3. Research Method
3.1. VECM Model
According to the conventional method of the VAR model, the stability of each time series variable needs to be checked before the model is built. If some time series variables are not stable, but there is a cointegration relationship, the simple VAR model will lose a large amount of useful information, resulting in errors in the results. Moreover, the VAR model only measures the short-term fluctuation relationship between variables, ignoring the long-term equilibrium relationship, thus affecting the determinable coefficient of the VAR model. It is necessary to transform an unstable time series into a stationary sequence by a differential method to establish a classical regression analysis model. To address this issue, Engle and Granger combined the cointegration and error correction models to establish the VECM model. Currently, the VECM model has become the standard analytical tool for time series measurement [
13]. The formulas for the VAR model and the VECM model are as follows:
First, create a
model:
In the formula, ; is the model variable; is the -order lag item of the model variable; represents the estimated coefficient of ; is an exogenous variable; represents the estimated coefficient of ; is a random disturbance project.
If the variable
in Equation (1) is unstable and there is a cointegration relationship between the variables, then the cointegration change can be used to obtain the VECM model:
In the formula, ; is an error correction term that reflects the long-term equilibrium relationship between variables. is the error correction coefficient, which reflects the speed at which the automatic correction mechanism adjusts the variable to the equilibrium state when the variable deviates from the long-term equilibrium. reflects the impact of short-term fluctuations of variables on other variables. The advantage of the cointegration-transformed VECM model is that all variables can be used as endogenous variables, avoiding endogeneity problems. On the other hand, the VECM model can simultaneously estimate the long-term equilibrium relationship between variables and the short-term dynamic error correction process. This paper uses Eviews 10.0 metrology analysis software to consider the interaction mechanism among urban expansion, economic development and population growth from the long-term and short-term perspectives on the basis of cointegration analysis.
3.2. Impulse Response Function
Cointegration analysis only shows whether there is a long-term equilibrium relationship between variables and does not show how the disturbance of a variable affects the whole system or the comprehensive response of each variable on these disturbances. The impulse response function can be used to measure the impact of a standard deviation shock from a random disturbance item on the current and future values of endogenous variables. Therefore, it is possible to more intuitively describe the dynamic interactions and effects between variables in order to obtain information such as the positive and negative direction, adjustment time lag, and stability process of the response generated by the impulse of the system [
46]. In this paper, the two-variable impulse response function is taken as an example to illustrate its implementation process. The planning formula is
In the formula,
;
,
,
,
are parameters; Disturbance item
. Assume that the white noise vector has the following properties:
Assume that the above system starts from
and sets
. It is assumed that the disturbance item
are set in the zeroth phase, and the subsequent values are all equal to 0. The initial given disturbance item is continuously transmitted in the system. After iterative calculation, the following can be obtained:
This result is called the response function of
caused by the pulse of
. Similarly, the following can be obtained:
This result is called the response function of caused by the pulse of . If a disturbance item are given when , the response function of and the response function of which are caused by the pulse of can be obtained. The above impulse response process can directly capture the effect of the system on a particular pulse.
3.3. Variance Decomposition
The impulse response function is able to capture the dynamic influence path of a variable’s impulse on other variables. The purpose of variance decomposition is to analyze the contribution of each structural pulse to changes in endogenous variables (usually expressed in terms of variance). Therefore, the relative importance of different structural pulses can be more clearly evaluated. The intensity of its influence is expressed by the relative variance contribution (RVC). The formula is as follows:
According to VMA (∞), Sims proposes a variance decomposition method for quantitatively calculating the influence relationship between variables [
47]:
In the formula,
,
, the content in parentheses is the sum of the influence of the
-th disturbance item
on the variable
from the past to the present. In the case of assuming that the disturbance term
has no sequence correlation, the variance of Equation (7) can be obtained as
In the formula,
. Assuming that the covariance matrix of the disturbance item vector is a diagonal matrix, then the
of the above variance is summed to obtain the variance of the variable
as
In the formula,
. The variable
can be decomposed into
unrelated impacts. To measure the different contribution degree of each disturbance item to
, this paper uses RVC to calculate. According to the relative contribution of the variance of the
variable to the variance of
as the scale for observing the influence of the
-th variable on the
-th variable. In practice, if the model satisfies the stationary condition, only limited
items are needed. The formula for RVC is
In the formula, the larger is, the greater the contribution of the -th variable to the -th variable. In contrast, the smaller is, the smaller the contribution of the -th variable to the -th variable.
4. Indicator Selection and Data Sources
4.1. Indicator Selection
This paper mainly examines the interactive relationship among the three elements of urban expansion, economic development, and population growth. Based on the availability and quality of the data, this paper selects the following three variables:
(1) Built-up area (BUIL). The unit is km2. According to the regulations of the National Bureau of Statistics of China on the statistical division of urban and rural areas in 2008, the urban area refers to the actual construction of the municipal, district, and municipal government resident areas and connected to the residents committee and other areas. The China Urban Statistical Yearbook currently provides two indicators for the area of urban built-up areas and the total area of urban areas. The urban built-up area refers to the land that has been requisitioned within the municipal area as well as the non-agricultural production and construction area that has been constructed and developed in practice. These areas include urban contiguous sections as well as urban construction land with well-established municipal utilities, the sites of which are scattered around the city. Therefore, the urban built-up area is consistent with the definition of the city. This indicator is closer to the nature of urban entities in China. Therefore, this paper uses the change in the area of the built-up area to characterize urban expansion.
(2) Gross domestic product (GDP). The unit is 10
4 yuan. This paper uses GDP to reflect the level of urban economic development. To eliminate the impact of price factors on the analysis, the consumer price index (cpi) was used to deflate the nominal GDP of 1980–2016, and the real GDP of each year was obtained. The calculation formula is
(3) Non-agricultural population (POP). The unit is 104 people. The population can be divided into urban population and rural population according to the division of residence. According to the current household registration system, the population can be divided into agricultural and non-agricultural populations. In the urban, the urban population is often higher than the non-agricultural population, because a considerable number of people with agricultural hukou live in urban. However, due to economic factors (differences in urban and rural consumption levels), institutional factors (hukou system), and psychological factors (land attachment), the agricultural population that has moved to the urban has the possibility of returning to the countryside. Moreover, the current urban population statistics in China are not continuous, resulting in poor comparability of urban population in time and region. Therefore, this paper selects the non-agricultural population as a representative indicator of the urban population because the statistics of the non-agricultural population are continuous and the data are richer.
4.2. Data Sources
The basic data of this study are mainly from the “China Statistical Yearbook (1994–2017)”, “China City Statistical Yearbook (1994–2017)”, “China Urban Construction Statistical Yearbook (1994–2017)”, and the China City Database in EPS Data Platform.
In order to eliminate the influence of dimension, heteroscedasticity and outliers on the model as much as possible, and to make the degree of influence of each factor more comparable, all variables are logarithmized. The properties of the data will not change as a result of using the natural logarithm of the time series data. The processed variables are named , , .
6. Discussion
This study reveals the interactive relationship between urban expansion, economic development and population growth. It can provide reference for the Chinese government to guide the rational expansion of urban land use, promote sustainable economic development, and coordinate the development of population urbanization and land urbanization. Although this paper has made clear conclusions, there are still some problems that need to be solved and improved.
(1) This study focuses on the interaction between quantity, urban expansion, economic development, and population growth. In the theoretical analysis and model construction, the discussion of factors other than the three is slightly insufficient, and there are certain limitations. Urban expansion not only affects the number of economic development, but also affects the quality of economic development through industrial structure upgrading, urbanization, ecological environment, economies of scale, investment in education, and investment in science and technology. For example, with the further expansion of the urban, the negative impacts of insufficient cultivated land, food crisis, and urban diseases will reduce the quality of economic development. For example, Yue [
55] believes that due to the limitations of data, few scholars have explored the effects of rapid urban expansion in China from the perspective of coordinated development of economy and environment. Yue studied urban expansion in Shanghai and examined the dynamic relationship between economic development and environmental consequences. The results show that the imbalance between economic development and environmental development in Shanghai is mainly attributed to four institutional factors: (I) the role of government; (II) multi-level urban planning system; (III) land market reform; (IV) economic restructuring. In addition, since the reform and opening-up, land urbanization has been significantly faster than population urbanization. The Chinese government emphasizes the importance of giving full play to the role of market mechanism in the process of urbanization. However, the urban–rural segregation policy based on the household registration management system is often seen as a major obstacle to the urbanization process of the population [
56]. Moreover, population growth can stimulate capital demand and thus promote economic growth. However, it will also cause the consumption rate of non-renewable resources and the continuous increase of the environmental pollution index. For example, Liu [
57] believes that encouraging green and sustainable population urbanization can promote economic growth without sacrificing the environment. There are many studies in the academic community that use the urban expansion, economic development and population growth as the dependent variables to conduct driving force analysis, and many worthy findings have been obtained (see
Table 1). Therefore, in the future research, a variety of factors should be included in a unified empirical analysis framework. In order to supplement and improve the discussion of the relationship between the three, establish a long-term equilibrium relationship between the three, and form a coordinated development mechanism.
(2) Although the VECM model can examine the dynamic characteristics between variables, the structural relationship between variables is difficult to visually observe. Because complex systems are made up of several interacting subsystems. When a certain factor changes, not only the system itself is affected, but also the operation of other systems will be triggered. The impulse response function is an effective way to implement this function. The advantage of the impulse response function is the ability to visually characterize the dynamic interactions between variables and their effects. The analysis combined with variance decomposition technology can further demonstrate the impact of urban expansion, economic development and population growth on each other.
Section 5.2 shows that the improvement of the quality of economic development can promote the intensive use of urban land through the improvement of technological efficiency and technological progress. Technological advances can change the elasticity of substitution between elements, increase the intensity of land use, and change the structure of land use, thereby inhibiting urban expansion [
66]. Improvements in technical efficiency can inhibit urban expansion through economies of scale, improved level of management, and the development of rational land systems. Therefore, the Chinese government should formulate and improve policies, create a fair institutional environment, encourage technological innovation, and actively implement technology introduction. On the other hand, the increase in urban population is a major factor in the urban expansion. Moreover, the imbalance of the proportion of population urbanization and land urbanization leads to the decentralization of urban form and layout, showing a trend of low-density growth. Therefore, it is necessary to improve the coordination level of population urbanization and land urbanization, and then achieve intentional urban growth.
However, the drawback of the VECM model, the impulse response function, and the variance decomposition technique is that there are few variables involved, and there is a problem of insufficient information. Urban expansion, economic development, and population growth are mutually causal relationships. Therefore, when assessing the impact of economic development and population growth on urban expansion, economic development, and population growth are endogenous variables. Therefore, the estimator obtained by the ordinary least squares method for regression analysis are biased and have no causal inference. Although the VECM model can solve the endogeneity problem to some extent, it has the problem of missing variables. The instrumental variable method has unique advantages in solving endogenous problems and in causal inference in social sciences. Therefore, in future research, in order to accurately estimate the impact of economic development and population growth on urban expansion, scholars can find suitable instrumental variables for economic development and population growth. This instrumental variable can explain changes in economic development and population growth, but apart from the two specific pathways mentioned above, they do not directly or indirectly affect urban expansion. If the indirect impulse of the selected exogenous variable on urban expansion can be statistically proven to be significant, then the true magnitude of the impact of economic development or population growth on urban expansion can be derived. At present, few scholars use the instrumental variable method to explore this research issue, which can become a research direction in the future.
7. Conclusions and Policy Implications
7.1. Conclusions
Based on data of urban construction land, economic development and population growth in China from 1980 to 2016, this paper first examines whether there is a long-term equilibrium relationship among the three factors by using a cointegration test. Based on the VECM model, the interactive mechanism and dynamic effects among the three are studied using the impulse response function and the variance decomposition model system. The conclusions are as follows:
(1) The sequences of urban expansion, economic development, and population growth in China are all first-order single sequences. In the long run, the three can maintain a balanced state and have a stable cointegration relationship. From the perspective of the two VECM models, the coefficient of economic development and population growth is negative. This result shows that when economic development and population growth show a short-term deviation, the reverse correction mechanism of the long-term equilibrium trend deviation of the two variables can pull the two back to an equilibrium state with strengths of −0.17703 and −0.02174, respectively. Therefore, this mechanism can play a strong adjustment role. However, urban expansion is a phenomenon of imbalance and deviation in the short term; when urban expansion deviates from the equilibrium state, the error correction mechanism will cause the deviation to further expand.
(2) Based on the impulse response function among urban expansion, economic development and population growth, it can be seen that the impact of a standard deviation shock of urban expansion on economic growth has a positive effect of continuous fluctuations and is a powerful force. The impact of a standard deviation of economic growth on urban expansion is relatively small and even has a negative effect. The impulse of population growth on urban expansion has a positive effect overall, and population growth has a certain long-term impact on urban expansion, but the short-term impact is more significant. Urban expansion will cause a rapid increase in population in the short term and will have a long-term positive and persistent impact, showing that there is a mutually reinforcing statistical relationship between urban expansion and population growth. Economic development is highly responsive to population growth. In the long run, population growth has a positive pulse effect on economic growth, and this effect gradually declines after reaching a peak. Conversely, with the gradual increase in the level of economic development, it will have a negative impact on population growth.
(3) The results of variance analysis indicate that urban expansion in China is mainly affected by the contribution of population growth, and it tends to be stable after it increases. The impact of economic development on urban expansion is decreasing and is generally low. Combined with the impulse response function graph, it can be shown that economic development has a certain inhibitory effect on urban expansion, but the suppression intensity is still insufficient. In the short term, the main factor that causes economic development to change is its own factors. However, with the passage of time, urban expansion, and population growth have become the main factors affecting economic development. After the variance decomposition of population growth, half of the predicted variance comes from urban expansion. However, the degree of contribution of economic development is only approximately 10%. This result shows that population growth is mainly affected by urban expansion, followed by the role of population itself, and minimally affected by economic development.
7.2. Policy Implications
Based on the above empirical analysis, this paper proposes the following policy recommendations:
(1) Protect limited land resources in China and promote sustainable urbanization. First, we should accelerate the reform of the land taxation system, adjust the land income distribution policy, rationally distribute the rights and financial power of the central government and local governments, and alleviate the excessive emphasis on economic indicators in the local performance appraisal system. At the same time, we should guide local governments to rationally examine and approve the transfer of commercial and residential land on the basis of ensuring that people have the services to optimize their livelihood and by following the laws of the market, thus abandoning the strategy of raising the price of commercial and residential land to obtain huge land sales revenue. For cities in coastal areas, we should continue to increase industrial integration and use limited land to develop new, highly competitive industries to achieve smart growth in cities and increase tax revenue. This will prevent the government from over-promoting urban expansion for political reasons and to generate fiscal revenues and consequently distorting the allocation of urban land resources. Cities in western China should regulate and rationally use fiscal revenue from transfer payments. Therefore, it is possible to abandon the old pathway of sacrificing land replacement capital for development, achieve intensive development, and alleviate urban expansion.
(2) The traditional economic development model not only wastes land resources, increases environmental pollution pressure, and threatens national food security; but it also causes economic development to lack vitality and motivation. Therefore, the economic growth model should be transformed, and more investment in land resources should be transformed into dependence on technology and capital investment to promote the upgrading and transformation of the industrial structure. First, the government should adopt the intensive use of land as a guiding ideology and prioritize the reuse of existing industrial land (especially inefficient industrial land). At the same time, it is necessary to give full play to the market mechanism and promote the structural reform of the supply side of industrial land so that scarce industrial land can truly serve the development of essential and advanced industries. Therefore, the rational allocation of land resources and the healthy development of the industrial economy can be promoted. On the other hand, the government should focus on promoting the development of emerging industries such as the internet technology industry, biotechnology, and new energy sources. The government should strive to improve the industrial level of leading regional industries and use its true economic value and leadership position to optimize and upgrade the regional industrial structure. In addition, the government should further improve the level of intensive land use and comprehensive land-use efficiency.
(3) Suburbanization is a process in which the surrounding towns assume the functions of the city center. The purpose is to create a reasonable spatial scale through a multi-center pattern, thereby inhibiting the sprawling expansion of the central city. In view of the current mismatch of residential and employment space in the suburbs, we should actively promote the integration and development of suburbs. On the one hand, it is necessary to actively and synergistically promote the suburbanization of housing and employment. This requires uniting the central urban population (that has moved to the suburbs) with employment, as well as moving urban functions to the suburbs. On the other hand, it is necessary to promote the interactive and coordinated suburbanization of the manufacturing and service industries and to reverse the phenomenon of excessive suburbanization, in which the manufacturing and service industries significantly lag behind residential suburbanization or do not match each other. At the same time, due to the sprawl of urbanization, it is easy to build a single type of residential real estate that cannot meet the demands of residents for public service infrastructure and objectively deprives residents of opportunities for health-promoting activities by imposing space restrictions. Therefore, there is an urgent need to explore a people-oriented suburbanization development policy. The formulation of urban planning and public policy requires more consideration of the issue of spatial fairness. It is necessary to rationally allocate the public activity resources of the suburbs according to the needs of residents and to compensate for the lack of urban public amenities caused by commercial capital-chasing interests. These changes will help provide an environment conducive to the physical and mental health of individuals [
67].
(4) Human capital has an important impact on economic development in China. The rational use and development of human capital as well as a better economic system, political system, and education system will help China’s human capital to positively promote its economic development. On the one hand, in the current situation of limited resources, the government should focus on investing in human capital to develop the economy. The government can accumulate abundant human capital through foreign investment, increase education expenditure, and adjusting the educational structure to achieve sustained and stable endogenous economic development. On the other hand, as the economy develops and the industrial structure is upgrading, the requirements for skill-based human capital will also increase. Therefore, the proportion of investment in vocational education can be improved to better serve the further development of the economy. From the perspective of public policy, local governments should continue to increase training intensities for low-skilled labor (including migrant workers), strengthen the combination of training and actual demand in the labor market, and improve the existing training system to improve the efficiency of training funds. These measures will help ordinary workers adapt to the challenges brought about by the upgrading of China’s industrial structure and help enterprises to more smoothly upgrade and transform the industrial structure.