities， autonomous prefectures， leagues and municipalities. However， because regions such as Hong Kong， Macao， and Taiwan present special geographical and social barriers and use inconsistent statistical procedures， these cities and region were not included in the present study.

2.2Methods

2.2.1Measuring the development level of "four modernizations"

To accurately estimate the FMCD of the 343 prefecture-level units in China， this study established a comprehensive index system. Indicators listed in Table 1 were selected to construct industrial G（g），urbanization C（c）， informatization X（x） and agricultural modernization developmental indices N（n） to measure the development level of "four modernizations". The index system in this study contains four first-grade indices and 16 basic indicators. The models can be written as:

where， gi， ci， xiand nirepresent indicators which can mostly depict the state of industrialization， urbanization， informatization and agricultural modernization，respectively （all of them are dimensionless values of the original data）； αi， βi， γiand μimean the weights of corresponding indicators， calculated by Analytic Hierarchy Process （AHP） based on the Delphi method（Rushton et al.， 2014）. We standardized the data using Equations （2） and （3） in order to eliminate the influence of dimension and positive and negative orientation （Wang et al.， 2014）:

For positive indicator:

For negative indicator:

where， xijdenotes the value of indicator j in year i；is the standardized xij； max（xj） and min（xj） are the maximum and minimum values of j indicator. Thus， all the index values fall within the range ［0， 1］.

Furthermore， the comprehensive development index can be calculated by averaging the industrial， urbanization， informatization and agricultural modernization developmental indices. The formula is:

Table 1　Indicator system for assessing the development level of industrialization， urbanization，informatization and agricultural modernization

2.2.2Measuring the coupling degree of "four modernizations"

The coupling degree of "four modernizations" can be written as （Qu et al.， 2013）:

where， C is the coupling degree of "four modernizations". The value ranges between 0 and 1， and the bigger the value， the higher the coupling degree of "four modernizations". If the values of G（g）， C（c）， X（x）and N（n） are the same and not 0， C equals 1. If all of these four values are 1， the system gets to the coupling resonance state.

2.2.3Measuring the coordination degree of "four modernizations"

Nevertheless， Equation （5） can only reflect the strength of the coupling degree but not the coordinated development level. Therefore， the coordinated degree model was introduced， taking into consideration both the interaction strength among them and the comprehensive development level of industrialization， urbanization， informatization and agricultural modernization， to better evaluate the coordination degree of "four modernizations". The calculation formula is as follows （Li et al.， 2012）:

where， D is the coordinated development index of "four modernizations"， C is the coupling degree of "four modernizations" and T is the comprehensive development index of "four modernizations" in Formula （6）.

2.2.4DEA model

Suppose we have n administrative units， where each unit （DMUi， i=1， …， K） produces M outputs yim（m=1， …， M） by utilizing L inputs xil（l=1， …， L）. Here，xilis the lth input for unit i （l=1， …， L） and yim（m=1， …，M） is the mth output for unit i （m=1， …， M）. On the hypothesis that the sum of convexity， cone， and invalidity of unit n （n=1， …， K） are minimized and constant returns to scale （CRS） DEA （data envelopment analysis） model can be expressed by the following equation:

where， θ （0＜θ≤1） is the objective function's value； λj≥0 is convex coefficient； s-（s-≥0） is slack variable； s+（s+≥0） is residual variable； ε is non-Archimedean infinitesimal； êT=（1， 1， …，1）∈ELand eT=（1， 1， …，1）∈EMare m-dimensional and k-dimensional unit vector space， respectively. In this paper， we chose the per capita consumption expenditure of urban and rural residents， per capita local fiscal budget， per capita social investment in fixed assets and per capita local or foreign currency in each prefecture-level cities as inputs； the coordinated development index is the output of "four modernizations".

2.2.5Exploratory spatial data analysis (ESDA)

1） Global spatial autocorrelation—Moran's I

Moran's I is a classic measure for spatial autocorrelation. The global Moran index （GMI） is calculated as follows （Anselin， 1996）:

where， wijis the row-standardized contiguity matrix， xiis the frequency count of a certain coordinated value and its efficient value at location i， and μ is the average frequency count of this issue. This study uses a Queen contiguity weights matrix， which defines a location's neighbors as those with either a shared border or vertex， since all prefectures distribute freely and can access every place in China.

2） Local spatial autocorrelation （LISA）

To determine the location of clusters or spatial outliers， LISA is employed by applying a local Moran statistic for evaluating spatial autocorrelation at the level of every observation. LISA is calculated as follows （Anselin et al.， 2006）:

The local Moran allows us to examine the presence of local spatial patterns by classifying the local Moran statistic into four groups: high-high［HH］ and low-low［LL］ that represent local spatial clusters having similar attributes with neighbors， and high-low［HL］ and low-high［LH］ that represent local spatial outliers.

3） Hot spot analysis

In order to statistically test the morphology and intensity of the coordinated development of "four modernizations" and its efficiency， a Hot Spot Analysis（Getis-Ord Gi* statistic） with the 343 measuring studies were performed. The resultant z-scores and p-values of the Getis-Ord Gi* statistic indicate where features with either high or low values cluster spatially. The Gi* statistic returned for each feature in the dataset is a z-score（Getis and Ord， 1992）. For statistically significant positive z-scores， the larger the z-score， the more intense the clustering of high values （a hot spot）.

2.2.6Geographically weighted regression (GWR) model

GWR estimates point parameter in sequence using local weighted ordinary least squares and the weights is the distance function of the geospatial location of the regression point to the geospatial location of other observation points （Fotheringham et al.， 2002）. The formula of GWR model in our study is similar to global regression models； however， the parameters vary with spatial location （Hu et al.， 2012）:

where， （Si， Ti） denotes the coordinates of the ith location point （census tract centroid in this study） in the study area； α0（Si， Ti） is a realization of the continuous function α0（Si， Ti） at location i， εiis random error.

In this study， we chose both univariate and mixed GWR models to investigate the factors' separate and combined explanatory effects. Factors we selected should have great relevance with the efficiency（Richard et al.， 2014）. Furthermore， these factors must meet the criteria of non-collinearity and AICc （Akaike Information Criterion correction） minimization. Spatial autocorrelation of model's residuals are selected to check the significance of estimated local parameters（Hu et al.， 2012）.

3　Results

3.1Comprehensive evaluation of "four modernizations" development

3.1.1The spatial pattern of the development level of "four modernizations" and its efficiency

The comprehensive， coupling and coordinated developmental indices of "four modernizations" can be calculated based on Formulae （1） to （6）. The coordi-nated development efficiency can be calculated by Formula （7） based on the software DEAP2.1. The pattern of comprehensive， coupling and coordinated developmental indices are presented in Figure 1. The overall efficiency of the coordinated development of "four modernizations" is revealed in Figure 2.

Figure 1　Spatial pattern of comprehensive development level and coupling and coordination degrees of "four modernizations" from 2001 to 2011. Note: The inclined line is called "Hu Huanyong Line"， a "geo-demographic demarcation line" discovered by Chinese population geographer Hu Huanyong in 1935. The imaginary Heihe （in Heilongjiang）-Tengchong （in Yunnan）line divides the territory of China into two parts: northwest of the line covers 64% of the total area but only 4% of the population； however， southeast of the line covers 36% of the total area but 96% of the population

Figure 2　Spatial distribution of FMCDE from 2001 to 2011

1） Comprehensive development index: the average of comprehensive development index is 0.215 and 0.233， standard deviation is 0.087 and 0.086 in 2001 and 2011， respectively. In 2001， prefectural units with higher comprehensive indices are mainly located in northeastern China. Prefectures with lower comprehensive indices are mainly distributed in southwestern China， central China， Qinghai-Tibet Plateau and along the 'Hu Huanyong Line'. Compared with 2001， there is no essential change with the overall spatial pattern of comprehensive index in 2011.

2） Coupling development index: the average of coupling development index is 0.614 and 0.672，standard deviation is 0.143 and 0.157 in 2001 and 2011， respectively. In 2001， units with higher coupling development indices are mainly distributed in eastern coastal regions like northeastern China， Bohai Rim Region， Yangtze River Delta， Pearl River Delta. Sichuan-Shannxi border area， Chongqing， Xinjiang and several units in Inner Mongolia also have had a higher coupling development value. Prefectural units with lower value are mainly distributed in the central traditional agricultural areas， due to vast out-migration， the pace of urbanization and informatization in these areas is rather slow. Lower coupling development index areas are also distributed in Qinghai-Tibet Plateau，southwestern hilly areas， Loess Plateau and other places predominated by old liberated areas and mountainous areas. There are numerous mountains in these areas， thus restricting the development of cities and towns， and the transformation of traditional agriculture to a modernized one. Regions along with 'Hu Huanyong Line'， which have had a lower coupling index in 2001， were changed to have higher coupling index in 2011.

3） Coordinated development index: the average of coordinated development index is 0.359 and 0.391，standard deviation is 0.102 and 0.106 in 2001 and 2011， respectively. Regions with higher coordinated development indices are mainly distributed in northwestern China， Inner Mongolia， major cities in eastern coastal and Hubei-Jiangxi border areas， while the indices in southwestern China， central China and Qinghai-Tibet Plateau are much lower. The major constraints on development in these regions are the complex natural and geographical conditions and fragile ecological environment. The spatial pattern of the coordinated development was more broken and separated in 2011， compared with 2001.

In general， the comprehensive， coupling and coordinated developmental indices have obvious spatial difference and show diverse regional patterns. The comprehensive index， coupling degree， and coordinated index showing spatial differences are likely divided by the 'anti-Huhuanyong Line' from northwest to southeast. The units southwest of the 'anti-Hu huanyong Line' have a higher value of comprehensive，coupling and coordinated index， while the northeast have a much lower value.

According to the existing literature classification method （Huang et al.， 2013）， the efficiency value equals 1 for high efficiency， between 0.8 and 1 for moderate efficiency， between 0.6 and 0.8 for low efficiency， while less than 0.6 mean no efficiency. The results indicate that the average of the coordination development efficiency in Chinese 343 prefecture-level cities in 2001 and 2011 were 0.686 and 0.671， respectively. The standard variation of the efficiency decreased from 0.168 to 0.158， showing that the difference between units was reduced. Therewere only eight units， Wuhai， Suqian， Shangrao，Jingmen， Shaoyang， Liupanshui， Yushu and Yili，respectively， reaching the effective stage. These units only possessed 2.33% of the total number of research units， and they are basically distributed in western and central China except Suqian. Compared with 2001， the number of effective units increased to twelve in 2011. These twelve units are mainly located in western and central China. Prefecture-level units with no efficiency accounted for 30% of the total number of study units， representing a low level of efficiency. The spatial pattern of high efficiency are mainly distributed in central provinces of China，such as Henan， Anhui， Hubei， Hunan. These units，which possess high efficiency， hold smaller populations and economic scales. The efficiency value of the megalopolis was generally lower. For example，the efficiency of all sub-provincial cities except Xi'an was less than 0.7 in 2011. The efficiency of Beijing， Shanghai and Guangzhou were only 0.279，0.299 and 0.314， respectively， in 2011. These results reflect that the input-output ratio of the efficiency is higher in these cities， which possess a lower scale of populations and economy. This is a valuable finding，which can be explained by the fact that the gap is widening between urban and rural areas in those big cities in China. The core urban areas have better traffic conditions， mature urban development，well-developed infrastructure， efficeint social services and high-quality of life， however， the socio-economic development level of its governed counties was relatively low. It is necessary to speed up the reformation and development in rural areas，stimulate rural vitality of entrepreneurship and innovation， and promote on-site urbanization.

Compared with 2001， regions with high efficiency values gradually shifted to the eastern coastal areas，which present a more diverse spatial distribution（Figure 2）.

3.1.2Hot and cold spots in prefecture-level cities and its surroundings

This paper calculated the GMI of coordinated development index by using Geoda （Anselin et al.， 2006）in 2001 and 2011 for the coordinated development index of "four modernizations" and normal statistics Z values of the efficiency of GMI greater than 0.05 under the condition of the confidence level of the critical value of 1.96. The spatial relationship characteristics and its efficiency in the Chinese 343 prefecture-level cities are found to be as follows: the GMI of the coordinated development were 0.505 and 0.546 in 2001 and 2011， respectively， and the GMI of FMCDE were 0.463 and 0.497， respectively. This shows that coordinated development index of "four modernizations" and its efficiency presented obvious spatial autocorrelation of prefecture level cities. The GMI value showed a significantly positive tendency for Moran's I， and the units with high value of the coordinated degree and high efficiency tend to gather in space， the units with low coordinated degree and low efficiency also tend to gather in space.

On the basis of global spatial autocorrelation，this paper further detects target property in the apparent position of spatial agglomeration and regional relevance， to look for units' contribution to higher GMI values， and reveal that GMI of spatial autocorrelation can conceal the extent of local instability by using hot spot analysis. This paper calculated the Getis-Ord Gi* coefficient， which represented the regional spatial relationship between the coordinated development index and its efficiency. The result of the Getis-Ord Gi* coefficient was spatialized by GIS software. According to the numerical size of Gi* statistic of the FMCD and its efficiency， the Gi* values was divided into cold spots， secondary cold spots，secondary hot spots and hot spots by using the natural breaks classification. The spatial pattern of Gi* are presented in Figure 3 which shows that cold spots regions and hot spots regions presented the spatial structure characteristics of staggered distribution. The cold and hot spots' spatial pattern does not show substantive transformation during 10 years，only the number changes. Hot spots are mainly distributed in two parts of China. One part was in order from west to east through the northern part of Xinjiang， northwestern Gansu Province， Inner Mongolia，Jilin Province， and Heilongjiang Province， and the other part was in order from west to east through the border of Shandong Province and Hebei Province，border of Shandong， Anhui and Henan provinces. Cold spot units are basically symmetrically distributed in 'Hu Huanyong Line' on both sides. The hot spots are mainly located in the east of contiguous 'Hu Huanyong Line'， Liaodong Peninsula， Shandong Peninsula， the Yangtze River Delta， Pearl River Delta and other coastal units， scattered in the northern slope of Tianshan Mountains and other border areas. The units of hot cold spots changed significantly， mainly distributed in Guangdong.

The cold spots and hot spots are presented in a spatially staggered distribution. The distribution pattern has changed drastically during the last 10 years， compared with the cold spots and hot spots. In general， the hot spots were the most concentrated and stable， mainly located in central provinces of Henan， Anhui and Hunan in 2001 and 2011. The cold spots of Fujian，Guangdong， Guangxi and Hainan provinces formerly changed into secondary hotspots， which showed that the efficiency has improved. The reduction number of cold spots areas was the most dramatic.

Figure 3　Hot spot evolution of FMCD and its efficiency from 2001 to 2011

3.1.3The spatial correlation between the coordinated development index and its efficiency

This paper analyzed the spatial mutual influential relationship， which represents the coordination development index of "four modernizations" in one certain prefecture-level unit and the efficiency in the surrounded prefecture-level units by using local spatial correlation method of double variables. LISA and its significance （p=0.05） of both the coordinated development index and efficiency between 2001 and 2011 were calculated and presented on the cluster map （Figure 4）. In the period of 2001-2011， the FMCD and its efficiency showed an obvious pattern of spatial heterogeneity at the 0.05 significance level. Four types of spatial patterns can be classified using local Moran statistic: （1） High-High， where the unit and surrounding units have a higher FMCDE value，which are the significantly positive correlation units. There were six units of this type in 2001. The spatial malposition distribution of these units in two periods illustrates the frequent change of famous areas in 10 year time. （2） Low-Low， which has a notably positive correlation level， its efficiency is low and its surrounding areas also have relatively low FMCD indices. There were 26 units in 2001， while the number was reduced to 23 units in 2011. The spatial distribution of Type 'LL' did not change in the course of the study period. They were mainly located on the border of Shaanxi， Gansu and Ningxia， and scattered distribution in Guizhou，Sichuan， Chongqing and Yunnan provinces. These districts need to accelerate the coordinated development and improve its efficiency. （3） Low-High， with strongly negative spatial correlation level units. The region has low efficiency， while its surrounding units have higher coordination. The number of units of this type was 32 and 39 in 2001 and 2011， respectively. The spatial distribution is relatively steady， and they were mainly located in the west and east belts of China， respectively. （4） High-Low， with strongly negative spatial correlation level units. The region has high efficiency， while its surrounding units have lower coordination. The number of units of this Type was 24 and 33 in 2001 and 2011， respectively. They weremainly located in west regions. Compared with 2001，the added units were mainly located in Guangxi， Qinghai， and Yunnan provinces and some units in the national minority regions in 2011.

Figure 4　LISA cluster map of FMCD and its efficiency from 2001 to 2011

3.2The influence factors about FMCDE from the perspective of balancing urban and rural development based on GWR model

Analyzing the influencing mechanisms of FMCDE， the first step was to find the related factors. The coordinated development of urban and rural areas was an important content in promoting the coordinated development of regional economies and the strategic decision in narrowing the differences between urban and rural areas， promoting the synchronous development of "four modernizations" and solving the dualistic structure in urban and rural areas， accounting for the realistic need and strategic orientation of promoting regional development and urban and rural synchronization of "four modernizations". Therefore， this paper analyzed factors that influence the efficiency from the perspective of coordinated urban and rural development.

It can be concluded from the aforementioned analysis that the spatial distribution of FMCDE in Chinese prefecture-level units has obvious spatial autocorrelation and spatial heterogeneity. The adoption of the GWR model can effectively solve the local variation problem between dependent and independent variables caused by the spatial position， thereby revising the classical regression model and reducing the spatial autocorrelation of traditional model residual. We calculated the mean value of the cross-section data between 2001 and 2011 in order to avoid errors caused by abnormal data fluctuation. It preceded standardized treatment of standard deviation data on each index，carried out the colinearity test through the stepwise regression method， and eliminated collinear indexes. Then， select five indices， namely， the per capita GDP with the tolerance value over 0.7， income ratio of urban and rural residents， the per capita retail sales of consumer goods， per capita expenditure on education and per capita fixed asset investment ratio between urban and rural residents as explanatory variables to establish the GWR model and adopt the bandwidth method which minimizes the AICc through adaptive kernel function for local estimation.

Firstly， we analyzed regional unit efficiency by using the ordinary least square （OLS） model. The results were as follows: the determination coefficient R2was 0.66， the sum of squared residual was 7.48，and AICc was 802.47. However， the result of R2by using GWR mode was 0.80， the sum of squared residuals was 3.19， and AICc was 730.25. After a global spatial correlation inspection for residuals of the OLS and GWR models， we found that the Moran' I index are -0.012 and -0.008 respectively， which indicated that the residual spatial correlation of GWR model is smaller than the OLS model. Other relevant indicators are presented in Table 2. The R2， AICc and the residual correlation showed that the result of GWR simulation was more reasonable than OLS（Table 2）. Moreover， the AICc value of GWR model with the AICc value of OLS gap was more than 3（Akaike， 1974）， which proved that GWR fitting results are better than OLS. In order to further detect the rationality of GWR model， we used a univariate model to check the relationship between efficiency and five potential influencing factors. The results show that the R2of per capita GDP， per capita income ratio between urban and rural residents， per capita total retail sales of consumer goods， per capita expenditureon education and the difference between urban and rural per capita investment in fixed assets were 0.56，0.46， 0.50， 0.47 and 0.47， respectively. We then tested all the independent variables using a mixed GWR model. The mixed model's R2of determination was 0.8， which was larger than each of the univariate GWR models. Therefore， the mixed GWR model can appropriately analyze the coordination development efficiency's variation.

The difference between urban and rural per capita investment in fixed assets boasted the greatest influence on FMCDE （Figure 5）. Compared with the other four factors' regression coefficient， it has an extreme domino effect， along with a minimum and maximum regression coefficient greater than other similar factors， and gives us a clue where the majority change and the distribution of fixed assets in urban and rural are closely connected. The Pearl River Delta， Fujian Province， Zhejiang and other coastal provinces have the minimum regression coefficient for two reasons. First， highly developed industrialization entitled the area higher fixed assets both in urban areas and rural areas， and the gap between urban areas and rural areas is less. Second， we may inevitably face a situation where production levels may not meet its input for a long period of time， as further development and opening may result in lower efficiency of the coordinated development in some regions， e.g.， the Pearl River Delta and Yangtze River Delta. Benefited from the policy of West Development in China， the regression coefficient is higher in northern and western China. Also， because of substantially increasing funds for city infrastructure， economy， science， and education， the quality of FMCDE will improve.

Urban and rural investment in fixed assets per capita has a maximum interpretation into efficiency，followed by GDP per capita. The distribution trend of GDP per capita regression coefficients is similar to that of urban and rural investment in fixed assets per capita， except the higher spatial fragmental internal interpretation characteristics. The influence degree of GDP per capita efficiency decreased from the northwestern to southeastern regions. The high value region is located in Xinjiang， Tibet， and Qinghai provinces and some units in Heilongjiang. GDP per capita could fundamentally improve efficiency， especially in those undeveloped areas. The junctional region between Guangdong， Hunan， Jiangxi and Fujian provinces have the lowest value， and the relation between efficiency and level of regional economic development lacks direct links.

Both high-value units and low-value units， of which the per capita total retail sales of consumer goods influencing efficiency was distributed in minority nationality areas. The high-value units were located in northwestern provinces such as Yunnan，Guizhou and Guangxi. These units should carry out active consumption strategies to improve FMCDE. The low-value units were also distributed in those provinces under developing social economies such as Qinghai， Tibet and Xinjiang. These units have a low per capita total retail sale of consumer goods.

Both positive and negative correlations were observed between FMCDE and per capita expenditure on education. All units with positive coefficients were mainly located in western provinces， which are less developed provinces in China. Also in these regions，the foundation of education is weak and the per capita expenditure on education was also low. The more education expenditure invested by local finance， the more benefits that "four modernizations" will have. The units with negative coefficients are mainly distributed in the junction areas of Shanxi， Shaanxi and Henan provinces. The increasing proportion of urban income to rural income in urban and rural areas must be controlled， so that FMCDE can be improved.

Figure 5　Spatial distribution on the local relationship between FMCDE and five factors

Local R2values show how well the model fits the data in each district. The R2explanatory power of GWR for each area ranged from 7.3% （minimum） to 88.8% （maximum） as presented in Figure 6. Explanatory power increased from west to east China and increased slightly from southwest to southeast China. The regions with high R2values are located in coastal area of east China， north of Xinjiang and several units of Tibet and Inner Mongolia. Most of these regional units have more developed units， which indicates that the leading factor that influences the coordination development efficiency of these units are mainly social economic elements. The units， which GWR model can't explain well， are mainly located inthe southwest hilly areas， south Tibet and mountainous regions of Longnan. Also， these regions have had a complex physiographic condition， fragile ecological environment and complex natural geographical conditions， so it was hard to explain well with this model in these units. These conclusions are consistent with previous research of Liu and Li （2010）.

Figure 6　Spatial distribution of the determination coefficient（R2） in each region

4　Discussion and conclusion

4.1Discussion

The results of this study have provided some political enlightenment for improving the development of "four modernizations" in China. First， FMCDE has the reality demand in distinct space in the new stage of urban and rural restructuring development， to promote FMCD. We need innovated top design， common policy and different development strategies in different regions. We need to strengthen the leading function of the new industrialization， unleashing the promoting function of information technology， increase the guiding function of new urbanizations， and reinforce the basic function of agricultural modernization to change and promote the single policy of the present structure and department. Second， the difference between urban and rural per capita investment in fixed assets is the first important factor in FMCDE. This fact requires us to strengthen support for agriculture and urban areas promoting rural areas， with the agricultural information technology as an important tool， stimulate the capital market's input into agricultural modernization and realize the leaping development. Third， the research conclusions of FMCDE in megacities remind us that the emphasis and difficulty of promoting the "four modernizations" exist in metropolis. At present，the metropolis has not contributed in solving the "three agricultural problems" （agriculture， farmer and rural area） and balancing urban and rural development. Thus， we should pay more attention to the quality of urbanization， provide improved industry structure and service facilities， and the carrying ability to realize urban and rural equalization of basic public services. Fourth， after the GWR model has explained efficiency，we find that different regions should make policies according to their conditions. The northwest should start with improving the level of economic development， and the southwest should start with putting forward the consumption of urban and rural residents. Shanxi， Shaanxi and Henan provinces can start with narrowing the residents' income level of urban and rural areas. In addition， from the view of prefectural level unit， the obvious differences in social economic factors in China should not just start from macro scale and microscopic perspective and ignore the mesoscale-prefectural level units.

The meaning of FMCD is far more abundant than that reflected by the current indicator system. Due to a lack of data， it is difficult to wholly describe the urbanization quality， new industrialization and agricultural modernizations. Moreover， it is worth further discussing the mechanism， regional development mode and multi-scale features of the FMCD. Due to the amount of data and the difficulty of obtaining data，we only choose 2001 and 2011 to make a comparative analysis. This study needs the support of multiple time cross-sections to reflect changes and trends of the efficiency in the prefecture-level units more accurately and scientifically. In addition， more in-depth studies in the scientific links of FMCD and its developing efficiency should be initiated.

4.2Conclusions

This paper evaluated the industrialization， urbanization， informatization and agricultural developmental indices of China's 343 prefecture-level administrative units， and calculated their comprehensive， coupling， coordinated and coordination development efficiency indices in 2001 and 2011 respectively. There is an obvious spatial difference between coordinated development and its efficiency and show diverse regional patterns. The comprehensive index， coupling degree， and coordinated index show spatial differences which are likely divided by the 'anti-Huhuanyong Line' from northwest to southeast. FMCD has a low efficiency in general. It can be confirmed that China's FMCD has obvious spatial differences and shows diverse regional patterns， especially at the meso scale. Different regions tend to have different problems and thus need different preferential policies. As such， the traditional one-size-fits-all policies should be improved in a timely manner.

The difference between urban and rural per capita investment in fixed assets boasts the greatest influence on FMCDE. Per capita GDP is the second largest influencing factor. Mixed GWR shows that the spatial regression model has a poor explaination for mountainous and hilly regions， which indicates that FMCDE may be affected by topography， climate and social economy. Overall， this paper enhanced our knowledge of FMCD， and may benefit the improvement of China's regional policies and thus contribute to the sustainable development of China in the new era of urban-rural transformation.

Acknowledgments:

This work was supported by the National Natural Science Foundation of China （No. 41361040） and the Fundamental Research Funds for the Provincial Universities of Gansu Province （No. 2014-63）.

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*Correspondence to: JingHu Pan， Associate Professor of Northwest Normal University. No. 967， Anning East Road，Lanzhou， Gansu 730070， China. E-mail: panjh_nwnu@nwnu.edu.cn

August 17， 2015Accepted: November 20， 2015