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Research areaThe YREB covers Shanghai, Jiangsu, Zhejiang, Anhui, Jiangxi, Hubei, Hunan, Chongqing, Sichuan, Guizhou, and Yunnan. It includes the Yangtze River Delta urban agglomerations (YRDUA), Yangtze River midstream urban agglomeration (YRMUA), and Chengdu-Chongqing urban agglomeration (CCUA). With a regional area of 2.05 million km2, the YREB runs through the eastern, central and western regions in China32. In 2019, the total GDP of YREB is 45.8 trillion yuan, accounting for 46.2% of the national GDP. The YREB plays a pivotal strategic support and leading role in the overall situation of stable economic growth in China33. At the same time, the contradiction between the shortage of land resources and economic growth in the YREB is very prominent. Therefore, this paper selects 107 cities in YREB as the research sample. The specific geographic locations are shown in Fig. 2. This article uses ARCGIS 10.2 version to draw the map. The URL link is http://demo.domain.com:6080/arcgis/services.Figure 2The geographic location of the YREB in China.Full size imageResearch methodsGlobal Malmquist–Luenberger indexUGLUE refers to the effective utilization degree of land elements under certain input of other elements. The green utilization of urban land mainly comes from three aspects: first, improve the utilization intensity of the existing actual input land, that is, increase the input intensity of other elements of the unit land area. Second, reduce the input of land in the production process to avoid excessive waste of land. Third, promote the optimal allocation of land elements among production units. Technical efficiency refers to the maximum degree that all factor inputs need to expand or shrink in equal proportion when all production units reach the production frontier. However, for production units with high technical efficiency, the factor allocation structure may not be reasonable. The land factors may still have the problem of under-input or over-input, resulting in the reduction of UGLUE.Pastor and Lovell34 proposed a global index, which uses all the inspection periods of each decision-making unit as a benchmark to construct the production frontier. According to the current benchmark construction period t, the production possibility set reference set is defined as follows:$$P_{C}^{t} (x^{t} ) = left{ {left. {(y^{t} ,b^{t} )} right|x^{t} {kern 1pt} can{kern 1pt} , produce{kern 1pt} , b^{t} ,y^{t} } right}$$
(1)
The global benchmark is defined as: (P_{G} = P_{C}^{1} , cup ,P_{C}^{2} , cup , cdots ,P_{C}^{t}), The subscripts C and G represent the current benchmark and the global benchmark respectively. The ML index of decision-making unit i is calculated based on the current reference benchmark:$$ML^{S} (x^{t} ,y^{t} ,b^{t} ,x^{t + 1} ,y^{t + 1} ,b^{t + 1} ) = frac{{1 + D_{C}^{S} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{C}^{S} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}}$$
(2)
Among them, the superscript S indicates two adjacent periods, t period and t + 1 period. The subscript C indicates the current benchmark, which is a simplified directional distance function. (ML^{s} > 1), indicates that the productivity increases. (ML^{s} < 1), indicates that the productivity decreases.According to Hofmann et al.35, the GMLI is defined as follows:$$GMLI^{t,t + 1} (x^{t} ,y^{t} ,b^{t} ,x^{t + 1} ,y^{t + 1} ,b^{t + 1} ) = frac{{1 + D_{G}^{T} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{G}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}}$$ (3) Among them, (D_{G}^{T} (x,y,b) = max left{ {alpha |(y - alpha y,b - alpha b) in P_{G} (x)} right}). (GMLI^{t,t + 1} > 1) indicates that the productivity has increased. (GMLI^{t,t + 1} < 1) indicates that the productivity decreases. The GMLI is further broken down as follows:$$begin{aligned} & GMLI^{t,t + 1} (x^{t} ,y^{t} ,b^{t} ,x^{t + 1} ,y^{t + 1} ,b^{t + 1} ) = frac{{1 + D_{G}^{T} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{G}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}} \ & quad = frac{{1 + D_{G}^{t} (x^{t} ,y^{t} ,b^{t} )}}{{1 + D_{G}^{t + 1} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} )}} times left[ {frac{{(1 + D_{G}^{T} (x^{t} ,y^{t} ,b^{t} ))/(1 + D_{C}^{T} (x^{t} ,y^{t} ,b^{t} ))}}{{(1 + D_{G}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} ))/(1 + D_{C}^{T} (x^{t + 1} ,y^{t + 1} ,b^{t + 1} ))}}} right] \ & quad = frac{{TE^{t + 1} }}{{TE^{t} }} times left( {frac{{BPG_{t + 1}^{t + 1} }}{{BPG_{t}^{t + 1} }}} right) = EC_{t}^{t + 1} times BPC_{t}^{t + 1} \ end{aligned}$$ (4) Among them, TE is the change of technological progress. EC is the change of technological efficiency. The change of technological progress reflects the change of the highest technical level. The improvement of the highest technical level often requires the introduction and innovation of advanced technology, which often requires a large amount of investment. The change of technical efficiency reflects the gap with the highest technical level. Narrowing the gap with the highest technical level often requires improvements in internal management and governance structures. (BPG_{t}^{t + 1}) is the “best practitioner gap” between the current period and overall technological frontier. (BPC_{t}^{t + 1}) measures the changes in the “best practitioner gap” between two periods (technological changes). (BPC_{t}^{t + 1} , > , 1 ,) indicates technological progress. (BPC_{t}^{t + 1} < 1) indicates technology regress.Econometric techniques of industrial agglomeration on UGLUEIn recent years, many scholars used the traditional SPM for empirical analysis, which is a basic measurement model suitable for panel data. Therefore, this article firstly uses the traditional SPM to analyze the impact of industrial agglomeration on UGLUE. The formula is:$$begin{aligned} ln UGLUE_{it} & = alpha_{0} + alpha_{1} ln RZI_{it} + alpha_{2} ln RZI_{it} *ln RZI_{it} + alpha_{3} ln RDI_{it} + alpha_{4} ln EC_{it} \ & quad + alpha_{5} ln GDP_{it} + alpha_{6} ln TEC_{it} + alpha_{7} ln ROAD_{it} + alpha_{8} ln GOV_{it} + varepsilon_{it} \ end{aligned}$$ (5) Among them, ε is the disturbance term. i represents the city, i in this paper involves 107 cities in YREB. t represents the time, and the range of t in this paper is from 2007 to 2016. UGLUE is the explained variable, which represents the UGLUE. RZI and RDI are explanatory variables, representing industrial specialization agglomeration and industrial diversification agglomeration. EC is the industrial structure. GDP is the level of economic development. TEC is the level of technology. ROAD is the level of infrastructure. GOV is the degree of government intervention. (alpha_{1}) to (alpha_{8}) is the coefficient of each variable.Formula (5) assumes that the UGLUE changes with the changes of various influencing factors in the current period. That is, there is no time lag effect. But in reality, land use often has a time lag effect. The previous level has a non-negligible impact on the current results. Therefore, this paper selects the dynamic panel model for empirical analysis. However, there is often a two-way causal relationship between industrial agglomeration and UGLUE, which may cause endogenous bias. For example, cities with higher UGLUE levels tend to have higher levels of economic development, which promotes industrial agglomeration in this city. Therefore, this paper adopts the method of system GMM for regression analysis of dynamic panel model. Compared with mixed OLS, system GMM can make full use of sample information, select appropriate lag terms as instrumental variables36. It can effectively solve the endogeneity problem between industrial agglomeration and UGLUE. Based on the above analysis, this paper introduces the first-order lag term of UGLUE on the basis of formula (5). The DPM is as follows:$$begin{aligned} ln UGLUE_{it} & = beta_{0} + tau ln UGLUE_{i(t - 1)} + beta_{1} ln RZI_{it} + beta_{2} ln RZI_{it} times ln RZI_{it} + beta_{3} ln RDI_{it} \ & quad + beta_{4} ln EC_{it} + beta_{5} ln GDP_{it} + beta_{6} ln TEC_{it} + beta_{7} ln ROAD_{it} + beta_{8} ln GOV_{it} + varepsilon_{{{text{it}}}} \ end{aligned}$$ (6) Among them, (tau) is the first-order lag coefficient of UGLUE, reflecting the time lag effect of UGLUE.Variable descriptionExplained variableThe GMLI is used to measure the UGLUE of 107 cities in YREB. According to existing research37, the following core evaluation index of UGLUE are selected (see Table 1). Regarding input indicators, we mainly choose land element input M, labor element input L, and capital element input K as input indicators. Regarding output indicators, we choose the added value of the secondary and tertiary industries in the municipal area as the expected output, and use the GDP deflator to convert it into a comparable value. At the same time, pollution indicators such as industrial wastewater emissions, industrial sulfur dioxide emissions, and industrial smoke (dust) emissions are selected as undesired output. Since the GMLI reflects the growth rate of UGLUE, this paper assumes that the GMLI in 2006 is 1, and then multiplies the calculated GMLI year by year to obtain the development level of UGLUE in each city from 2007 to 2016.Table 1 Input and output index.Full size tableExplanatory variablesIndustrial specialization index ZI is usually used to measure the specialization level of urban industries. The specialization index is represented by the share of the employment of the industry in the total employment of the city:$$ZI_{i} = Max_{j} (S_{ij} )$$ (7) Nextly, we use the relative specialization index to make a horizontal comparison of the specialization level between different cities:$$RZI_{i} = Max(S_{ij} /S_{j} )$$ (8) The most common measure of the level of industrial diversification is the Herfindahl–Hirschman Index (HHI). For city i, the HHI is the sum of the square sum of employment shares of all industries in the city. The diversification index is the reciprocal of the HHI:$$DZ_{i} = frac{1}{{sumlimits_{j} {S_{ij}^{2} } }}$$ (9) The expression of relative diversification index is as follows:$$RDI_{i} = {1 mathord{left/ {vphantom {1 {sumlimits_{j} {left| {S_{ij} - S_{j} } right|} }}} right. kern-0pt} {sumlimits_{j} {left| {S_{ij} - S_{j} } right|} }}$$ (10) Among them, Sij is the employment proportion of j industry in city i, and Sj is the proportion of the total employment of the national j industry. The greater value of RZI and RDI, the higher level of industrial specialization and diversification.Control variablesRegarding control variables, we choose the following variables as control variables.Industrial structure (EC): The continuous optimization of industrial structure promotes the improvement of UGLUE through three aspects: saving land, increasing land income and promoting the optimal allocation of land resources. This paper selects the added value of the tertiary industry as a percentage of GDP (take the logarithm) to express.Technological level (TEC): The higher the technological innovation level of a city is, the more it promotes the use of input elements and the transformation of innovation results, thereby improving the UGLUE. This paper selects the proportion of science and technology expenditure to fiscal expenditure (take the logarithm) to represent.Economic development level (GDP): The continuous economic development promote the rational allocation of various production factors and increase the level of urban land output, thereby improving the UGLUE. This paper selects GDP per capita (take the logarithm) to express.Road infrastructure level (ROAD): The continuous improvement of infrastructure reduces transportation costs and transaction costs, and promotes communication externalities between producers, consumers, and between producers and consumers. This paper selects the average road area per capita (take the logarithm) to express.Government behavior (GOV): Fiscal expenditure is an important means for the government to carry out macro-control. Appropriate fiscal expenditure makes up for market shortages, improves factor flow and resource allocation efficiency, and realizes positive economic externalities. This paper selects the proportion of fiscal expenditure to GDP (take the logarithm) to express. We can see the meaning of specific variables from Table 2.Table 2 The descriptive statistics of variables.Full size tableData sourceThe object of this thesis is the 107 cities in YREB from 2007 to 2016. The urban construction land area data comes from the "China Urban Construction Statistical Yearbook", and the rest of the index data all come from the "China City Statistical Yearbook". The URL link is https://www.cnki.net/. In order to maintain the integrity of the data, this article uses the average method to fill in the missing values. In addition, because Chaohu City began to be under the jurisdiction of Hefei City in 2011, Bijie City and Tongren City in Guizhou Province only became prefecture-level cities in 2011. The three cities and Pu'er City are taken from the sample to maintain the continuity of data. More

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