Total Investment in Fixed Assets and the Later Stage of Urbanization: A Case Study of Shanghai

After more than 40 years’ opening-up and reform, China’s urbanization has entered a new type of urbanization. In order to reveal the rule of different infrastructure investments and urbanization relationships, this paper uses Shanghai as a case by applying econometric methods to study the detailed relationship between different indicators from 1990 to 2019. Firstly, we quantify that each variable has a long-term co-integration relationship with urbanization by co-integration test. And we found that the real estate is a main driving force of urbanization while the construction project investment plays an important role in promoting the urbanization rate in the studied period. Secondly, according to the Granger test, our study illustrates that each variable has a bilateral Granger relationship with urbanization while the urbanization rate has more Granger causality impact on the studied variables. Thirdly, based on impulse response test and variance decomposition analysis, we found that urbanization rate with other variables accounts for the majority of the percentage of impacts while the total investment in fixed assets and its three categories contribute a small amount to the urbanization rate. Finally, we propose policy suggestions to strengthen healthy urbanization development in Shanghai.


Introduction
Urbanization research has been a global issue since the first industrial revolution. Urbanization is the result of, for example, the social production reform of the human production method, the way of life, and residential type, and a natural, historical urban social evolutional process of the population centralization and intensification from rural areas to urban areas [1], Urbanization is necessary for social progress and considered an engine of modernization and economic growth [2]. China is undergoing unprecedented urbanization, which we propose is the greatest human-resettlement experiment in world history.
The urbanization of countries or regions differs in, for example, starting period, development speed, and current urbanization rate. However, Ray M. Northam (1979) pointed out that global urbanization can be summarized as an "S" curve [3]. Furthermore, the urbanization rate curve can be divided into two main stages-early and later-according to the acceleration of the urbanization rate growth. Notably, in Figure 1, point A in the urbanization rate curve is an inflection of two stages. In the early stage, the curve is no more than the inflection point and the curve is characterized by acceleration; thus, it can be classified into the starting period and acceleration period. In the later stage, the curve is can be classified into the starting period and acceleration period. In the later stage, the curve is more than the inflection point and changes from an accelerating state to a decelerating state or stationary state, and it can be divided into a deceleration period and stationary period. Chinese cities' urbanization has distinct characteristics. Specifically, after China's opening-up and reform, especially after the 1998 real estate reform, a population shift occurred from rural to urban areas. However, with the development of urbanization, China's economy has a new normal, and its economic growth rate has shifted from high to medium; therefore, China is promoting a "new type of people-centered urbanization" policy to continue the current economic situation [4].
Shanghai is the biggest city in China. Its urbanization rate increased from 58.7% in 1978 to 90.4% in 2019, and after the policy of 1990 Pudong District development was implemented, the Shanghai urban population increased from 13.34 million (1990) to 24.28 million (2019). As is shown in Figure 1, Shanghai's current urbanization state is in a stationary period of the later stage of urbanization.
The growth in the urban population caused substantial demand for basic needs, for example, urban infrastructure for daily life including residential buildings; therefore, the Shanghai government had to use the total investment in fixed assets (i.e., construction project investment, real estate investment, farmers' investment) every year to fulfill the needs resulting from urbanization. In this paper, the total investment in fixed assets is considered an urban infrastructure investment, which is the foundation of a city or, as one historian proposed, "technological sinews" built to fulfill the needs of society [5]. The total investment in fixed assets is the amount of work involved in the construction and purchase of fixed assets in monetary terms and a comprehensive index reflecting the investment scale, speed, proportional relationship, and utilization direction.
Thus, in this context, we aim to determine the influencing mechanism between urbanization and the total investment in fixed assets, which is dominated by the government.
Studies had attempted to explain the mechanism of the urbanization process [2] and the infrastructure investment [6]. For example, Tian et al. (2017) examined the driving forces of Shanghai land use change from the perspectives of state-led growth and bottomup development by analyzing Landsat Thematic Mapper(TM) images and land use maps; they concluded that state-led growth played an important role in the non-agricultural land expansion and that urban planning played a main role in regulating the space to accommodate the migratory population and economic growth [7]. Chinese cities' urbanization has distinct characteristics. Specifically, after China's opening-up and reform, especially after the 1998 real estate reform, a population shift occurred from rural to urban areas. However, with the development of urbanization, China's economy has a new normal, and its economic growth rate has shifted from high to medium; therefore, China is promoting a "new type of people-centered urbanization" policy to continue the current economic situation [4].
Shanghai is the biggest city in China. Its urbanization rate increased from 58.7% in 1978 to 90.4% in 2019, and after the policy of 1990 Pudong District development was implemented, the Shanghai urban population increased from 13.34 million (1990) to 24.28 million (2019). As is shown in Figure 1, Shanghai's current urbanization state is in a stationary period of the later stage of urbanization.
The growth in the urban population caused substantial demand for basic needs, for example, urban infrastructure for daily life including residential buildings; therefore, the Shanghai government had to use the total investment in fixed assets (i.e., construction project investment, real estate investment, farmers' investment) every year to fulfill the needs resulting from urbanization. In this paper, the total investment in fixed assets is considered an urban infrastructure investment, which is the foundation of a city or, as one historian proposed, "technological sinews" built to fulfill the needs of society [5]. The total investment in fixed assets is the amount of work involved in the construction and purchase of fixed assets in monetary terms and a comprehensive index reflecting the investment scale, speed, proportional relationship, and utilization direction.
Thus, in this context, we aim to determine the influencing mechanism between urbanization and the total investment in fixed assets, which is dominated by the government.
Studies had attempted to explain the mechanism of the urbanization process [2] and the infrastructure investment [6]. For example, Tian et al. (2017) examined the driving forces of Shanghai land use change from the perspectives of state-led growth and bottomup development by analyzing Landsat Thematic Mapper(TM) images and land use maps; they concluded that state-led growth played an important role in the non-agricultural land expansion and that urban planning played a main role in regulating the space to accommodate the migratory population and economic growth [7]. Maparu et al. (2017) studied different sub-sectors of transport infrastructure to find its long-run relationship and direction of causality with economic development and urbanization. Their results indicated existence of long-run relationship between transport infrastructure and economic development [8].
Grafe and Mieg (2019) discussed a conceptual model for critically engaging with the effects of financialization on contemporary cities. It concluded by outlining some of the spatial effects of the UK's changing financial ecology of urban infrastructure [9]. Shannon et al. (2018) contributed to debates on urban land governance and sustainable urban development in Africa by providing an empirical analysis of forced displacement and resettlement associated with infrastructure development in Beira city, Mozambique. They concluded by arguing that forced displacement and resettlement should be understood as a deliberate and systematic feature of urban infrastructure development, through which new social-spatial arrangements are created [10].
The literature has also studied the overinvestment problem in China, for example, Tang et al. (2017) found that China's economy is a strong investment driver [11]. Guo and Shi (2018) studied high investment in public infrastructure in China and found that public infrastructure investment increases when local governments capture returns from investment in land improvement [12].
However, few studies have investigated the detailed relationship between urbanization and the total investment in fixed assets. Notably, the studies of construction project investment, real estate investment, and farmers' investment have received little attention in the literature, and these are the composition of the total investment in fixed assets. Therefore, this study attempts to fill the gap in the literature by exploring the relationship between these three factors and urbanization in the context of Shanghai as a case study.
The second contribution of this paper is its use of the generalized impulse response to trace the effect of a shock on current and future values of endogenous variables and to compare the influencing magnitude between indicators. We conduct this investigation by applying the variance decomposition technique.

Literature Review
An extensive literature has explored the relationship between urbanization and various aspects, for example, urbanization and economic growth, and urbanization and infrastructure investment, in the context of developing and developed countries by using different methodologies.
Traditionally, China's land-centered urbanization is a type of "low-quality urbanization" characterized by high investment and expansion and a low level of quality and sustainability [2].
The research on the relationship between urbanization and economic aspects is diverse. Some researchers have proposed that urbanization has substantially promoted economic development in the past few decades [13] and that regional economic integration can improve urbanization efficiency [14]. Other researchers have focused on foreign direct investment (FDI), to reveal the relationship between FDI and urbanization. For example, Wu and Heerink (2016) found that the FDI growth rate has a positive and significant impact on the growth rate of illegal land use when there is a high degree of fiscal decentralization [15], and Vongpraseuth and Choi (2015) [16], Lin and Benjamin (2018) [17] have conducted similar research. By contrast, one study found that FDI has a limited role in urban investment [18].
Regarding the relationship between urbanization and infrastructure investment, the conclusions in the literature are diverse, and the relationship is unclear. Some studies have found that higher infrastructure investment may lead to a higher urbanization rate, and most of the literature has focused on various infrastructure investments and urbanization rate. More specifically, four strands of literature are related to infrastructure investment and urbanization.
The first strand of the literature has focused mainly on the real estate or housing market. Generally, urban land expansion is affected by the market forces [19], especially the real estate or housing market. Cao et al. (2018) found that the real estate market is the major source of urban infrastructure construction funding and a main driving force of urbanization [20]. However, the real estate market may negatively influence Sustainability 2021, 13, 3661 4 of 29 urban sustainable development [21], especially the economic "bubble" that burst in the construction sector [22].
The second strand of the literature has focused on the relationship between urbanization and specific urban infrastructure, for example, transport infrastructure [8,[23][24][25], water infrastructure [26], or spatial infrastructure distribution [27]. Most of this research has attempted to examine the roles of different infrastructure investments in promoting economic development, environmental change, urbanization, or quality of life for residents. For example, Chen et al. (2016) investigated the impact of high-speed rail investment on the economy and environment in China by using a computable general equilibrium model [24]; their results suggest that rail investment in China over the past decade has been a positive stimulus to the economy and that the economic impacts of rail investment are achieved primarily through induced demand and output expansion; by contrast, the contribution from a reduction of rail transportation costs and rail productivity increases were modest. Kim and Yook (2018) analyzed how the benefit assessment of roadway investment projects changes when Value of Time (VOT) is applied according to trip length and found that applying the differentiated VOT by trip length tends to increase the benefit [23].
The third strand of the literature has investigated the topic of urbanization from multiple perspectives, for example, from five aspects including population, resources, environment, development and satisfaction [28], four aspects including economic growth, energy consumption and financial development [29], three aspects including urbanization, human capital and ecological footprints [30], three aspects including settlements isolation, land use changes and poverty [31], three aspects including economic growth, urbanization and air pollutants [32], and three aspects including population inflow, social infrastructure and urban vitality [33].
The fourth strand of the literature has been related to mainly sustainable urbanization or green investment [34]. For example, Kennedy et al. (2016) discussed China's urbanization, climate change, and interactions between infrastructure sectors, and the transformation of its industry [34]. The solutions that have been proposed are, for example, green investment [34], sustainable urban infrastructure [35], urban green infrastructure (UGI) planning [36], and low-carbon growth strategies or planning for China's development. For example, Davies and Lafortezza (2017) found that UGI planning principles and related concepts are present to some degree in strategic greenspace planning in Europe and suggest that enhancing network connectivity is key to the development of UGI [36].
Additionally, many studies have focused on urban and rural areas because a higher urbanization rate may cause social problems such as gentrification [39], spatial inequality [40], and differentiation between urban and rural areas [41]. For example, Gao et al.
(2020) focused on Shanghai rural-urban land transition and found that the material stocks from residential buildings in Shanghai increased 41-fold from 1950 to 2010 and that the material stocks experienced asynchronized growth in rural areas, central urban areas, and rural-urban land transition zones (RULT zones) [42].
Moreover, some literature has investigated social problems caused by the related infrastructure investment. For example, Wesołowska (2016) illustrated that the location and construction process of new public investments of urban infrastructure, technical and social, lead to numerous protests held by local communities [43]. Huang and Wei (2016) found that the spatial inequality of FDI can intensify uneven economic development. Agglomeration effects have replaced institutional factors to become one of the most significant factors influencing the FDI inequality among cities [40].
Although some of the literature has attempted to examine the relationship between infrastructure investment and urbanization, most have focused on environmental or economic impacts but not the detailed relationship between infrastructure investment and urbanization and their impacts on urbanization processes, such as investments in construction projects, real estate, and farmers. Notably, because China's urbanization has entered a new type of urbanization, it is important to reveal the rules of different infrastructure investments and urbanization relationships to fulfill the goal of high-quality urbanization by adjusting the infrastructure investment strategy.
Investments in construction projects, real estate, and farmers would substantially shape the space, urban or rural, contributing to the urbanization rate.
Therefore, to explore the detailed relationship between different infrastructure investments and urbanization, we use Shanghai as an example and consider different infrastructure investments, namely, total investment in fixed assets, construction project investment, real estate investment, and farmers' investment, by using multiple econometric methods to explore, in detail, the relationship between infrastructure investment and urbanization.

Data Source
We collected the raw data from the Shanghai Statistical Yearbook (1990-2019) [44], including total investment in fixed assets (TI t ) and urbanization rate (UR t ). Total investment in fixed assets can be classified into three categories: construction project investment (CPI t ), real estate investment (REI t ), and farmers' investment (FI t ). These data are shown in Table A1 (see Appendix A).
According to the World Urbanization Prospects published by the United Nations [45], the percentage of the urban population in the total population is one of the most important indices of urbanization. The raw datasets can be extracted from the annual urban population (UP t ) and annual total population (P t ). The urbanization rate (UR t ) can be defined as Equation (1).
where t is the year. In addition, to prevent the data of each time series from generating heteroscedasticity before conducting the methodology, the data are analyzed by the logarithm transformation, making it easy for the obtained data to become a stationary sequence.

Unit Roots Test
In this paper, to confirm the time series are stationary, we conduct multiple unit roots tests: the augmented Dickey-Fuller (ADF) test, the Phillips-Perron (PP) test, the Dickey-Fuller test that uses a generalized least squares test (DF GLS), and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test.
The ADF test is commonly used because it can avoid higher-order serial correlation effects and can be described as follows: considering that the time series of (X t ) has the pth-order autoregressive process [46,47].
Equation (2) can be transformed into Equation (3) by adding a time-trend term.
In the ADF test, the null hypothesis is H 0 : r = 0. If this is true, x t has no root. Dickey and Fuller (1981) found that the critical values for r = 0 depend on the form of the regression and sample size [46]. Dickey and Fuller (1979) have provided three additional F-statistics (ϕ 1 , ϕ 2 , and ϕ 3 ) to test a joint hypothesis on the coefficients [47]. The null hypothesis r = a 0 = 0 is tested by using the ϕ 1 statistic. When a time trend is included in the regression, the joint hypothesis a 0 = r = a 2 = 0 is tested by using the ϕ 2 statistic, and the joint hypothesis r = a 2 = 0 is tested by using the ϕ 3 statistic.
However, although the ADF test has been widely used, its disadvantage is low efficacy, especially when the sample size is too small and there is high autocorrelation in the dataset. Thus, we conduct four different unit root tests to examine the variables stationarity.
Furthermore, Maddala and Kim (1999) demonstrated the problems of different unit root tests and proposed the method of ADF, DFGLS, PP, and KPSS [48].
The details of the unit tests are in the literature [48,49].

Johansen Co-Integration Test
The time series stability test and co-integration test are usually conducted to avoid spurious regression before the Granger causality test.
Granger causality can be implemented if the long-term co-integration relationship is significant. In this study, the Jahansen and Juselius co-integration (JJ) test is employed to investigate the co-integration relationship. The JJ test can be expressed as Equations (4) and (5): where γ ni and α ni (n = 1,2,3,4) are the coefficient parameters, α n (n = 1,2) are the constant terms, ∆ represents the first-order difference of the variables, p is the maximum lag period, and u nt (n = 1,2) is the stationary time series. The null hypothesis (H n0 : υ n = δ n = 0), supposing no co-integration relationship between variables, is tested against the alternative hypothesis (H n1 : υ n = δ n = 0) of the existence of co-integration relationships.

VAR Model and Granger Causality Test
After the co-integration test, we build the corresponding two vector error regression models (VARs) with CO 2 emission and four other indicators, respectively. Next, the modified Granger causality test based on [50] is used to verify whether any lag value of a variable affects the current value. The specification of the Granger causality test can be described in the following forms: The VAR 1 model describes the relationship between the UR t and TI t : The VAR 2 model describes the relationship between the UR t and CPI t : where α ni and β ni (n = 1,2,3,4,5,6,7,8) are the coefficient parameters, α n (n = 1,2,3,4) is the constant term, dmax is the optimal lag period, and ε nt (n = 1,2,3,4) represents the stochastic terms for fitted models. We applied the logarithm transformation of these time series data to prevent the data of each time series from generating heteroscedasticity, making it easy for the obtained data to become a stationary sequence. The advantage of the aforementioned Equations (4)-(9) is that they can be applied without considering the long-term co-integrated variables.

Impulse Response Functions and Variance Decomposition
Following the related literature, we employ impulse response analysis and variance decomposition, proposed by Sims [51], to examine how an unexpected shock in one of the variables influences the dynamic behavior of other variables and uncovers simplifying structures in a large set of variables.
In macroeconomic analysis, the term "variance decomposition" or, more precisely, "forecast error variance decomposition," is used more narrowly for a specific tool for interpreting the relations between variables described by VAR models.
Specifically, while impulse response functions trace the effects of a shock to one endogenous variable on to the other variables in the VAR, variance decomposition separates the variation in an endogenous variable into the component shocks to the VAR. Thus, the variance decomposition provides information on the relative importance of each random innovation in affecting the variables in the VAR.

Empirical Results
In this section, we first analyze the descriptive statistics data to ascertain the change in the variables. Second, the variables are tested by different unit root test to ascertain the stationary series of all the variables. Third, we conduct the co-integration test to reveal whether the total investment in fixed assets related variables had a long-run relationship with urbanization rate. Finally, we use the VAR model to further analyze the Granger causality between the carbon urbanization rate and other indicators. The reason for this may be twofold: the continuous growth of GDP and the considerable financial revenue in Shanghai, and policies such as the establishment of the Pudong New Area in 1993, the 1998 economic crisis the and the 2010 Shanghai World Expo. Thus, the Shanghai government has a sustained investment ability in the total investment in fixed assets, with a fluctuation of the amount due to the special events.

Descriptive Statistics Analysis
Specifically, as shown in Figure 3, the trend of construction project investment and farmers' investment is decreasing during the studied period. The percentage of two categories decreases from 87.66% (1990) and 8.75% (1990) to 47.28% (2019) and 0.08% (2019), respectively. By contrast, the proportion of real estate investment increases from 3.59% (1990) to 52.63% (2019).
In addition, the amount of construction project investment increases from 19.  The reason for this may be twofold: the continuous growth of GDP and the considerable financial revenue in Shanghai, and policies such as the establishment of the Pudong New Area in 1993, the 1998 economic crisis the and the 2010 Shanghai World Expo. Thus, the Shanghai government has a sustained investment ability in the total investment in fixed assets, with a fluctuation of the amount due to the special events.
Specifically, as shown in Figure 3, the trend of construction project investment and farmers' investment is decreasing during the studied period. The percentage of two categories decreases from 87.66% (1990) and 8.75% (1990) to 47.28% (2019) and 0.08% (2019), respectively. By contrast, the proportion of real estate investment increases from 3.59% (1990) to 52.63% (2019).
In addition, the amount of construction project investment increases from 19.91 billion yuan (1990)  Possible reasons for the aforementioned changes are Shanghai's urban policies (i.e., 1998 real estate reform) and its special city events (i.e., 2010 Shanghai World Expo).
Moreover, the urbanization rate had a changing trend similar to other indicators between different periods. However, the urbanization rate had a fluctuation in 2014-2015 but increased again after 2015 and reached 90.4% in 2019.

Results of Stationarity Test
The time series should be a stationary sequence before this dataset is analyzed by other econometric methods [52]; moreover, the time series must be turned into the firstorder differencing stationary series if the estimated parameters are biased that making it Possible reasons for the aforementioned changes are Shanghai's urban policies (i.e., 1998 real estate reform) and its special city events (i.e., 2010 Shanghai World Expo).
Moreover, the urbanization rate had a changing trend similar to other indicators between different periods. However, the urbanization rate had a fluctuation in 2014-2015 but increased again after 2015 and reached 90.4% in 2019.

Results of Stationarity Test
The time series should be a stationary sequence before this dataset is analyzed by other econometric methods [52]; moreover, the time series must be turned into the first-order differencing stationary series if the estimated parameters are biased that making it hard to give an effective explanation to the reality [53].
Furthermore, because different lag structures may have different unit root test results, we conduct our analysis by using the Akaike information criterion (AIC), which is widely used in the literature.
Tables A1-A4 (Appendix A) provide the results of four traditional unit root tests: ADF, PP, DF GLS, and KPSS. All four tests demonstrate that all the variables are non-stationary in their level data (Intercept, Intercept and trend, None), namely, I(0). However, all the variables are integrated of the first-order, namely, I(1). Therefore, we can proceed with the co-integration test.
We also use the characteristic root test [54] to examine the stability of the VAR models (Appendix A Figures A1 and A2), and the results show that the VAR models are stable because the characteristic roots are less than 1 or are within the unit circle. Thus, the VAR models are valid.

Results of Co-Integration Test
Next, we apply Jonhanse and Juselius co-integration test to assess if there is a longterm relationship between the selected indicators. More specifically, both the trace test and maximum eigenvalue test are used to identify co-integration relationship. The results of Jonhanse and Juselius tests are shown in Table A6.
Moreover, the Jonhanse and Juselius co-integration test configuration of the cointegration test is set up to be "no intercept or trend in test VAR," and the lag intervals are selected to be "1 to 1".
As shown in Table 1, the trace test and Max-eigenvalue test demonstrate that there is at least one long-run co-integrating relationship between urbanization rate and other indicators at the 0.05 level. And on the basis of the regression results, the linear relationship between the urbanization rate and selected indicators can be transformed into Equations (10) and (11): The standard errors are marked in parentheses. Equation (10) illustrates the relationship of urbanization rate (lnUR) and three categories of the total investment in fixed assets (lnFI, lnCPI, and lnREI), and Equation (10) reveals that a positive long-run relationship between lnUR and lnFI, lnCPI, and lnREI. Equation (11) shows the relationship of urbanization rate (lnUR) and the total investment in fixed assets (lnTI) and reveals a positive long-run relationship between lnUR and lnTI.
Furthermore, the estimated coefficients of Equations (10) and (11). can be used as the long-run elasticities to analyze the relationship between the variables. Therefore, on the basis of the aforementioned equations, we can infer that the construction project investment (CPI t ) has a higher impact on urbanization rate than real estate investment (REI t ) and farmers' investment (FI t ). As the construction project investment (CPI t ) increases by 1%, the urbanization rate (UR t ) would increase by almost 0.48%, while real estate investment (REI t ) and farmers' investment (FI t ).increases by 1%, the urbanization rate would increase by 0.04% and 0.25%, respectively.
Regarding the relationship between urbanization rate (UR t ) and total investment in fixed assets (TI t ), we can infer from Equation (2) that when the total investment in fixed assets (TI t ) increases by 1% investment, the urbanization rate (UR t ) increases by almost 0.52%.

Results of Granger Causality Test
Before conducting the Granger causality test, we employ the sequential modified LR test statistic (LR), final prediction error (FPE), AIC, Schwarz information criterion (SC), and Hannan-Quinn information criterion (HQ) as the optimal lag length test types to ascertain the optimal lag length of different Granger causality tests. According to Liew [55] and Gutierrez et al. [56], AIC and FPE are superior to other criteria because they can provide considerable advantages in terms of selecting the correct VAR model, and AIC is the most preferable one in their studies. Therefore, we identify the optimal lag according to AIC, FPE, LR, SC, and HQ in sequence. Appendix A Table A5 is the optimal lag length results, which demonstrate the different optimal lag lengths of different variables' groups by using different test methods. Next, we conduct the Granger causality test by integrating all the optimal lag lengths results.
In addition, Appendix A Table A7 presents the details of the Granger causality test of urbanization and the other seven indicators. The results are summarized in Figure 4.
In Figure 4, the relationship between urbanization rate and total investment in fixed assets has a bilateral Granger causality relationship in lags 1, 3, and 4 and has a one-way Granger causality relationship in lags 2, 5, 6, 7, and 8.
Regarding the relationship between urbanization rate and the other three indicators, in different lag periods, both bilateral Granger causality relationship and one-way direction Granger causality relationship are observed. Specifically, there is a bilateral relationship in lags 3, 4, and 5 (CPI t and UR t ); lags 6, 7, and 8 (REI t and UR t ); and lags 7 and 8 (FI t and UR t ) and a one-way relationship in lags 1 and 2 (CPI t and UR t ); lags 1, 2, 4, and 5 (REI t and UR t ); and lags 1, 2, 3, 4, 5, and 6 (FI t and UR t ), respectively. ing all the optimal lag lengths results. In Table 2, the optimal lag lengths between urbanization rate and other indicators are as follows: Group ( , , and ) are lag 2-4, Group ( , ) are lags 2, 3, and 8. In addition, Appendix A Table A7 presents the details of the Granger causality test of urbanization and the other seven indicators. The results are summarized in Figure 4. In Figure 4, the relationship between urbanization rate and total investment in fixed assets has a bilateral Granger causality relationship in lags 1, 3, and 4 and has a one-way Granger causality relationship in lags 2, 5, 6, 7, and 8. Regarding the optimal lag length, it indicates that urbanization rate and total investment in fixed assets mutually influence each other, especially in the optimal lag length (lag = 3).
Specifically, the urbanization rate may have a mutual impact on construction project investment (lag = 2, 3) and real estate investment (lag = 3) in the optimal lag lengths, respectively, and has no mutual impact on farmers' investment in any optimal lag lengths.
This finding indicates that among the three categories of total investment in fixed assets, construction project investment and real estate investment have a close Granger causality relationship with urbanization rate, and this may be related to the specific investment policies of the total investment in fixed assets (Figure 3).

Impulse Response Analysis
Because the generalized impulse response functions can explain dynamic feedback between indicators, we use this methodology to explore the influence of innovations on the explanatory variables.
As depicted in Figures 5 and 6, the y-axis shows the impulse response amplitude and direction of different variables.
Moreover, the dotted line represents the positive and negative standard deviation of the impulse response function, and the solid line is considered to be the impulse response function (IRF) image. Figure 5 presents the dynamic IRF images of urbanization rate, (ln(UR t )) and construction project investment, (ln(CPI t )), real estate investment (ln(REI t )), and farmers' investment (ln(FI t )). Each curve has its IRF characters, and we focus on combinations related to our research objects, for example, (ln(UR t ), ln(CPI t )), (ln(UR t ), ln(REI t )) and (ln(UR t ), and ln(FI t )). There are six combinations. The IRF data can be checked in Appendix A Table A8.
In the first picture in Figure 5, the curve is fluctuated around 0; specifically, ln(UR t ) is negatively affected by ln(REI t ) in the first five periods, and a positive impact is observed in the next five periods.
The second picture illustrates the impact of ln(UR t ) on ln(REI t ). ln(REI t ) responds negatively in the first period and then positively after the second period; thus, the increase in the urbanization rate may inevitably promote the growth of real estate investment.
The third curve of Figure 5 depicts the impulse response path of ln(UR t ) to ln(FI t ) over time, and the curve is always under the horizontal axis, indicating that ln(FI t ) has a negative influence on ln(UR t ) from lags 1 to 10.
The fourth curve of Figure 5 elaborates the impulse response path of ln(FI t ) to ln(UR t ) from lags 1 to 10: the curve shows that the ln(UR t ) has a negative influence on ln(FI t ) and that the absolute IRF value is higher than that of ln(UR t ) to ln(FI t ). This result indicates that the urbanization rate might have more influence on farmers' investment than the impact from farmers' investment on urbanization rate. This coincides with the Granger causality test in Section 4.4, that is, urbanization rate has more Granger causality lags with farmers' investment than those of farmers' investment with the urbanization rate. Regarding the Group ( , ) IRF results, as shown in Figure 6, both curves are always above the x-axis, and we can easily assess that the response of ( ) to ( ) is larger than that of ( ) to ( ). Therefore, we can infer that the urbanization rate's impact on total investment in fixed assets is greater than total investment in fixed assets' influence on the urbanization rate. Likewise, this also coincides with the Granger causality test in Section 4.4. The IRF data of the Group ( , ) can be checked in Appendix A Table A9. Similarly, the last two images in Figure 5 reflect the same phenomenon of the IRF of two indicators, that is, the two impacts of impulse responses are positive, and the response of ln(CPI t ) to ln(UR t ) is smaller than that of ln(UR t ) to ln(CPI t ). This result also coincides with the Granger causality test in Section 4.4.
Regarding the Group (lnUR, lnTI) IRF results, as shown in Figure 6, both curves are always above the x-axis, and we can easily assess that the response of ln(TI t ) to ln(UR t ) is larger than that of ln(UR t ) to ln(TI t ). Therefore, we can infer that the urbanization rate's impact on total investment in fixed assets is greater than total investment in fixed assets' influence on the urbanization rate. Likewise, this also coincides with the Granger causality test in Section 4.4. The IRF data of the Group (lnUR, lnTI) can be checked in Appendix A Table A9. Regarding the Group ( , ) IRF results, as shown in Figure 6, both curves are always above the x-axis, and we can easily assess that the response of ( ) to ( ) is larger than that of ( ) to ( ). Therefore, we can infer that the urbanization rate's impact on total investment in fixed assets is greater than total investment in fixed assets' influence on the urbanization rate. Likewise, this also coincides with the Granger causality test in Section 4.4. The IRF data of the Group ( , ) can be checked in Appendix A Table A9.

Variance Decomposition Analysis
The Variance decomposition (VD) methodology can decompose the variance of a variable in a VAR model into each perturbation term and can help measure the contribution that the shocks have on the variables; thus, we use it to analyze the urbanization rate and other variables as a complementary analysis of the aforementioned methods (Granger causality test and impulse response analysis) in this study.
Regarding Group ( , ), Figure 7 (for detailed data, see Appendix A Table  A10), demonstrates that on impact, 99% of the variation in ( ) is accounted for by ( ), and ( ) only accounts for approximately 1% of shocks.

Variance Decomposition Analysis
The Variance decomposition (VD) methodology can decompose the variance of a variable in a VAR model into each perturbation term and can help measure the contribution that the shocks have on the variables; thus, we use it to analyze the urbanization rate and other variables as a complementary analysis of the aforementioned methods (Granger causality test and impulse response analysis) in this study.
Regarding Group (lnUR, lnTI), Figure 7 (for detailed data, see Appendix A Table A10), demonstrates that on impact, 99% of the variation in ln(UR t ) is accounted for by ln(UR t ), and ln(TI t ) only accounts for approximately 1% of shocks. In Figure 8, the variance decomposition results (for detailed data, see Appendix A Table A11 ), demonstrate that on impact, 90% of the variation in ( ) is accounted for by ( ), and ( ), ( ), and ( ) account for approximately 5%, 1%, and 2% of shocks, respectively. The result suggests that in the long run, the construction project investment shocks and the farmers' investment shocks are relatively more important than In Figure 8, the variance decomposition results (for detailed data, see Appendix A Table A11), demonstrate that on impact, 90% of the variation in ln(UR t ) is accounted for by ln(UR t ), and ln(CPI t ), ln(REI t ), and ln(FI t ) account for approximately 5%, 1%, and 2% of shocks, respectively. The result suggests that in the long run, the construction project investment shocks and the farmers' investment shocks are relatively more important than the real estate investment. In Figure 8, the variance decomposition results (for detailed data, see Appendix A Table A11 ), demonstrate that on impact, 90% of the variation in ( ) is accounted for by ( ), and ( ), ( ), and ( ) account for approximately 5%, 1%, and 2% of shocks, respectively. The result suggests that in the long run, the construction project investment shocks and the farmers' investment shocks are relatively more important than the real estate investment.

Discussion and Conclusions
Shanghai has been experiencing rapid urbanization since China's opening-up and reform, especially after implementing the strategy of Pudong District development in the 1990s. Additionally, the total investment in fixed assets has substantially changed during the studied period. The purpose of this paper is to investigate the role of total investment in fixed assets in the later stage of urbanization in Shanghai.
A summary of the main findings of the relationship between the total investment in fixed assets and the urbanization rate is as follows (Figure 9):

1.
Both Group (lnUR, lnFI, lnCPI, and lnREI) and Group (lnUR, lnTI) have a longterm co-integration relationship among the studied variables, and construction project investment plays an important role in promoting the urbanization rate in the studied period.

3.
The impulse response analysis illustrates that the urbanization rate has a positive impact on the total investment in fixed assets in the short term and long term. A similar conclusion is found in [21], that is, government investment policy has substantially affected Egypt and its sustainable development.

4.
Variance decomposition analysis reveals that the urbanization rate in Group (lnUR, lnFI, lnCPI, and lnREI) and Group (lnUR, lnTI) accounts for the majority of percentage impacts, and the total investment in fixed assets and its three categories contribute a small minority to the urbanization rate.
Based on our co-integration test results, our finding is that construction project investment (CPI t ) has a higher impact on urbanization rate than real estate investment (REI t ) and farmers' investment (FI t ), and we can infer that construction project investment (CPI t ) plays an important role in promoting the urbanization rate in the studied period. This result differs from the conclusion of [13] that real estate is a main driver of urbanization and differs from this statement: "the real estate may have negative influences on the urban sustainable development [21]".
Moreover, both impulse response analysis results and the variance decomposition results coincide with the co-integration results. The impulse response analysis results show that only the curve of construction project investment (ln(CPI t )) to urbanization rate (ln(UR t )) is positive: thus the accumulation of the impulse response of ln(CPI t ) to ln(UR t ) must be positive, and the variance decomposition results suggest that ln(CPI t ) has a greater proportion than that two other variables.
Furthermore, we integrated other tests in this paper and found that the three types of total investment in fixed assets have a bilateral relationship with urbanization rate. However, considering the optimal lag length, in the short term (lag = 2,3,4), both construction project investment and real estate investment have a bilateral Granger relationship with urbanization rate, and farmers' investment has a one-way direction Granger relationship with urbanization rate. This result indicates that in the short term, both the construction project investment and real estate investment are important to urbanization promotion, and the two investments are also affected as the Shanghai urbanization rate increases. Additionally, the urbanization rate affects farmers' investment, but farmers' investment does not have an obvious impact on urbanization rate in the short term.
The reason for this finding may be related to the majority of the total investment in fixed assets composition being construction project investment and real estate investment, and the farmers' investment constitutes less than 8.75% during the studied period.
The finding coincides with that of [57], who found that the urban municipal public infrastructure plays an important role in promoting economic development and that the municipal public infrastructure construction levels and investment efficiency have a close relationship with sustainable socioeconomic development and urbanization.
Notably, construction project investment and real estate investment increase substantially as the Shanghai urbanization rate increases, especially when the main events occur in characteristic years, such as the establishment of Pudong New Area in 1993, the 1998 economic crisis, and the 2010 Shanghai World Expo. The amount of these investments changes during these special times. The urbanization rate also changed in the studied period and the curve of urbanization rate is gentler than that of the other variables.
A similar result is found in Zeng [27], who propose a rational spatial optimization of infrastructure construction and sustainable regional development strategies for improving resource use efficiency, achieving balanced development, and promoting integrated urbanrural development.
In addition, considering the optimal lag length, in the short term (lag = 8), farmers' investment has a bilateral Granger causal relationship with urbanization rate. Notably, as urbanization rate increases, the urban area would provide an increasing amount of help to the rural area, although as the percentage of farmers' investment in the total investment in fixed assets was decreasing, the amount of the farmers' investment was increasing; therefore, rural area construction would increase. This phenomenon coincides with the recent "rural revitalization" in China.
In addition, considering the optimal lag length, in the short term (lag = 8), farmers' investment has a bilateral Granger causal relationship with urbanization rate. Notably, as urbanization rate increases, the urban area would provide an increasing amount of help to the rural area, although as the percentage of farmers' investment in the total investment in fixed assets was decreasing, the amount of the farmers' investment was increasing; therefore, rural area construction would increase. This phenomenon coincides with the recent "rural revitalization" in China. Figure 9. Results of Granger causality test, impulse response analysis and variance decomposition analysis.

Policy Implication
This study contributes a novel insight into the current reality of the urbanization rate and total investment in fixed assets. In summary, according to our results, in terms of the related policies, to strengthen the healthy urbanization development in Shanghai, improve the rational total investment in fixed assets of Shanghai, and maintain coordinated rapid economic growth in manners similar to green investment [34], sustainable urban infrastructure development [35], and UGI planning [36], eco-system services and integrated urban planning [58],we suggest that policy makers should prioritize strategy policy, economy policy, industrial policy, and population policy. Based on our research, our policy suggestions as follows: Figure 9. Results of Granger causality test, impulse response analysis and variance decomposition analysis.

Policy Implication
This study contributes a novel insight into the current reality of the urbanization rate and total investment in fixed assets. In summary, according to our results, in terms of the related policies, to strengthen the healthy urbanization development in Shanghai, improve the rational total investment in fixed assets of Shanghai, and maintain coordinated rapid economic growth in manners similar to green investment [34], sustainable urban infrastructure development [35], and UGI planning [36], eco-system services and integrated urban planning [58], we suggest that policy makers should prioritize strategy policy, economy policy, industrial policy, and population policy. Based on our research, our policy suggestions as follows: 1.
Strengthen the rational total investment in fixed assets. According to our results, the total investment in fixed assets has a one-direction Granger relationship with urbanization rate and a bilateral Granger relationship in the long term. Notably, urbanization is a process that needs time to comply with economic factors, such as the total investment in fixed assets. Thus, the city would not benefit from the higher urbanization rate. Similarly, the total investment in fixed assets also needs a process that would convert its investment into related beneficial interests of the city. Therefore, a rational investment strategy is necessary to ensure the healthy development of urbanization through, for example, conceptual infrastructure planning and investment project appraisal schemes. A similar implication can be found in [57].

2.
Set a more flexible policy on construction project investment. Generally, construction project investment is a critical factor that plays a substantial role as a drive of urban development. In addition, our results demonstrate a one-way Granger relationship between construction project investment and urbanization rate. Therefore, policymakers must balance the two indicators, for example, the related population policy and construction project investment policy, which can be implemented according to the current condition to solve urban problems (i.e., gentrification, polarization, and urban renewal) caused by urbanization [2].

3.
More rationally guide the development of the real estate industry. Theoretically, based on the characteristics of the other countries' urbanization experience, urbanization can be divided into four stages: initial, acceleration, deceleration, and stable. Similarly, the development of the real estate industry follows similar laws of urbanization development, summarized as four stages: formation, growth, maturity, and decline. However, the relationship between urbanization and the real estate industry should be harmonious, or it may cause serious economic problems. Notably, the real estate industry has developed rapidly since the commercial housing reform in Shanghai in 1998. However, the real estate industry has always been the economic pillar of Shanghai and has been criticized for its "excessively high housing price," the "real estate bubble," and other problems of the society. Moreover, according to our research, there is a bilateral direction of Granger causality between the real estate industry and urbanization, indicating that the two factors have a close relationship. Therefore, Shanghai should guide the rational development of the real estate industry in the later stage of urbanization. More specifically, the government should coordinate land financing policy [12] and eliminate the negative externalities of the policy, for example, the polarization effect and high housing prices; thus, the government must more practically manage the related social, economic, or environmental problems caused by real estate investment.

4.
Promote rural revitalization and coordinate the development of urbanization through scientific planning.
Urban planning should be in accordance with the requirements of building a harmonious society and the coordination of development between different regions and between urban and rural areas. Additionally, urban planning should make overall plans for economic and social aspects and construction.
Thus, Shanghai should accurately understand the urbanization progress to avoid excessive urban sprawl. Furthermore, regarding the amount of total investment in fix assets, Shanghai should make it compatible with urbanization development and the current level of economic development. Related policy should be implemented to balance the relationship between the two factors.  • DF GLS test    LNUR and LNTI Figure A2. Inverse Roots of AR Characteristic Polynomial of LNUR and LNTI. Figure A2. Inverse Roots of AR Characteristic Polynomial of LNUR and LNTI.    6. Impulse response function analysis