Rethinking the Contribution of Land Element to Urban Economic Growth: Evidence from 30 Provinces in China

Abstract

In China, disputes regarding the benefits and drawbacks of land finance have been heated, but the role of land in urban economic growth has received insufficient attention, particularly on a macro scale. This research used the Cobb–Douglas production function model to investigate the role of land in urban economic growth. Then, we conducted an empirical test using panel data from 30 provinces from 2000 to 2019, with the goal of revealing the role of land in urban growth and spatio-temporal inequalities in China. Furthermore, to find the spatial steady-state level of land contributions, σ convergence, absolute β convergence, and condition β convergence tests were applied. The results show that: (1) China’s urban economic development was influenced by the combined element of land, capital, and labor; (2) the contribution of land to China’s urban economy experienced a turning point during the “12th Five-Year Plan”; (3) the spatio-temporal convergence of the contribution of land showed convergence in the east but nonconvergence in the central and western regions; and (4) β convergence demonstrated convergence in eastern, central, and western China. Given the complex and turbulent international political and economic context, the Chinese government should think about how to foster continuous energy by supporting land-supply policies that are adapted to local needs.

1. Introduction

China has made significant progress in terms of urbanization during the last few decades. The urbanization rate climbed significantly from 17.9% in 1978 to 61.43% in 2020, while GDP increased from RMB 0.15 trillion to RMB 14.72 trillion ¹. In urban economic growth, the central and municipal governments frequently serve as managers [1]. According to city management, the government wants to achieve three goals: increasing the value of urban resources, increasing the competitiveness of the urban system, and increasing capacity for long-term development [2]. The object of city management is to put the concept of urban entrepreneurialism into practice [3], while aspects like labor [4,5] and capital [6,7] become commonplace.

Local governments generate fiscal revenue through land premiums and land tax revenues, this fiscal revenue strategy is generally referred to as “land finance”. Land finance becomes an important tool to combine diverse resources dedicated to city management [8], whether driven by a huge quantity of capital for city construction or to achieve relative advantages in rivalry with other cities [9]. The urban built-up area expanded from 7538 km² in 1980 to 60,312 km² in 2019 [10]. Sustainable urban growth cannot continue without a certain amount of urban land investment, and undoubtedly, land finance was a key factor to support the rapid development of China in the past 30 years [11,12].

However, throughout the years, land financing has earned its share of criticism for the hazards it presents to sustainable urban expansion [13]. Popular criticisms of land finance rely on the fact that local government frequently relied on selling land to bridge the gap between revenues and expenditures; in other words, land became an important source for local government to ease financial pressure and increase revenues outside of the traditional budget [14]. The share of land transfer fees to municipal financial receipts climbed from 28.4 per cent in 2002 to 56.91 per cent in 2017 [12]. Such development sparked questions about the future of sustainable urban expansion. For example, Liu (2020) likened land supply to the engine, which not only propelled quick economic expansion but also governed the rhythm of economic development; however, the role of the engine seems to have been diminishing since 2010 [12]. The high dependence on land-generated financial risks to sustainable urbanization, and underinvestment in land hampered economic development in several areas, especially in eastern China.

In any way, it would be arbitrary to estimate the merits and downsides of land financing if we overlook regional diversity in China. A further empirical investigation is important to explain the driving mechanism of land in urban economic growth, as well as the present perilous economic position both at home and abroad to reinforce the uncertain future [15]. Therefore, understanding how to properly examine the effect of land investment on urban economic development is an essential topic that must be tackled.

The main objectives of this study are to analyze the mechanistic role of land-element inputs on urban economic growth in China based on the Cobb–Douglas production function. It uses economic, social, and construction land-panel data from 30 provinces and municipalities (districts) across the country from 2000 to 2019 as a sample, and analyzes the spatial and temporal differences. Then we conduct a convergence analysis on the contribution of the land element.

This study makes the following contributions. First, we construct a production function model that includes the land element on the basis of the concept of urban management and then demonstrate its national applicability. Second, according to the empirical test, we argue that the Chinese government should think about how to foster continuous energy by supporting land-supply policies that are adapted to local needs.

2. Literature Review

The land has long provided a solid foundation for human productivity and daily activities, and social development has always been accompanied by land-use change [16]. The limited exploitation of land resources creates significant asymmetry with the rate of social development [17], and ecologically fragile regions of the world are characterized by severe constraints on regional economic development and unsustainable economic development dynamics because of the scarcity of land resources [18,19,20]. Overall, along with the steep increase in the real demands of world population growth and urbanization, this has triggered a continuous increase in the demand for land resources for development [21]. The increase or decrease in land demand is mainly influenced by changes in population size and the progress of urbanization [22], while land supply is constrained by factors such as land-resource endowment and land-use planning [23,24]. There is a different historical context for the development of China’s economy compared to the West. China’s unique reform and opening up brought about the rapid development of manufacturing and service industries, and the country entered a more rapid urbanization phase, which can be described as a “take-off” phase of economic development. The development process that accompanied this phase was a huge migration of the rural labor force to the cities: from just 17.9% of the entire population in 1978 to 59.6% in 2018—just four decades. This rate of urbanization meant that there was a huge demand for urban housing, which was accompanied by the implementation of the “housing reform” policy, resulting in the formation of a vast, stable, and inevitable value-added real estate market in China. This played a key role in the development of the entire national economy, and it has been the main driving force in China’s economic take-off phase. Against the backdrop of explosive economic growth, China’s economic development has always maintained a high demand for land resources [25].

As a basic means of production, the importance of land to socio-economic development is self-evident, and most studies have analyzed the impact of land factors on economic growth from the perspectives of land-use efficiency and land input quantity [26,27]. Studies have found that land-use efficiency significantly contributes to economic growth, while changes in land-use efficiency significantly influence the rate of economic growth [28]. The growth of land input was studied as a fundamental element of urban economic development, and it was found that continuous land input contributed significantly to urban economic growth [29], which required the implementation of different land-use plans in different cities to respond to the needs of economic development [30]. Further studies focused on the impact of land factors on the development of secondary and tertiary industries from the perspective of land input in time and space [31]. Meanwhile, other research provided analytical arguments on the influence of land policy on macroeconomic factors and the correlation between land input cycles and economic development cycles [32]. Some scholars focused on the development of the Shanghai metropolitan area and found that there is geospatial variation in land’s contribution to Shanghai’s urbanization progress [33]. Others showed that land input can promote coordinated urban economic development in Wuhan [34], but due to the different stages of development across regions, the contribution of land factors varies, and urban economic growth shows significant spatial correlation, indicating that there is a spillover effect of land factors on economic growth [35]. It is also important to note that land resources are consumed in productive activities and their quality decreases with the frequent occurrence of such activities [36]. Excessive demand for land for socio-economic development can create unsustainable patterns of economic growth, and land changes that squeeze out other factors that drive economic development will eliminate mechanisms for diversified economic growth [37].

Does land represent a factor of production or a package of economic levers? In China, the land is seen as a production factor not only for economic growth but also as a tool for implementing economic development strategies [29]. The importance of land in urban and regional development has long been recognized by Chinese scholars and policymakers [38,39]. Studies indicate that land development has two effects on urban growth. One is the expansion of urban building land, and the other is the significant increase in land revenue from urban construction [40,41]. More effective use of urban land is a reflection of the efficiency of urban administration, and urban growth necessitates the rational use of every inch of urban land [42]. Unrestricted expansion of urban land may pose financial, ecological, and administrative risks [16,43], especially in China where local governments may rely excessively on land revenues to promote economic growth [44]. Some studies suggest that some Chinese cities are being exposed to a certain degree of financial risk that is due to the expansion of urban land areas [45]. Urban land is bought and sold more frequently [46], and frequent transactions in the primary land market are likely to undermine the original urban land plan, resulting in the blind expansion of urban land [47]. Padeiro argues that changes in land plans are not beneficial for urban management and urban development [48].

The classical Cobb–Douglas production function is commonly used in the analysis of industrial development and resource endowment [49,50], and it contains three major elements: technology, capital, and labor. Some scholars have already used the Cobb–Douglas production function to analyze the role of urban land on the urban economy and showed that the expansion of urban land has a positive impact on the urban economy [51]. Stewart [52] uses the Cobb–Douglas model to assess the influence of the land element on urban housing prices and concludes that the land element has little impact. Liu et al. (2018) employ this model to assess the contribution of the land factor input to nonagricultural GDP growth in China, focusing on the differences between the eastern, central, and western areas of the country [53]. Montalbano and Nenci’s (2022) study also shows that selecting the land component as the key variable in the Cobb–Douglas output analysis is an acceptable choice that does not undervalue the amount to which the land factor contributes to output outcomes [54].

Many studies have been conducted on the role of the land element in shaping urban economic growth, which has laid a strong foundation for proposing the rational use of land resources for the orderly promotion of sustainable urban economic growth policies. However, there is a relative lack of studies that theorize the mechanism of the land element on urban economic development at the national level, so it is necessary to re-examine this relationship.

3. Methodology and Variable Selection

3.1. Methodology

The Cobb–Douglas production function model was created by mathematician Cobb and economist Douglas. The Cobb–Douglas production function model has been widely applied in the research of economics [55], environmental sciences [56], management [57], and so on.

Following the literature, we introduce land resources as an element of production distinct from capital and labor in the economic growth model when analyzing the relationship between land and economic growth. According to the classical analysis of the Cobb–Douglas production function in economic growth, we introduce land as an element of production independent of labor and capital and construct a three-element Cobb–Douglas production function where S is the amount of land-element input. The production function including the land element is expressed as:

$$Y=A{K}^{\alpha }{L}^{\beta }{S}^{\gamma }(A\ne 0,\alpha >0,\beta >0,\gamma >0)$$

(1)

We take the natural logarithm of both sides of Equation (1):

$$lnY=lnA+\alpha lnK+\beta lnL+\gamma lnS$$

(2)

If the other input element is constant, the rate of change in the quantity of output caused by a 1% increase in the element is the output elasticity of the element, and if the output elasticity of the land element is denoted by E_S, then we have:

$$E_S=\frac{\mathrm{\Delta }Y}{\mathrm{\Delta }S}\times \frac{S}{Y}\approx \frac{\partial Y}{\partial S}\times \frac{S}{Y}$$

(3)

We take the partial derivative of the land element S in Equation (2):

$$\frac{1}{Y}\times \frac{\partial Y}{\partial S}=\gamma \times \frac{1}{S}\Rightarrow \gamma =\frac{\mathrm{\Delta }Y}{\mathrm{\Delta }S}\times \frac{S}{Y}$$

(4)

From Equations (3) and (4), we obtain γ as the output elasticity of the land element. The simultaneous derivation of both sides of Equation (4) with respect to t yields:

$$\frac{1}{Y}\times \frac{\partial Y}{\partial t}=\alpha \times \frac{1}{K}\times \frac{\partial K}{\partial t}+\beta \times \frac{1}{L}\times \frac{\partial L}{\partial t}+\gamma \times \frac{1}{S}\times \frac{\partial S}{\partial t}$$

(5)

In Equation (5), $\frac{1}{Y}\times \frac{\partial Y}{\partial t}$ is the economic growth rate; $\alpha \times \frac{1}{K}\times \frac{\partial K}{\partial t}$ is the contribution of capital input to economic growth; $\beta \times \frac{1}{L}\times \frac{\partial L}{\partial t}$ is the contribution of labour input to economic growth; and $\gamma \times \frac{1}{S}\times \frac{\partial S}{\partial t}$ is the contribution rate of construction land input to economic growth.

3.2. Variable Selection and Data Sources

Urban economic development is influenced by various factors and it is impossible to exhaust all the elements that contribute to it [58,59]. We choose data for 30 provinces (cities and districts, excluding Tibet, Hong Kong, Macao, and Taiwan because of missing data) across China from 2000 to 2019 to construct a panel-data econometric model. We then empirically analyze the effects of capital, labor, and urban construction land on economic development using the following model:

$$lnGD{P}_{it}={\propto }_{it}+\alpha ln{K}_{it}+\beta ln{L}_{it}+\gamma ln{S}_{it}+{\mu }_{it}\left(i=1,\cdots ,N;t=1,\cdots ,T\right)$$

(6)

where lnGDP_it represents the natural logarithm of GDP at time t in region I, which quantifies the real output of the national economy in that region.

Furthermore, lnGDP_it is the only explained variable in this study, and the rest of the variables are explanatory variables.

The lnL_it represents the natural logarithm of the number of employees in secondary and tertiary industries at time t in region i. It is used to quantify the labor factor input of the region in that year.

The lnS_it index expresses the natural logarithm of urban construction land area in the ith region at time t. It is designed to identify the input of the land element in the region. Notably, considering that we want to identify the actual economic contribution of urban construction land to cities, the area of urban built-up areas is thus chosen as the variable to measure land-element inputs in this work. The urban built-up area is the area within a city administrative district that has been developed and constructed in a piecemeal manner, which may better represent the actual input of the land element in urban development.

Likewise, lnK_it represents the natural logarithm of fixed asset inputs at moment t in the ith region to quantify the number of capital factor inputs in the region. In economics, capital refers to the amount of investment that plays a role in the process of national production creation, and capital data are generally quantified using capital stock. Since there are no aggregate capital stock statistics in China, we adopt the perpetual inventory method pioneered by Goldsmith in 1951 and integrate the research and applications of other Chinese scholars [60] to calculate the physical capital stock based on capital flow data. The expressions are as follows:

$$K_t=\left(1-\delta \right)K_{t-1}+I_t$$

(7)

where K_t and I_t are the capital stock in period t and current-year investment, respectively; K_t−₁ is the capital stock in period t−1; and δ is the geometric depreciation rate. The current-year investment in fixed assets is chosen as the current-year investment, and the geometric depreciation rate is estimated for the provincial physical capital stock, which we set at δ = 9.6% [60]. The capital stock in the base period is based on the international common method:

$$K_{0=}{I}_0/\left(g+\delta \right)$$

(8)

where g is the average annual growth rate of real investment in the sample period.

All data in this report are from the China Urban Statistical Yearbook 2000–2019, the China Urban Construction Statistical Yearbook 2000–2019, and the provincial statistical yearbooks; the descriptive statistics are shown in

Table 1. Descriptive statistics.

Variable Type	Variables	Variable Explanation	Average	Max.	Min.	Std. Dev.
Explained variables	Economic growth(Y)	GDP (RMB 108)	16,112	11,060	117	17,758
Explanatory variables	Capital element (K)	Total value of fixed assets (RMB 108)	31,462	220,517	50	38,357
	Labor force element(L)	Number of people employed in secondary and tertiary industries (104 people)	240	1214	14	187
	Land element (S)	Construction land area (km2)	1369	5896	76	1016

.

4. Empirical Analysis and Results

4.1. Data Tests

Since the time-series data may lead to the pseudo-regression phenomenon, it is necessary to conduct smoothness tests on the data. There are many methods for testing the unit root of panel data, including the LLC test, IPS test, Fisher–ADF test, and Fisher-P test. To overcome the bias of using a single test method and to ensure the robustness of the results, we used the LLC, IPS, and Fisher–ADF tests to conduct unit root tests on the data for the following variables: lnY_it, lnK_it, lnL_it, and lnS. The results show that the variables lnY_it, lnK_it, lnL_it, and lnS_it can be regressed for the analysis. The specific results are shown in

Table 2. Tests for smoothness of variables.

Variables	lnYit	lnKit	lnLit	lnSit
LLC Inspection	−11.525	−12.213	−11.014	−9.145
	(0.0001)	(0.0002)	(0.0001)	(0.0003)
IPS Inspection	−6.008	−4.686	−11.428	−8.188
	(0.0002)	(0.0000)	(0.0002)	(0.0001)
Fisher–ADF Inspection	135.661	227.472	223.796	175.865
	(0.0002)	(0.0002)	(0.0000)	(0.0004)

.

4.2. Results

4.2.1. Element Output Elasticity Analysis

The output elasticity of element of production is the degree to which changes in element of production respond to changes in output. This reflects the demand for different elements of production for output and the importance of different elements in the production. Before estimating the panel model, it is necessary to determine the form of impact and the model form. The Hausman test results were used to determine the form of impact by choosing a random-effects model or a fixed-effects model. The original hypothesis of the Hausman test is that individual effects are not correlated with the explanatory variables in the random-effects model; if the original hypothesis is accepted, then the random-effects model should be chosen; otherwise, the fixed-effects model is used. The cardinality statistic value of the Hausman test is 94.877, and the corresponding p-value is 0.0001; therefore, the test results reject the original hypothesis and it is more appropriate to use a fixed-effects model. Next, it was essential to determine the correct form of the model. There are three forms of panel models: variable coefficient models, variable intercept models, and mixed models. The specific model to be selected can be judged by calculating the F-statistic. The sum of squared residuals obtained after estimating the variable coefficient model, variable intercept model, and mixed regression model are S₁, S₂, and S₃, respectively; N is the number of cross-sections; T is the number of periods, and k is the number of explanatory variables. The models are as follows:

$$F1=\frac{\left(S_2-S_1\right)/\left[\left(N-1\right)k\right]}{S_1/\left(NT-N\left(k+1\right)\right)}~F[\left(N-1\right)k,N\left(T-k-1\right)$$

(9)

$$F2=\frac{\left(S_3-S_1\right)/[\left(N-1\right)\left(k+1\right)}{S_1/\left(NT-N\left(k+1\right)\right)}~F[\left(N-1\right)\left(k+1\right),N\left(T-k-1\right)$$

(10)

The regression estimation of each model yields S₁ = 0.268, S₂ = 1.985, and S₃ = 8.568, where N = 30, T = 20, and k = 3. This results in the calculation of F₁ = 5.576 and F₂ = 23.885. The values of F₁ and F₂ are greater than the critical values corresponding to the 5% significance level; thus, the variable coefficient model should be selected for estimation.

Considering the regional differences in the estimation results, we divide the 30 provinces and administrative regions of China into three major regions—the eastern, central, and western regions—based on the National Bureau of Statistics. We then use Eviews to analyze the elemental output elasticity of the regions by applying the variable coefficient model.

Considering that the eastern, central, and western regions of China have varying degrees of economic development and notably diverse resources, we propose that the amount to which land-element inputs impact economic growth may vary among areas. For this reason, we further investigate the land-element contribution rates of the three main regions in China based on the study of the national rate. The results reveal that the output elasticities of all three elements are positive. Therefore, all elements can effectively promote the city’s economic growth. The capital element has the largest output elasticity (i.e., every 1% of capital input can create 0.482% of overall economic growth). Capital plays an important role in economic growth, mainly because China has always considered investment as the primary means to drive economic growth, which contributes to the large output elasticity coefficient of capital. The land has the smallest output elasticity coefficient (i.e., for every 1% increase in the land element, the entire economy will grow by 0.306%). Against the background of larger land finance, the contribution of land is minimal; we believe this is due to the lower share of land-factor inputs compared to total capital inputs in economic and social development.

We observed regional variations in the impact of land-element inputs on urban economic expansion. The results for the eastern region show the lowest land-element elasticity coefficient, and land sprawl is no longer efficient for economic growth. The highest land-element elasticity coefficient is found in the central region of China, where every 1% increase in land-element input is associated with 0.229% growth in the entire central economy. Consequently, when combining internal and external factors, the central region needs a large amount of land to achieve economic expansion. The western region has the lowest output elasticity; each 1% increase in land-element input can only create 0.155% economic growth (

Table 3. Table of element output elasticity coefficients.

Variables	National	East	Middle	West
K	0.482 *** (46.314)	0.608 *** (40.779)	0.456 *** (33.875)	0.436 *** (22.864)
L	0.324 *** (12.148)	0.217 *** (13.574)	0.315 *** (15.909)	0.428 *** (18.965)
S	0.306 *** (9.548)	0.176 *** (5.583)	0.229 *** (6.029)	0.155 *** (5.179)
R2	0.958	0.942	0.924	0.935

Note: *** represent the significance of the parameters at 1% confidence levels.

).

4.2.2. Contribution Rate Analysis of Production Element

The contribution rate of element of production is measured as the share of output derived from the inputs of element of production to the volume of total economic output. We estimate the output elasticity coefficients of each productive factor to further calculate the contribution of different factors to economic growth in eastern, central, and western China from 2000 to 2019.

We were surprised to find that, nationally, the contribution of capital input to economic growth reached 52.389%, the highest factor contribution, followed by the contribution of labor input, at 16.715%. The lowest contribution of land input was 6.835%, consistent with the output elasticity coefficients of the three elements.

In the eastern, central, and western regions of China, consistent with our initial hypothesis, there are substantial differences in the contributions of capital, labor, and the land element to the economy. The main underlying reasons for these differences are the different levels of economic development in the three major regions. Nevertheless, in terms of development dynamics, we believe that China’s development status fits the investment-based growth model, which means that the capital element makes the highest contribution to urban economic development.

It was surprising to find that the central region has the highest land-element contribution rate, at 9.135%. The eastern region has the lowest; each 1% increase in land input drives only 4.431% of economic growth. The western region ranks in the middle, with a land contribution rate of 6.337%, a result that also exceeds our expectations. This indicates that the impact of land on economic growth is influenced by the level of regional economic development. The eastern region has the highest level of development and a high degree of utilization of the land element, so land has ceased to be the main driver of economic development. The central region, by its own development and undertaking the industrial transfer from the east, is characterized by the rapid advancement of industrialization and urbanization, so the demand for the land element in the central region is larger. With the deepening of the western development strategy and the undertaking of related industries in central and western regions, it is not difficult to find that the land element plays an increasingly important role in the economic growth of the western region (

Table 4. Comparison of element contribution rates.

Category	Variables	National	East	Middle	West
Contribution rate of each element	K	52.389	54.039	61.353	58.642
	L	16.715	15.437	8.157	10.483
	S	6.835	4.431	9.135	6.337
	A	24.060	26.092	21.356	24.539

).

4.2.3. Land-Element Contribution Rate Analysis

In China, there are historical disparities in urban land use planning and policies, which indicates that the reality of various historical times has put distinct constraints on policies. For example, during the 12th Five-Year Plan period, Shanghai banned the growth of new construction land. To facilitate a comparative analysis of the time variation of land input, we divide the planning period from the 10th Five-Year Plan to the 13th Five-Year Plan and calculate the land-element contribution rate of each province (city) at different time periods.

Over the entire planning period, we observed that cities with generally high contribution rates of land inputs to economic growth include Beijing, Shanxi, Jilin, Heilongjiang, and Henan; the contribution rates in Qinghai, Ningxia, Xinjiang, and Yunnan are generally low. For most provinces (cities) in the eastern region, the contribution rate of the land element to economic growth first rises, then falls, with the turning point appearing during the 11th Five-Year Plan. In the past two decades, the eastern region has been fighting to achieve rapid growth of the national economy, but due to the insufficient national control of the rational use of urban land, most cities rely on large and disorderly urban expansion to achieve high economic growth. Consequently, the contribution of land to urban economic growth is relatively high. However, we also notice that the expansion of urban land has offered room for economic development but, unhappily, it has also given birth to exceptional human–land conflicts. [61]. When we concentrate on the central and western areas, we discover that the land-element contribution rate shows a tendency of varying yearly, and the growth rate is not constant. Specifically, the contribution of the land element in the central region has increased quicker than in western regions. We were shocked to see that, throughout the 12th Five-Year Plan period, the contribution of the land element to urban economic development in most provinces in the central area was even larger than in the eastern region. As for the western area, the efficiency of the land element in driving urban economic growth has progressively been evident, demonstrating a slightly increasing trend from the 10th Five-Year Plan to the 13th Five-Year Plan (

Table 5. Land element’s contribution to economic growth.

Region	Fifteen	11th Five-Year Plan	12th Five-Year Plan	13th Five-Year Plan
Beijing	6.793	7.924	5.435	3.214
Tianjin	4.344	5.542	4.172	3.582
Hebei	3.913	4.671	3.385	3.031
Shanxi	4.891	6.921	7.542	8.394
Inner Mongolia	2.943	4.314	4.861	5.342
Liaoning	3.701	5.792	3.983	3.751
Jilin	4.353	7.210	7.852	8.654
Heilongjiang	4.562	5.182	8.274	9.044
Shanghai	5.862	6.634	4.981	3.062
Jiangsu	5.021	6.921	4.635	3.965
Zhejiang	4.993	6.735	5.482	3.811
Anhui	4.361	7.842	8.436	9.045
Fujian	6.022	7.465	5.892	3.552
Jiangxi	4.161	5.372	7.454	8.946
Shandong	4.463	5.063	5.832	3.977
Henan	4.824	6.033	7.835	8.582
Hubei	4.943	5.931	8.591	9.651
Hunan	4.523	6.744	7.633	8.945
Guangdong	5.434	6.723	4.535	3.662
Guangxi	2.943	4.314	4.862	5.346
Hainan	4.991	5.735	4.686	3.812
Chongqing	3.040	4.036	4.492	5.036
Sichuan	3.941	4.497	4.984	6.341
Guizhou	3.593	4.823	5.831	6.815
Yunnan	2.892	4.195	4.855	5.932
Shaanxi	4.344	5.311	6.302	5.926
Gansu	4.592	5.195	5.984	6.272
Qinghai	3.983	4.932	5.532	5.381
Ningxia	3.482	4.016	4.494	6.315
Xinjiang	2.844	3.674	4.571	4.942

).

We conclude from the research findings that the land element has contributed to the growth of China’s urban economy from the beginning of the 21st century to the present. Previous research has found that Chinese cities are overly reliant on land for development and economic growth [62], that collecting property transaction fees provides the government with rapid economic benefits, and that land financing accounts for the majority of local fiscal revenue [63]. However, our findings show that prior research overestimated the role of urban land in city development to some extent. The maximum contribution value of land to urban growth is 9.651, implying that capital and labor, rather than land, drove China’s city development. The spatial–temporal inconsistencies imply that land, whether undeveloped or developed, plays an equal role in city growth. Without a doubt, the increased contribution across comparable underdeveloped provinces demonstrates a growing interest for land. Furthermore, the declining trend in developed provinces does not mean that land contributes less, but rather that it has contributed more.

4.2.4. The Convergence Analysis of the Contribution Rates of the Land Element

It is worth exploring whether the differences in the land-element contribution rates of different regions show a decreasing trend along with national economic development. Therefore, this paper conducts a convergence analysis of land-element contribution rates in different regions of China. There are usually three types of convergence analyses: σ convergence, absolute β convergence, and conditional β convergence [64]. σ convergence is used to judge whether there is a convergent effect based on the trend of land-element contribution rates in each region; if the standard deviation has a decreasing trend, this indicates the existence of σ convergence; otherwise, it is divergence. Absolute β convergence means that the land-element contribution rate in each region will converge to the same steady-state level. Over time, the less developed regions gradually catch up with the developed regions and reach the convergence state of stable development at the same rate. Conditional β convergence means that the land-element contribution rate of each region will converge to different steady-state levels. In short, both absolute β convergence and conditional β convergence meet the steady-state level, but the land-element contribution rate of each region in absolute β convergence is the same, while in conditional β convergence it differs.

(1)

σ convergence test. We know from existing research [64,65,66] that the standard deviation is used to calculate whether there is convergence in the whole country and the eastern, central, and western regions. The statistical method from Lichtenberg (1997) is used to test the σ convergence as follows:

$$\frac{{\hat{\mathsf{\sigma }}}_{T0}^2}{{\hat{\mathsf{\sigma }}}_T^2}~FN-2,N-2$$

(11)

where the numerator is the variance of the land-element contribution at the beginning, the denominator is the variance at the end, and N is the number of cross-sections in the sample.

Table 6. Results of σ convergence test for the whole country and different regions.

Test Statistic	National	East	Middle	West
Lichtenberg values	0.935	7.263	0.450	0.126
Threshold value (1% significance level)	2.431	2.943	6.153	4.453

shows the test results.

The results in Table 6 show that there is a σ convergence trend in the land-element contribution rate in the eastern region, but none at the national level or in the central and western regions. Its standard deviation fluctuates widely, indicating that the development levels of provinces and cities (regions) are not stable. This non-stability of economic development suggests that there are cognitive differences in the sustainability of land-element utilization in different regions. The variability of geographic policies, the different degrees of utilization of land resources, and the benefits of utilization lead to fluctuations in the contribution rate of the land element across the country. Although there are differences in economic bases and in resource and environmental endowments, as well as inconsistent development patterns and rates among provinces and municipalities (regions), such differences have not stabilized over time, and differences across provinces still exist. The development synergy among the provinces (cities) in the eastern region is high, the regional linkage is strong, and the contribution of the land element is in a more balanced development state.

(2)

Absolute β convergence test. In this paper, absolute β convergence is invoked to investigate whether the land-element contribution rates of different regions converge to the same steady-state level. At present, the contribution rates of the land element in the whole country and in the eastern, central, and western regions are different. When the absolute β convergence of land-element contribution rates across regions is measured, we observe a “catching-up effect” [67] from provinces with low land-element contribution rates to provinces with high land-element contribution rates. This “catching-up effect” will eventually lead to the same steady-state equilibrium level of land-element contribution across regions. We measure the absolute β convergence of land-element contribution rates in the three major regions and set the model as follows:

$$\frac{1}{T}\mathit{ln}\left(\frac{S_{i,t}}{S_{i,0}}\right)=\alpha +\beta \mathit{ln}{S}_{i,0}+\epsilon$$

(12)

where S_i,0 and S_i,t denote the contribution of the land element in the base and end periods of province i, respectively, and T represents the time span; $\alpha$ is a constant, $\beta$ is the absolute convergence coefficient, and $\epsilon$ is the random error term. If $\beta$ < 0 and significant, there is absolute convergence, which further indicates that provinces with lower land-element contribution rates have a “catch-up effect” on provinces with higher land-element contribution rates. Moreover, the land-element contribution rates of all regions converge toward the same growth rate.

The results in

Table 7. National and regional absolute $\beta$ convergence estimation results.

Coefficient	National	East	Middle	West
β	−0.048 **	−0.043 **	−0.035 **	−0.068
	(−5.13)	(−1.06)	(−8.71)	(−2.21)
α	0.002	0.003	0.002	0.003
	−3.970	−1.320	−2.680	−1.760
R2	0.496	0.535	0.915	0.137
N	30	11	11	8

Note: The numbers in parentheses below the parameter estimates indicate t-test values. ** represents parameter estimates significant at the 5% confidence level.

show that from the national perspective, the β values of provincial land-element contribution is less than zero, which indicates that there is absolute β convergence in the national provincial land-element contribution (i.e., the growth gap between provinces/municipalities is narrowing). For the three major regions, the β values of the eastern and central regions are less than zero, so there is an absolute β convergence effect in the eastern and central regions, but not in the western region. Thus, there is a “catch-up effect” of convergence of land-element contribution rates from lower provinces to higher provinces, as well as in the eastern and central regions. The “catch-up effect” among provinces is weaker in the western region because of the weak development foundation, the large differences in resource endowments, and the different development patterns across provinces. At the same time, although there are differences in the contribution rates of the land element across the country and the three regions, such differences will tend to advance together in different stages of urban economic development. Although there are still differences among provinces and cities, along with the continuous promotion of the national economic development strategy, the synergy among regions is increasing, which is bound to further reduce the inter-regional differences. This explains the absolute β convergence in the national, eastern, and central regions.

(3)

Conditional β convergence test. According to existing research, the conditional β convergence model is set as follows:

$$d_{it}=\mathit{ln}{S}_{it}-\mathit{ln}{S}_{it-1}=\alpha +\beta ln{S}_{it-1}+{\epsilon }_i$$

(13)

For ease of analysis, Equation (13) is presented as:

$$\mathit{ln}{S}_{it}=\alpha +\left(\beta +1\right)\mathit{ln}{S}_{it-1}+{\epsilon }_i$$

(14)

where $\alpha$ is the constant term; lnS_it is the logarithm of the land-element contribution rate of the ith province (city) in period t, and ε_it is the error term. The equation indicates the existence of conditional β convergence if (β + 1) is negative and significant.

The conditional β convergence model used is the panel-data model, and the Hausman test results for the panel data have no significant p-values, indicating that the fixed-effects model is better than the random-effects model. Therefore, this paper uses the fixed-effects model for analysis when conducting the panel-data regression; the results are shown in

Table 8. Conditional β convergence test for land-element contribution.

	National	East	Middle	West
α	0.081	0.184	0.053	0.036
	(1.065)	(1.263)	(0.548)	(0.298)
β + 1	−1.278 ***	−1.239 ***	−1.201 ***	−1.149 ***
	(−13.956)	(−12.067)	(−18.274)	(−11.063)
Adjusted R2	0.702	0.733	0.715	0.674

Note: *** represents the significance of parameters at the 1% confidence levels. T-test values are in parentheses.

.

The findings show that the β + 1 coefficient of all regions is negative and significant (p < 0.01). This indicates that there is a significant conditional β convergence effect on the land-element contribution rates of the country and the three regions. It also suggests that the land-element contribution rates of the east, central, and west will converge toward their steady-state levels over time. It is because of the different steady-state levels in each region that the contribution rates of the land element across regions remain continuously differentiated.

5. Conclusions and Discussion

5.1. Conclusions

In summary, based on the Cobb–Douglas production function, we analyze the contribution of land-element inputs to urban economic growth and its spatial and temporal evolution in the urban expansion of Chinese provinces (cities) during the period from the 10th to the 13th Five-Year Plan. We also conduct a convergence analysis on the contribution of the land element. The following conclusions are drawn.

The model of urban economic development including the land element has strong theoretical and practical explanatory power. China’s urban economic development is the result of the joint actions of capital, labor, and land. From the perspective of “city management” theory, the land element, together with the capital and labor elements, constitutes the basic elements of modern urban production. Moreover, the theoretical logic of urban economic development can be best explained by the Cobb–Douglas production function.

The contribution of the land element to urban economic development may be overestimated in existing studies, and the spatial and temporal differences are characterized here. In terms of the degree of contribution of the three major elements to urban economic development, the output elasticity coefficients of capital, labor, and land are 0.4823, 0.3243, and 0.3059, respectively. The respective contribution rates are 52.3891%, 16.7153%, and 6.8353%. Moreover, the contribution rate of land in the eastern region shows a trend of first increasing and then decreasing. In the central region, it increases gradually and this has occurred more rapidly in recent years. The contribution rate of land in the western region shows a slowly increasing trend, but the total contribution rate is small. Therefore, studies of land financing and urban sprawl may, to a certain extent, obscure the objective role of the land element in urban economic development.

There are different convergence effects of land-element contribution rates in China, including the eastern, central, and western regions, and the national and provincial regions have developed toward their respective steady-state levels. First, there is a σ convergence trend in the land-element contribution rate in the eastern region, but not nationally or in the central and western regions. There is an absolute β convergence effect nationally and in the eastern and central regions, but not in the west. Finally, there is a significant conditional β convergence effect in the land-element contribution rate nationally and in the three regions, and the rate will converge toward a steady-state level.

5.2. Discussion

As a result of a new series of scientific and industrial revolutions, our world has changed dramatically in recent years. Given the complicated and volatile international political and economic environment, China was committed to developing a development pattern by 2020 in which the bulk of the components are recycled locally. Undoubtedly, stringent policies or plans are required to manage land resources; yet, land use should also be tailored to local conditions. We engaged in considerable discussion about condemning the practice of obtaining large quantities of money quickly via land-transfer fees, but the next step is to reconsider how we use urban space. In the current context of slowing economic growth, rethinking the role of land deserves serious consideration, and we cannot overlook the fact that central and western areas take a long time to promote economic growth patterns. In this scenario, the government should think about how to support continuous energy for regional development, and it is time to reassess land’s function in urban development as a foundation for leveraging many aspects of city administration.

Our findings have policy implications. First, the central government should adopt varied land-supply policies based on regional development levels, with a focus on promoting economic growth by building land in the central and western regions. Second, the government must design a more scientific and visionary land-supply strategy to avoid inefficient use of urban construction land. Third, it will boost the economy of cities by sensibly distributing construction land for industrial development and public services. Land types such as industrial land, commercial land, residential land, and public administrative land have the potential to have a short-term driving effect. Fourth, to bring out the vibrancy of all parts of city management, a complete monitoring mechanism with a robust land-supply benefit evaluation system is required for this active land-supply strategy.

There are certain limitations to our research. On the one hand, China has 283 cities with significant regional and spatial variation in terms of natural resources and social development. This research seeks to reveal the urban growth mechanism on a macroscopic size; if we focus on a municipal scale, the production function model will reveal more specifics. On the other side, this article used urban construction land as a variable from a statistics yearbook; nevertheless, using remote sensing image data in the analysis will yield a more accurate result.