3.1. Theoretical Framework Analysis
LUE is mainly influenced by several parameters. From the opening-up of China, expansion of urban land and increase of construction land are mainly caused by the process of industrialization, globalization, urbanization, and marketization [
40,
41,
42,
43,
44,
45]. Therefore, this study tries to explore the theoretical framework of LUE from these four aspects.
LUE is significantly influenced by industrialization. Industrialization has greatly influenced landscapes both in rural and urban areas [
46]. During the process of industrialization, rural area is developed to urban area and farmland is changed into construction land. In order to improve the industrial development, infrastructural facilities such as of traffics, research and development and communication platforms should be considered into the urban planning. In another aspect, industrial land price is usually low in the industrial parks or economic development zone [
5]. Therefore, local government and enterprises are inclined to promote industrial agglomeration. External economies of scale is emerged within the industrial agglomeration [
12], which reflects in space as the prosperity of land output.
Globalization has been confirmed that it is an important driving force for urban land restructuring [
47]. With the opening-up policy of China since 1979, foreign direct investment (FDI) stimulated the emergence of rural industrialization, exo-urbanization, and an export-oriented economy especially in coastal areas [
40]. In order to attract foreign investment, infrastructure, research and development facilities and communication convenience are significantly improved [
48]. FDI leads to the emergence of industrial zones in peri-urban areas, changing landscapes of urban areas, and improving the economically efficient output of land.
Urbanization is another important factor leading to changes of LUE [
41]. With the process of urbanization, rural area is transferred to urban area, resulting in the remarkable expansion of urban scales in China. At the same time, a large amount of rural population has been migrating to cities to seek job opportunities. On the one hand, new urban residents are important labor force for the city. On the other hand, they are consumers with large consumption demands for housing, education, transportation, and communication [
49]. When formulating urban planning and management policy, the impacts of fast urbanization should be taken into consideration in order to achieve the economically efficient overall layout of a city.
Marketization also an important impetus for changes of urban land. During the rapid marketization in China, hierarchical government-controlled land system has been transferred to largely market-oriented [
44]. In the process of marketization, land system reform is continually carried out. In rural areas, collective-owned construction land has been permitted to enter market and have equal rights and prices with urban state-owned land [
50]. In urban area, land banking system and land bid invitation, auction and listing system are implemented [
51,
52]. These land systems have changed the capital investment environment both in rural and urban areas, improving the market mechanism in resource allocation and raising land values. The theoretical framework for urban LUE is shown in
Figure 1.
As discussed above, LUE in this study is calculated in terms of urban GDP per square kilometer of urban built land. The land use efficiency
of city
i is calculated as
where
is the GDP of city
i and
is the built-up area of city
i.
In the industrial agglomeration analysis, an expanded Cobb–Douglas production function is applied by many scholars to estimate agglomeration economies [
23,
38,
53]:
where
denotes the output per square kilometer of land (LUE),
is the total factor productivity,
is the employees per square kilometer of land,
is the human capital,
is the physical capital input per square kilometer of land and
and
are the output and area of a city, respectively. In Equation (2),
expresses the spatial density of output. If
λ > 1, then spatial density shows positive externality, and if
λ < 1, then spatial density shows negative externalities.
Therefore,
represents the externality of industrial agglomeration. To further measure the externalities of agglomeration economy,
is used to represent
qi and
is used to represent the externality of industrial agglomeration. Equation (2) can be expressed as follows:
where
denotes urban employment and
denotes physical capital stock.
Previous studies have concluded that infrastructure, human capital, foreign direct investment (FDI), capital investment, research and development and information communication are important factors affecting total factor productivity [
22,
54,
55,
56,
57]. The total factor productivity can be calculated as follows:
where
i represents city;
INF,
HC,
FDI,
CI,
RD and
IC denote infrastructure, human capital, FDI, capital investment, research and development and information communication, respectively; and
ε is a random disturbance term. On the basis of Equations (3) and (4), the econometric model of the relationship between industrial agglomeration and LUE can be given as follows:
where
LUE is land use efficiency,
agglo is the degree of industrial clustering and
X represents other important factors influencing LUE. In according with the theoretical framework of LUE, these factors include human capital, urban scale, infrastructure, FDI, capital investment environment, research and development, and information communication.
3.2. GWR Model
As China covers a large territory, its economic development may show strong characteristics of spatial heterogeneity. Thus, whether industrial agglomeration distribution and LUE show spatial differences among the eastern, central, and western areas is a common question. For robust empirical findings, spatial difference should be considered in estimations. [
58] proposed the GWR method to solve the spatial non-stationarity problem. Compared with the traditional average and global model, GWR model allows different parameters to exist in different spaces. In this way, the good performance of GWR model has been demonstrated in studies, and more reliable results have been obtained than those in traditional ordinary least squares (OLS) for estimations on subjects with spatial heterogeneity characteristics [
59,
60,
61]. Therefore, the GWR model is used in this study to reveal the spatial variations of industrial agglomeration effects on LUE. The GWR model is expressed as follows:
where
yi is the dependent variable, in this case the LUE at location
i,
denotes the intercept coefficient at location
i,
is the value of the
kth explanatory variable at location
i,
is the
kth local regression coefficient for the
kth explanatory variable,
is the projected coordinates of location
i and
ɛi is a random error term. Stated in matrix notation, the parameters of the model are estimated by the following equation:
where
denotes an estimate for
β and
W(
i) is an
spatial weighting matrix where diagonal elements represent the spatial weight of each location to location
i and off-diagonal elements are 0. As the bandwidth of the kernel function chosen is sensitive to the regression of GWR, the optimal value of bandwidth should be determined [
62]. By using the spatial weighting function, an adaptive bi-square function is applied to generate the geographic weights of each observation. Bi-square kernel has a clear-cut range where kernel weighting is non-zero and is suitable when local extents for model fitting need to be clarified. Adaptive bi-square function permits the bandwidth to increase its size when sample points are sparse and decrease the size when observations are dense [
63]. As the density of city in China change greatly in space, so the adaptive bi-square function is adopted in this study. The bi-square function can be expressed as follows:
where
i is the regression point index,
j is the locational index,
is the weight value of observation at location
j for estimating the coefficient at location
i,
is the Euclidean distance between
i and
j and
b is an adaptive bandwidth. The optimal bandwidth can be determined by cross-validation (CV) [
64,
65]:
where
is the fitted value of
and the corresponding
b is the optimal bandwidth when the CV is minimum.
3.3. Moran’s I
The spatial autocorrelation and heterogeneity of observations may contain traditional global estimation and lead to biased results. Before using the GWR model, whether spatial autocorrelation occurs in the variables should be estimated. Moran’s index (Moran’s I) is chosen to represent the global spatial autocorrelation of LUE. The formula of Moran’s I can be expressed as follows:
where
is the observation in the
ith city,
is the observation in the
jth city,
represents the spatial weight of adjacent units,
represents the mean of
or
and
n is the total number of cities. The value of Moran’s I is between −1 and 1. The correlation is positive when the value is greater than 0, which indicates that urban LUE shows a spatial positive correlation. The correlation is negative when the value is close to −1, which means that urban LUE represents spatial negative correlation. The closer the value to 1, the stronger the agglomeration effect is, whereas the closer the value to −1, the stronger the diffusion effect is. When Moran’s I is 0, no spatial relationship exists.
The proposed methodologies including expanded Cobb–Douglas production function, GWR model and Moran’s I improve city planning. First, when using expanded Cobb–Douglas production function, factors including industrialization, globalization, urbanization, and marketization which are influencing urban land output are all considered in the regression. In this way, the impacts of industrial agglomeration on LUE would be estimated more realistically than only without considering these factors, which will have practical meaning when doing urban planning. Second, indicator of Moran’s I shows that if LUE has a spatial correlation, making the regression more robust when using GWR model. Third, regional differences are fully considered in the GWR model, which is suitable for the economic development in China. When doing the regional planning of the whole country, planning policies for regional leading industries and development direction will be more practical considering the spatial differences of LUE.