1 Introduction

Since China adopted reform and opening-up policies in 1978,economic construction and social developmenthas become the focal point of the government,bring along at the same time theissues of urbanization,industrialization,informatization and agriculturalmodernization for both scholars and administrators(Chen et al., 2013; Fang et al., 2013; Wang et al., 2015). The drawbacks of urban-rural division,l and partition and man-l and 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 rapidurbanization becomes increasingly worsening,which comprehensively lead to thedifficulty of urban-rural coordinated development and sustainable developmentof rural areas(Liu et al., 2015). In 2012,the report of the 18thNational Congress of the Communist Party of China(CPC)pushed for an importantstrategic requirement and historic task of "the promotion of integratinginformatization and industrialization,the positive interaction of industrialization and urbanization, and the coordination of urbanization and agriculturalmodernization to boost the synchronous development of industrialization,informatization,urbanization and agricultural modernization"(so called "SihuaTongbu" in China, and hereinafter referred to as "fourmodernizations"),which acted as the new guidance for the regional developmentin the new era(Li et al., 2014). Industrialization is the core substance ofmodernization and will support and stimulate its development, and is also animportant transformation process from traditional agricultural society tomodern industrial society. Urbanization,accompanying with industrialization,is a process of population flowing into urban areas in the period of boostingindustrialization,or a period of second and tertiary industries gathering togetherin and around cities. Informatization is a modern social civilized developedperiod through the revolution of high technology and the spread of knowledge and information. Agricultural modernization is a period in which people usemodern productive tools to change traditional agriculture,whose development isaccompanied by the development of industrialization,urbanization and informatization.From the international perspective,currently,China has entered the middlestage of industrialization and urbanization development on the whole; informatizationis going through the accelerated development and expansion stage,but agriculturalmodernization is lagging behind. For the uneven,uncoordinated and unsustainable development and other issues existing in China's current "fourmodernizations",strategic guideline for the simultaneous developments of "fourmodernizations" with distinct era characteristics and Chinesecharacteristics has been proposed in the report to the 18th National Congressof the CPC. However,it is a complex and difficult task to solve the issues ofcoordinated development for "four modernizations"; it is the premise and necessary preparation for promoting comprehensive,coordinated,efficient and sustainable development of "four modernizations" to correctly underst and their development connotation and mutual relationships. In addition,significant regional differences exist in the economic and social developmentof various regions in China, and imbalanced development is also prevalent evenwithin 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 "XinChangtai" in Chinese), and the changing economic development mode and thetransformation of urban-rural development are imperative(Liu et al., 2014). In the critical period of the current economic transition of China,ithas important theoretical and practical significance for achieving scientific,comprehensive and integrated underst and ing of the degree of synchronization forthe regional "four modernizations" to carry out objective evaluationsof the level of coordinated development and spatial-temporal differentiation ofthe regional "four modernizations".

Informatization was enhanced to the height of nationaldevelopment strategy for the first time in the report to the 18th NationalCongress of the CPC. The literature related to the studies of "fourmodernizations" published by scholars was scarce,but the interactivedevelopment of industrialization,urbanization and agricultural modernizationin the "four modernizations" has been the focus of attention in academiccircles. From the overall perspective,the study contents of existing "fourmodernizations" involved among others the connotation and mechanism,evolutionlocus of the concept,realization path,evaluation index system and the measurementof developmental level for "four modernizations"(Qian et al., 2012).However,few studies concentrated on China's coordinated development and efficientmeasurement of the "four modernizations". The study scale was mostlyprovincial, and nationwide comprehensive studies based on the prefectural level and county-level administrative units were scarce.

In addition,if "fourmodernizations" have had a higher or lower level of coordinateddevelopment,how about their investment level, and what are the cost to achievea high or low level of coordination? Namely,how about the efficiency of "fourmodernizations" coordinated development(FMCD)? In response,one of theobjectives of this study is therefore to contribute to knowledge surroundingthe 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 amore efficient allocation of resource factors,better management and morerational utilization. Much effort has previously been dedicated to developing simulationmethods for measuring efficiency. In a relatively short period,dataenvelopment analysis(DEA)has grown into a powerful quantitative,analyticaltool for evaluating performance,which has been successfully applied to a hostof different types of entities engaged in a wide variety of activities in manycontexts world-wide(Assafa and Matawieb, 2010). Input-output efficiencymeasurement and analysis are being taken seriously as a research method in relationto cities(Morais and Camanho, 2011). Unfortunately,theefficiency of FMCD has received much less attention amongst the research community(Li et al., 2014). The FMCDE was a process including funds,resources and technical inputs,production,conversion and output. Based on this,FMCDEcan be defined as the output effect of coordinated development generated byvarious resource factors of "four modernizations" within a specifictime(such as a year) and under certain input conditions(labor,financial and material resources),which was used to reflect the level of coordination forthe regional "four modernizations"; higher FMCDE indicated thatvarious factor allocations of the region was more reasonable, and the resources and factor input can achieve better effect. FMCDnot only can grasp the utilization efficiency and existing problems of regionalresource factors in a timely manner,but also can provide a scientific basisfor adjusting and optimizing the allocation and utilization of various factorsfor the future regional "four modernizations", and developingeffective regional development policy to study the FMCDE and its spatial-temporalpattern. 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 discussregional problems(Ding et al., 2013; Li et al., 2014). Thispaper aims to investigate the spatial patterns and influencing factors of FMCD and its efficiency in China at prefecture level administrative units from bothexploratory and analytical perspectives, and reveal the change tendency inrecent 10 years, and corresponding implications for regional polices. Firstly,a comprehensive evaluation index system will be establish to evaluatecomprehensive,coupling and coordinated development of "fourmodernizations". Secondly,this paper proposes an input-output efficiencyevaluation indicator system of the efficiency, and a DEA method is used inorder to evaluate the input-output efficiency of China's prefecture levelcities,based upon data drawn from 2001 and 2011. ESDA,which explores temporal and spatial changes in the coordinated development and its efficiency from anexploratory perspective,is applied to form visual spatial patterns in China. Thirdly,we explore the spatial association of efficiency with several potentialdeterminants to examine potential spatial variations in assumed relationshipsbetween these factors and the efficiency by using GWR model.

The socio-economic dataneeded in this study were mainly extracted from the China City StatisticalYearbook(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 Centerfor Resources and Environmental Sciences,Chinese Academy of Sciences( http://www.resdc.cn/). We have collected the data of 343 prefecture-leveladministrative 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 specialgeographical and social barriers and use inconsistent statistical procedures,these cities and region were not included in the present study.

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

where,g_i,c_i,x_i and n_i represent indicators which canmostly depict the state of industrialization,urbanization,informatization and agricultural modernization,respectively(all of them are dimensionless valuesof the original data); α_i,β_i,γ_i and μ_i mean the weights of corresponding indicators,calculated by Analytic Hierarchy Process(AHP)based on the Delphi method(Rushton et al., 2014). We st and ardized 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:

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

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

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

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

where,D is thecoordinated development index of "four modernizations",C isthe coupling degree of "four modernizations" and T is thecomprehensive development index of "four modernizations" in Formula (6).

Suppose we have nadministrative units,where each unit(DMU_i,i=1,…,K)produces M outputs y_im (m=1,…,M)by utilizing L inputs x_il (l=1,…,L). Here, x_ilis the lth input for unit i(l=1,…,L) and y_im(m=1,…,M)is the mth output for unit i (m=1,…,M). On the hypothesis thatthe sum of convexity,cone, and invalidity of unit n (n=1,…,K)are minimized and constant returns toscale(CRS)DEA(data envelopment analysis)model can be expressed by the followingequation:

where,θ (0<θ≤1)is theobjective function's value; λ_j≥0 is convex coefficient; s⁻(s⁻≥0)is slack variable; s⁺(s⁺≥0)is residual variable; ε is non-Archimedean infinitesimal;ê^T=(1,1,…,1)ÎE^L and e^T=(1,1,…,1)ÎE^M are m-dimensional and k-dimensionalunit vector space,respectively. In this paper,we chose the per capita consumptionexpenditure of urban and rural residents,per capita local fiscal budget,percapita social investment in fixed assets and per capita local or foreigncurrency in each prefecture-level cities as inputs; the coordinated developmentindex is the output of "four modernizations".

1)Global spatialautocorrelation—Moran's I

Moran's I is a classicmeasure for spatial autocorrelation. The global Moran index(GMI)is calculatedas follows(Anselin,1996):

where,w_ij is therow-st and ardized contiguity matrix,x_i is the frequency countof a certain coordinated value and its efficient value at location i, and μis the average frequency count ofthis issue. This study uses a Queen contiguity weights matrix,which defines alocation's neighbors as those with either a shared border or vertex,since allprefectures distribute freely and can access every place in China.

2)Local spatialautocorrelation(LISA)

Todetermine the location of clusters or spatial outliers,LISA is employed byapplying a local Moran statistic for evaluating spatial autocorrelation at thelevel 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 byclassifying the local Moran statistic into four groups: high-high[HH] and low-low[LL] that represent local spatial clusters having similar attributeswith neighbors, and high-low[HL] and low-high[LH] that represent local spatialoutliers.

3)Hot spot analysis

In order to statisticallytest the morphology and intensity of the coordinated development of "four modernizations" and its efficiency,a HotSpot Analysis(Getis-Ord G_i* statistic)with the 343measuring studies were performed. The resultant z-scores and p-values of theGetis-Ord G_i* statistic indicate where features with eitherhigh or low values cluster spatially. The G_i* statisticreturned 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,themore intense the clustering of high values(a hot spot).

GWR estimates point parameterin sequence using local weighted ordinary least squares and the weights is thedistance function of the geospatial location of the regression point to thegeospatial 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,(S_i,T_i)denotes the coordinates of the ithlocation point(census tract centroid in this study)in the study area; α₀(S_i,T_i)is a realization of the continuous function α₀(S_i,T_i)at location i,ε_i is r and om error.

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

The comprehensive,coupling and coordinated developmental indices of "fourmodernizations" can be calculated based on Formulae(1) to(6).The coordinated 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 overallefficiency of the coordinated development of "four modernizations" isrevealed in Figure 2.

Figure 1 Spatial pattern of comprehensive development level and couplingand coordination degrees of "four modernizations" from 2001 to2011. Note: The inclined lineis called "Hu Huanyong Line", a "geo-demographic demarcationline" discoveredby Chinese population geographer Hu Huanyong in 1935. The imaginary Heihe(in Heilongjiang)-Tengchong (in Yunnan) linedivides the territory of China into two parts: northwest of the line covers 64%of the total area but only 4% ofthe population; however, southeast of the line covers 36% of the total area but96% of the population

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Figure 2 Spatial distribution of FMCDE from 2001 to 2011

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1)Comprehensive developmentindex: the average of comprehensive development index is 0.215 and 0.233,st and ard deviation is 0.087 and 0.086 in 2001 and 2011,respectively. In 2001,prefectural units with higher comprehensive indices are mainly located innortheastern China. Prefectures with lower comprehensive indices are mainlydistributed in southwestern China,central China,Qinghai-Tibet Plateau and along the 'Hu Huanyong Line'. Compared with 2001,there is no essential changewith 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,st and ard deviationis 0.143 and 0.157 in 2001 and 2011,respectively. In 2001,units with higher coupling development indices are mainly distributed in eastern coastalregions like northeastern China,Bohai Rim Region,Yangtze River Delta,PearlRiver Delta. Sichuan-Shannxi border area,Chongqing,Xinjiang and several unitsin Inner Mongolia also have had a higher coupling development value.Prefectural units with lower value are mainly distributed in the central traditionalagricultural areas,due to vast out-migration,the pace of urbanization and informatization in these areas is rather slow. Lower coupling development indexareas 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,thusrestricting the development of cities and towns, and the transformation oftraditional agriculture to a modernized one. Regions along with 'Hu HuanyongLine',which have had a lower coupling index in 2001,were changed to havehigher coupling index in 2011.

3)Coordinated developmentindex: the average of coordinated development index is 0.359 and 0.391,st and ard deviation is 0.102 and 0.106 in 2001 and 2011,respectively. Regionswith higher coordinated development indices are mainly distributed in northwesternChina,Inner Mongolia,major cities in eastern coastal and Hubei-Jiangxi borderareas,while the indices in southwestern China,central China and Qinghai-TibetPlateau are much lower. The major constraints on developmentin these regions are the complex natural and geographical conditions and fragile ecological environment.The spatial pattern of the coordinated development was more broken and separatedin 2011,compared with 2001.

In general,thecomprehensive,coupling and coordinated developmental indices have obvious spatialdifference 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 tosoutheast. The units southwest of the 'anti-Hu huanyong Line' have a highervalue of comprehensive,coupling and coordinated index,while the northeasthave a much lower value.

According to the existingliterature classification method(Huang et al., 2013),the efficiency value equals 1 for high efficiency,between 0.8 and 1for moderate efficiency,between 0.6 and 0.8for low efficiency,while less than 0.6 mean no efficiency. The resultsindicate that the average of the coordination development efficiency in Chinese343 prefecture-level cities in 2001 and 2011 were 0.686 and 0.671,respectively. The st and ard variation of the efficiency decreased from 0.168 to0.158,showing that the difference between units was reduced. There were onlyeight units,Wuhai,Suqian,Shangrao,Jingmen,Shaoyang,Liupanshui,Yushu and Yili,respectively,reaching the effective stage. These units only possessed2.33% of the total number of research units, and they are basically distributedin western and central China except Suqian. Compared with 2001,the number ofeffective units increased to twelve in 2011. These twelve units are mainly locatedin western and central China. Prefecture-level units with no efficiencyaccounted for 30% of the total number of study units,representing a low levelof efficiency. The spatial pattern of high efficiency are mainly distributed incentral 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,theefficiency 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 ofthe efficiency is higher in these cities,which possess a lower scale ofpopulations and economy. This is a valuablefinding,which can be explained by the fact that the gap is widening betweenurban and rural areas in those big cities in China. The core urban areas havebetter traffic conditions,mature urban development,well-developedinfrastructure,efficeint social services and high-quality of life,however,the socio-economic development level of its governed counties was relativelylow.It is necessary to speed up the reformation and development in rural areas,stimulate rural vitality of entrepreneurship and innovation, and promoteon-site urbanization.

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

This paper calculated the GMIof coordinated development index by using Geoda(Anselin et al., 2006)in 2001 and 2011 for the coordinated development index of "fourmodernizations" and normal statistics Z values of the efficiency of GMIgreater than 0.05 under the condition of the confidence level of the criticalvalue of 1.96. The spatial relationship characteristics and its efficiency inthe Chinese 343 prefecture-level cities are found to be as follows: the GMI ofthe 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 itsefficiency presented obvious spatial autocorrelation of prefecture levelcities. The GMI value showed a significantly positive tendency for Moran's I, and the units with high value of the coordinated degree and high efficiencytend to gather in space,the units with low coordinated degree and lowefficiency also tend to gather in space.

On the basis of global spatial autocorrelation,this paper further detects targetproperty 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 hotspot analysis. This paper calculated the Getis-Ord G_i*coefficient,which represented the regional spatial relationship between thecoordinated development index and its efficiency. The result of the Getis-Ord G_i*coefficient was spatialized by GIS software. According to the numerical size ofG_i* statistic of the FMCD and its efficiency,the G_i*values was divided into cold spots,secondary cold spots,secondary hot spots and hot spots by using the natural breaks classification. The spatial patternof G_i* are presented in Figure 3 which shows that cold spotsregions and hot spots regions presented the spatial structure characteristicsof staggered distribution. The cold and hot spots' spatial pattern does notshow substantive transformation during 10 years,only the number changes. Hotspots are mainly distributed in two parts of China. One part was in order fromwest to east through the northern part of Xinjiang,northwestern Gansu Province,Inner Mongolia,Jilin Province, and Heilongjiang Province, and the other partwas in order from west to east through the border of Sh and ong Province and HebeiProvince,border of Sh and ong,Anhui and Henan provinces. Cold spot units arebasically symmetrically distributed in 'Hu Huanyong Line' on both sides. Thehot spots are mainly located in the east of contiguous 'Hu Huanyong Line',Liaodong Peninsula,Sh and ong 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,mainlydistributed in Guangdong.

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

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The cold spots and hot spotsare presented in a spatially staggereddistribution. The distribution pattern has changed drastically during the last10 years,compared with the cold spots and hot spots. In general,the hot spotswere the most concentrated and stable,mainly located in central provinces ofHenan,Anhui and Hunan in 2001 and 2011. The cold spots of Fujian,Guangdong,Guangxi and Hainan provinces formerly changed into secondary hotspots,which showedthat the efficiency has improved. The reduction number of cold spots areas wasthe most dramatic.

This paper analyzed the spatial mutual influential relationship,which representsthe coordination development index of "four modernizations" in one certainprefecture-level unit and the efficiency in the surrounded prefecture-level unitsby using local spatial correlation method of double variables. LISA and itssignificance(p=0.05)of both the coordinated development index and efficiency between 2001 and 2011 were calculated and presented on the clustermap(Figure 4). In the period of 2001-2011,the FMCD and its efficiency showedan 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 correlationunits. There were six units of this type in 2001. The spatial malpositiondistribution of these units in two periods illustrates the frequent change offamous areas in 10 year time.(2)Low-Low,which has a notably positivecorrelation level,its efficiency is low and its surrounding areas also haverelatively low FMCD indices. There were 26 units in 2001,while the number wasreduced to 23 units in 2011. The spatial distribution of Type 'LL' did notchange in the course of the study period. They were mainly located on theborder of Shaanxi,Gansu and Ningxia, and scattered distribution in Guizhou,Sichuan,Chongqing and Yunnan provinces. These districts need to accelerate thecoordinated development and improve its efficiency.(3)Low-High,withstrongly negative spatial correlation level units. The region has lowefficiency,while its surrounding units have higher coordination. The number ofunits of this type was 32 and 39 in 2001 and 2011,respectively. The spatial distribution is relatively steady, and they were mainly located in thewest and east belts of China,respectively.(4)High-Low,with stronglynegative spatial correlation level units. The region has high efficiency,whileits surrounding units have lower coordination. The number of units of this Typewas 24 and 33 in 2001 and 2011,respectively. They were mainly located in west regions. Compared with2001,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

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Analyzing the influencingmechanisms of FMCDE,the first step was to find the related factors. The coordinateddevelopment of urban and rural areas was an important content in promoting thecoordinated development of regional economies and the strategic decision innarrowing 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 therealistic 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 perspectiveof coordinated urban and rural development.

It can be concluded from theaforementioned analysis that the spatial distribution of FMCDE in Chinese prefecture-levelunits has obvious spatial autocorrelation and spatial heterogeneity. The adoptionof the GWR model can effectively solve the local variation problem betweendependent and independent variables caused by the spatial position,thereby revisingthe classical regression model and reducing the spatial autocorrelation of traditionalmodel residual. We calculated the mean value of the cross-section databetween 2001 and 2011 in order to avoid errors caused by abnormal data fluctuation. It preceded st and ardized treatment of st and ard 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 capitaGDP with the tolerance value over 0.7,income ratio of urban and ruralresidents,the per capita retail sales of consumer goods,per capita expenditureon education and per capita fixed asset investment ratio between urban and rural residents as explanatory variables to establish the GWR model and adoptthe b and width method which minimizes the AICc through adaptive kernel functionfor local estimation.

Firstly,we analyzed regionalunit efficiency by using the ordinary least square(OLS)model. The resultswere as follows: the determination coefficient R² was 0.66,the sum of squared residual was 7.48, and AICc was 802.47. However,the result of R² by using GWRmode 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 GWRmodels,we found that the Moran' I index are −0.012 and −0.008respectively,which indicated that the residual spatial correlation of GWRmodel is smaller than the OLS model. Other relevant indicators are presented inTable 2. The R²,AICc and the residual correlation showed that the result of GWR simulation wasmore reasonable than OLS(Table 2). Moreover,the AICc value of GWR model with the AICc value of OLSgap was more than 3(Akaike,1974),which proved that GWR fitting results arebetter than OLS. In order to further detect the rationality of GWR model,we used a univariate model to check therelationship between efficiency and five potential influencing factors. Theresults show that the R² of per capita GDP,per capita incomeratio between urban and rural residents,per capita total retail sales of consumer goods,per capita expenditure oneducation and the difference between urban and rural per capita investment infixed assets were 0.56,0.46,0.50,0.47 and 0.47,respectively. We then testedall the independent variables using a mixed GWR model. The mixed model's R²of determination was 0.8,which was larger than each of the univariateGWR models. Therefore,the mixed GWR model can appropriately analyze thecoordination development efficiency's variation.

The difference between urban and rural per capita investment in fixed assets boasted the greatest influenceon FMCDE(Figure 5). Compared with the other four factors' regression coefficient,it has an extreme domino effect,along with a minimum and maximum regressioncoefficient greater than other similar factors, and gives us a clue where themajority change and the distribution of fixed assets in urban and rural areclosely connected. The Pearl River Delta,Fujian Province,Zhejiang and othercoastal provinces have the minimum regression coefficient for two reasons.First,highly developed industrialization entitled the area higher fixed assetsboth in urban areas and rural areas, and the gap between urban areas and ruralareas is less. Second,we may inevitably face a situation where productionlevels 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 insome regions,e.g.,the Pearl River Delta and Yangtze River Delta.Benefited from the policy of West Development in China,the regressioncoefficient is higher in northern and western China. Also,because ofsubstantially increasing funds for city infrastructure,economy,science, and education,the quality of FMCDE will improve.

Figure 5 Spatial distribution on the localrelationship between FMCDE and five factors

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Urban and rural investment infixed assets per capita has a maximum interpretation into efficiency,followedby GDP per capita. The distribution trend of GDP per capita regressioncoefficients is similar to that of urban and rural investment in fixed assetsper capita,except the higher spatial fragmental internal interpretationcharacteristics. The influence degree of GDP per capita efficiency decreasedfrom the northwestern to southeastern regions. The high value region is locatedin Xinjiang,Tibet, and Qinghai provinces and some units in Heilongjiang. GDPper capita could fundamentally improve efficiency,especially in thoseundeveloped 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 goodsinfluencing efficiency was distributed in minority nationality areas. Thehigh-value units were located in northwestern provinces such as Yunnan,Guizhou and Guangxi. These units should carry out active consumption strategies toimprove FMCDE. The low-value units were also distributed in those provincesunder developing social economies such as Qinghai,Tibet and Xinjiang. Theseunits have a low per capita total retail sale of consumer goods.

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

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 toeast China and increased slightly from southwest to southeast China. Theregions with high R² values are located in coastal area ofeast China,north of Xinjiang and several units of Tibet and Inner Mongolia. Mostof these regional units have more developed units,which indicates that theleading factor that influences the coordination development efficiency of theseunits are mainly social economic elements. The units,which GWR model can'texplain well,are mainly located in thesouthwest hilly areas,south Tibet and mountainous regions of Longnan. Also,these regions have had a complex physiographic condition,fragile ecologicalenvironment and complex natural geographical conditions,so it was hard toexplain well with this model in these units. These conclusions are consistentwith previous research of Liu and Li(2010).

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

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The resultsof this study have provided some political enlightenment for improving thedevelopment of "four modernizations" in China. First,FMCDE has thereality dem and in distinct space in the new stage of urban and rural restructuring development,to promote FMCD. We need innovated topdesign,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 theguiding function of new urbanizations, and reinforce the basic function ofagricultural modernization to change and promote the single policy of thepresent 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 areaspromoting 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 FMCDEin megacities remind us that the emphasis and difficulty of promoting the "fourmodernizations" exist in metropolis. At present,the metropolis has notcontributed in solving the "three agricultural problems"(agriculture,farmer and rural area) and balancingurban and rural development. Thus,we should pay more attention to the qualityof urbanization,provide improved industry structure and service facilities, and the carrying ability to realize urban and rural equalization of basicpublic services. Fourth,after the GWR model has explained efficiency,we findthat different regions should make policies according to their conditions. Thenorthwest 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 narrowingthe residents' income level of urban and rural areas. In addition,from theview of prefectural level unit,the obvious differences in social economicfactors 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 moreabundant than that reflected by the current indicator system. Due to a lack ofdata,it is difficult to wholly describe the urbanization quality,newindustrialization and agricultural modernizations. Moreover,it is worth furtherdiscussing the mechanism,regional development mode and multi-scale features ofthe FMCD. Due to the amount of data and thedifficulty of obtaining data,we only choose 2001 and 2011 to make acomparative analysis. This study needs the support of multiple timecross-sections to reflect changes and trends of the efficiency in theprefecture-level units more accurately and scientifically. In addition,morein-depth studies in the scientific links of FMCD and its developing efficiencyshould be initiated.

This paper evaluated the industrialization,urbanization,informatization and agricultural developmental indices of China's 343 prefecture-level administrativeunits, and calculated their comprehensive,coupling,coordinated and coordinationdevelopment efficiency indices in 2001 and 2011 respectively. There is anobvious 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-HuhuanyongLine' from northwest to southeast. FMCD has a low efficiency in general. Itcan be confirmed that China's FMCD hasobvious spatial differences and showsdiverseregional patterns,especially at the meso scale. Different regions tendto have different problems and thus need different preferential policies. Assuch,the traditionalone-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 influenceon FMCDE. Per capita GDP is the second largest influencing factor. Mixed GWRshows 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 thuscontribute to the sustainable development of China in the new era of urban-ruraltransformation.

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