Data Analysis of the Factors Influencing the Industrial Land Leasing in Shanghai Based on Mathematical Models

the By analyzing the background of land leasing in Shanghai, the hypotheses of the mathematical models of industrial land leasing in Shanghai are proposed, and then, the mathematical models of the land price and land area are presented for analyzing the factors of industrial land leasing. Based on the mathematical models and the district data of Shanghai from 2007 to 2015, the factors inﬂuencing industrial land leasing by the district government are studied. It is shown that the inﬂuencing factors, such as the land area, GDP, tenure of district mayor, and the distance between the land and the nearest subway station, aﬀect the government behavior on industrial land leasing.


Introduction
e development of industry is very important for the economics of a country. With rapid development of the economics in China, it is necessary to study the industrial land leasing in China.
For the industrial land uses, the local governments in China must consider the development of the economics of the city when leasing land, and it is important to study the factors that influence industrial land leasing by the government [1].
Shanghai is an international metropolis and the largest city in China. Studying the industrial land leasing in Shanghai will show the development of industry in the large cities in China, and with the gradual implementation of new urbanization plan in China, the mode of the industrial land leasing in Shanghai will offer a reference for the development of other new large cities. e constraint of land availability affects urban economic growth, and the importance of land conversion in land leasing was explained [2]. With the rapid urban development, the demand for land use should be balanced by the governments, and the distribution of rural land and urban land should be considered [3]. e local public goods, such as transportation system, are very important for industry development of a city, and these will influence land prices and house prices. Transportation nodes and distance between the location of the land and the city center affect the land price in Shanghai [4]. Rail transit and mass transit can attract land development and expand the urbanization [5,6]. Public transit, high-quality schools, universities, and environmental amenities near the land can also affect the land price [7]. Proximity to the subway can increase the economic activities and consumer amenities [8]. Municipal governments in China establish subway stations in suburban districts to decrease the transportation cost of people and gain more revenues from future land transactions [9]. e subway system shows a positive effect on commercial property values in Wuhan in China [10]. e role of built, human, social, and natural capital can impact land values [11].
At present, most industrial land is leased by listing. e government policy and intention can affect the industrial land leasing greatly. e corresponding researches based on the district data need to be done for the large cities including Shanghai and Beijing.
In this paper, by analyzing the background of land leasing in Shanghai, the hypotheses of the mathematical models of industrial land leasing in Shanghai are proposed, and then, mathematical models of land price and land area are presented for analyzing the factors of industrial land leasing. Based on the mathematical models and the district data of Shanghai from 2007 to 2015, the factors influencing industrial land leasing by the district government are studied.
It is shown that the land area, GDP, and the distance between the land and Hongqiao International Airport have positive associations on the industrial land price. e mode of land leasing, the location of the district, paid-in foreign investment, unemployment, tenure of district mayor, gross industrial production, total industrial asset, the distances between the land and Shanghai Railway Station, the nearest subway station, the nearest entrance or exit of highway, and the nearest industrial park have negative associations on the industrial land price, and the number of entrances and exits of highways in the district and the location of the district have positive associations on the total industrial land area by the government in Shanghai. ese factors can influence the government on making decisions to lease industrial land in Shanghai.
is study will help the governments propose more efficient and sustainable land use policies and better land leasing decisions in the coming decades.

Hypotheses of Mathematical Models of Industrial Land Leasing in Shanghai
To present the mathematical models for the factors influencing industrial land leasing, 3 hypotheses are proposed in this paper.
Hypothesis 1. e land characteristics have significant influences on industrial land leasing by the government. e land characteristics include the area of the land, floor ratio of the land, modes of land leasing, and location of the district.
e land area is a basic factor for land leasing. e floor area ratio of the land is the ratio of built area to land area. It is a very important factor associated with the land prices. e modes of land leasing, such as tender and listing, can affect land leasing and land prices [12]. In Shanghai, the districts are divided into three levels, including the center districts, suburban districts, and county, which are shown in Section 3. e location of the district affects land prices.

Hypothesis 2.
e district characteristics have significant influences on industrial land leasing by the government. e district characteristics include GDP of the district, tenure of district mayor, paid-in foreign investment, unemployment, gross industrial production, total industrial asset, and industrial employees.
GDP is associated with the economic development of the district, and it is one of the influencing factors of land leasing by the government decision in this research. e district leaders, such as district mayor and the party secretary, can decide land leasing.
For industrial land use, attracting foreign investment is very important. e foreign investment affects the developments of economics and industry.
Unemployment is associated with the economic development of the district and the income of employees. Unemployment will decrease with the increase of the industrial land leasing.
Industrial characteristics reflect the state of an industry. ey include gross industrial production, total industrial asset, and industrial employees. Moreover, they are considered as the factors influencing land leasing for industrial land use.

Hypothesis 3.
e location characteristics have significant influences on industrial land leasing by the government. e location characteristics include the distances of the land to city center, district center, airports, railway station, the nearest subway, the nearest highway, and the nearest industrial park.
People's Square is regarded as the city center of Shanghai, and the locations of the district governments are considered as the district centers.
Hongqiao International Airport and Pudong International Airport are considered as major airports in Shanghai. Shanghai Railway Station is regarded as the main railway station in Shanghai.
According to the Introduction section, subway is an important factor influencing land leasing, land prices, and house prices. e newly completed highway affects the land value [13]. e less the distance between the distribution center and the nearest entrance or exit of highway is, the higher the rent is [14]. us, highways have a strong relationship with land value.
Industrial parks are very important for urban land use planning, and their locations depend on the accessibility and economic indicators [15]. ese hypotheses consider different aspects, which are the variables to present mathematical models to analyze the factors influencing land leasing by the district government comprehensively.

Data of Influencing Factors of Industrial Land
Leasing in Shanghai  Figure 1 shows the distribution of 19 districts in Shanghai.
In this paper, the data of GDP, tenure of district mayor, paid-in foreign investment, unemployment, gross industrial production, total industrial asset, and e data of the distances of the land to the city and district centers, airports, railway station, the nearest subway, nearest highway, and nearest industrial park are obtained by using the software ArcGIS. 98 industrial parks are considered in Shanghai. Figure 3 shows the subway stations and highways in Shanghai in 2015. Figure 4 shows the distribution of industrial parks in Shanghai.

Mathematical Models of Industrial Land Leasing in Shanghai
In this paper, the model used for the regression for the industrial land leasing in Shanghai is   Table 1. In the table, "Obs." denotes observations, and "Std. Dev." denotes standard deviation.
Equation (1) can be written as where en, there are the expected value and the covariance where A j is the component of the vector A. For given sample data, we can estimate a, which is the approximation of the coefficient vector a, and and then, we have where N is the sample number. From equation (8), we have then a � y − aA n , Because of the arbitrariness of the number of the samples, equation (9) can be rewritten as Substituting equation (11) into equation (14) yields i.e.,

Mathematical Problems in Engineering
en, we have e model used in this paper for the regression for industrial land area and its influencing factors is where LA it is the area of total leased industrial land of district i in year t, V mit is the location characteristic V m of district i in year t, M is the number of location characteristics, Yr_dum is the year dummy variable, Dis_dum is the district dummy variable, a is the constant, and u it is the error term for district i in year t. e definitions and summary statistics of the variables of land area and influencing factors for industrial land use in Shanghai are shown in Table 2.
Equation (18) can be written as where en, there are the expected value   Mathematical Problems in Engineering where V j is the component of the vector V. For given sample data, we can estimate a, which is the approximation of the coefficient vector a, and a � a 1 , a 2 and then, we have From equation (25), we have then a � y − aV n , where Because of the arbitrariness of the number of the samples, equation (26) can be rewritten as i.e., en, we have (34) Table 3 shows the results of models for the influencing factors of industrial land leasing by the district government in Shanghai.

Results and Discussions
From the results of influencing factors of industrial land use in Shanghai in Table 3, for the land characteristics, the variable of the area of leased land is statistically very significant for land leasing by the government. e price of industrial land use increases by 0.98% when the area of leased land increases by 1%. e larger is the area of industrial land use, the higher is its price. e variable of the mode of land leasing is statistically significant for land leasing by the government. e price of industrial land use for listing is higher than that for tender. Tender is one of the modes of land leasing that invites many tenderers to participate in and allows only one bid before the deadline. Listing allows bidders to bid continuously and repeatedly before the deadline, and generally the bidder with the highest price can get the bid. e difference between tender and listing is the bid times. e industrial land price will be higher for listing than tender because in listing bidders can know others' bidding prices and as such the bidding prices can be higher than expected. e variable of the location of the district is statistically very significant for land leasing by the government. e decrease of the grade of location of the district increases the price of industrial land leasing. e industrial land in center districts is very scarce in Shanghai, and most industrial land is in the suburban districts and the county. e industrial land price will be higher in suburban districts than that in the county. Suburban districts have better transportation systems that can help develop industry.
For the district characteristics, the variable of the GDP of the district is statistically significant for land leasing by the government. e land price of industrial land use increases by 0.23% when the GDP of the district increases by 1%. If the GDP of the district is high, the government may focus on leasing industrial land for sustainable development and profits making. e variable of the paid-in foreign investment of the district is statistically significant for land leasing by the government. e land price of industrial land use decreases by 0.1% when the paid-in foreign investment of the district increases by 1%. e foreign investments promote the industry development variously, and the government intends to offer preferential prices to the companies with foreign investments. e variable of the unemployment of the district is statistically very significant for land leasing by the government.
e land price of industrial land use decreases by 1.17% when the number of the unemployment of the district increases by 1%. Unemployment influences economic development, especially for the industry. Increase in unemployment adversely affects the state of industries. e variable of the tenure of district mayor is statistically very significant for land leasing by the government. e decrease of the tenure of district mayor increases the land price of industrial land use. e district mayor may pay more attention to industrial land use in the short run for a better development of the district. us, the price of industrial land use increases. e variable of the gross industrial production of the district is statistically very significant for land leasing by the government. e land price of industrial land use decreases by 0.46% when the gross industrial production of the district increases by 1%. e gross industrial production increases, which shows that industrial development is very good, the district government hopes to lease industrial land at a lower price than before. e variable of the total industrial asset of the district is statistically significant for land leasing by the government. e land price of industrial land use decreases by 0.54% when the total industrial asset increases by 1%. When the total industrial asset increases, in order to use the industrial asset to promote economic development, the district government hopes to lease industrial land at a lower price than before.
As regards the number of industrial employees, the land price of industrial land use decreases by 0.44% when the number of industrial employees of the district increases by 1%. When the number of industrial employees increases, in order to offer more jobs, the district government will lease industrial land at a lower price than before.
For the location characteristics, the variable of the distance between the land and Hongqiao International Airport is statistically very significant for land leasing by the government. e land price of industrial land use increases by 0.34% when the distance between the land and Hongqiao International Airport increases by 1%. Hongqiao International Airport is close to the center districts in Shanghai, but the industrial land is relatively far away from the center districts.
e variable of the distance between the land and Shanghai Railway Station is statistically very significant for land leasing by the government. e land price of industrial land use decreases by 1.29% when the distance between the land and Shanghai Railway Station increases by 1%. ere are some logistics industries and other types of industries around the railway station. 8 Mathematical Problems in Engineering e variable of the distance between the land and the nearest subway station is statistically very significant for land leasing by the government. e land price of industrial land use decreases by 0.05% when the distance between the land and the nearest subway station increases by 1%. e variable of the distance between the land and the nearest entrance or exit of highway is statistically very significant for land leasing by the government. e land price of industrial land use decreases by 0.03% when the distance between the land and the nearest entrance or exit of highway increases by 1%. e subway and highway are two important means of transportations in a large city, and the developers of industrial land prefer the locations closer to them as it enables transportation of products and external communications. e variable of the distance between the land and the nearest industrial park is statistically very significant for land leasing by the government. e land price of industrial land use decreases by 0.01% when the distance between the land and the nearest industrial park increases by 1%. e industrial parks are the places with plenty of industrial land and strong characteristics of industry; thus, the land price of industrial land use is higher when it is closer to an industrial park.
For the industrial land area and its influencing factors, the variable of the number of entrances and exits of highways is statistically very significant for industrial land area by the government. When there are more entrances and exits of highways in the district, the total land area of industrial land use increases. e government will lease more industrial land with the increase of the number of entrances and exits of highways. For the industrial land use, it is important to have good accessibility to the highway as it enables the transfer of goods and makes it easier for external communication. e government is more likely to lease industrial land to the districts with more entrances and exits of highways.
e variable of the location of the district is statistically very significant for land leasing by the government. e higher the grade of the location of the district, the higher is the total area of industrial land use. As the grade of the location of the district increases, the government leases more industrial land. e county is the highest grade (i.e., LOC it � 3), the center district is the lowest grade (i.e., LOC it � 1), and LOC it � 2 is for the suburban district. Hence, the county and suburban districts have more industrial land than center districts. e government prefers to lease industrial land to the suburban districts.
In summary, the land area, mode of land leasing, location of the district, GDP, paid-in foreign investment, unemployment, tenure of district mayor, gross industrial production, total industrial asset, and the distances of industrial land to Hongqiao International Airport, Shanghai Railway Station, the nearest subway station, the nearest entrance or exit of highway, and the nearest industrial park affect the industrial land price. Moreover, the number of entrances and exits of highways in the district and the location of the district affect the total industrial land area. From the analysis mentioned above, it is shown that the government is more likely to lease industrial land with larger area or listing mode. When the GDP of the district is high or the paid-in foreign investment, gross industrial production, total industrial asset, and industrial employees are under low status, the government prefers to lease industrial land. Not only the land nature and the economic development but also the political promotion affect the industrial land price and decisions made by the government. e district mayors with shorter tenures prefer to lease more industrial land. Location of the land influences the government behavior on land leasing. Suburban districts are the priority of the government for industrial land leasing. Also, the government prefers leasing industrial land near Shanghai Railway Station, subways, highways, and industrial parks. e government is more likely to lease industrial land to the districts with more entrances and exits of highways.

Conclusion
In this paper, the factors influencing industrial land leasing by the government in Shanghai are analyzed based on the district data from 2007 to 2015. e hypotheses and mathematical models for the factors influencing industrial land leasing by the government in Shanghai are proposed.
In conclusion, the land area, mode of land leasing, location of the district, GDP, paid-in foreign investment, unemployment, tenure of district mayor, gross industrial production, total industrial asset, and the distances of industrial land to Hongqiao International Airport, Shanghai Railway Station, the nearest subway station, the nearest entrance or exit of highway, and the nearest industrial park affect the industrial land price. Moreover, the number of entrances and exits of highways in the district and the location of the district affect the total industrial land area. e high transaction price of industrial land also means large profits gained by the government; therefore, the government likes leasing industrial land with higher price.
From the results, it is shown that the government in Shanghai prefers to lease industrial land with larger area or mode of listing. Also, the government tends to lease industrial land in suburban districts or counties. Meanwhile, when the GDP of the district is high or the paid-in foreign investment, gross industrial production, total industrial asset, and industrial employees are under low status, the government prefers to lease industrial land. Also, the government prefers to lease industrial land near Shanghai Railway Station, subways, highways and industrial parks. e government is more likely to lease industrial land to the districts with more entrances and exits of highways.
ere are some policy implications from the results. First, the district government needs to lease industrial land when the industrial indicators are under low status, which will promote the industrial development of the city and make more comprehensive urban development. Second, the district mayors with shorter tenures prefer to lease more industrial land to focus on more sustainable development of the city. ird, the district government pays more attention on suburban districts and transportation accessibility when leasing industrial land, which will promote the formulation of industrial land pattern in the long run.
is study can promote land use planning system and sustainable urban development. Moreover, it will offer a reference for other large cities in China and other counties implementing public land ownership.
Data Availability e data used to support the findings of this study are available within the article. Conflicts of Interest e author declares that there are no conflicts of interest regarding the publication of this paper.