An Empirical Analysis of Port-City Relationship : Based on the Comparison of the Yangtze River Delta and the Pearl River Delta

This paper first analyzes the status quo of the port-city relationship of the Yangtze River Delta and the Pearl River Delta through the relative concentration index. It is found that the port-city relationship of the Yangtze River Delta trends to be coordinated, while the port-city relationship of the Pearl River Delta is still in a state of uncoordinated. Then it analyzes the specific correlation between urban economy development and port development by gray relational analysis; it is found that the GDP and industrial output have high correlation with port cargo throughput, and the average correlation value of Yangtze River Delta is higher than that of the Pearl River Delta. Through the impulse response analysis, it is found that the urban GDP and industry have a significant effect on the development of the port in the short term, and the development of the port has no obvious influence on urban GDP and industry.


Introduction
Peace and development have become the theme of the world.Economy development is the primary task of the development of a country.With the unique geographical conditions, the port city has become an important node in the national and global economic circulation system.In recent years, China's major coastal port cities have developed rapidly.In the future, there are many ports needed to be built and the existing ports also need to be optimized.In this paper, we first use the relative concentration index to quantitatively analyze the port-city relationship of the Yangtze River Delta and the Pearl River Delta, and then we analyze the specific relationship between the urban economy development and the port through the gray relational analysis method.Based on the results of the gray relational analysis, we analyze the dynamic relationship of GDP and industrial output with the port cargo throughput, and analyze the empirical results.

Relative Concentration Index (RCI)
Relative concentration index (RCI) is used to measure the relative size of the port to the size of the city, Vallega (1979) first used the index to analyze the cities in the Mediterranean region to explore how the regional and population areas of the region were organized.Vallega found that the RCI of trade cities was higher than 1, while The RCI of the densely populated cities is less than 1, and the RCI of cities with close port size and city size is close to 1 [1].Vigarie (1968) also used similar index to measure the country's dependence on the port (the number of tons of commercial maritime goods owned by each resident) [2].Kenyon (1974) measured the importance of the transshipment function of the US port city relative to the size of the city (the tonnage of maritime goods owned by each resident) [3].China's scholar Chen Hang (2009) first used the index to analyze the time series development characteristics of China's port city [4].
In this paper, the RCI is improved as follows: After analyzing the previous research methods.First, we use economy scale (GDP) to reflect the urban concentration instead of population scale, mainly because this study is about the relationship between urban economy development and the port development.The second is that we use port cargo throughput to reflect the port development instead of the container throughput, mainly because the port cargo throughput is more generally applicable to facilitate the comparison between different ports, and the data can be traced back to earlier.Third, taking into account the Yangtze River Delta and the Pearl River Delta port group also includes inland ports, so the object will be extended to the river port and harbor.Through the above improvements, RCI in this paper is calculated as: In the formulas (1) to (3), P ij represents the port scale of port i (reflected by port throughput), C ij represents the city economy scale of the port city (reflected by GDP), PR ij is the ratio of the port cargo throughput to the total port cargo throughput of the measured time interval, CR ij is the ratio of the city economy scale to the total economy scale of the measured time interval, RCI ij represents the RCI of the port city i.According to this formula, the larger the value of PR ij , the stronger the intermediary of the port city in year j; the larger the CR ij , the stronger the concentration of the city's economy.If RCI ij is greater than 1, it indicates that the intermediary is higher than the concentration, which means the development of the port is faster than the urban economy development; if RCI ij is less than 1, it means that the intermediary is lower than the concentration, which means the port development is slower than the urban economy development; if RCI ij is the close to 1, it indicates that the development of urban economy and the development of port are coordinating.Based on the data from 2005 to 2014, the RCI index of the major port cities in the Yangtze River Delta and Pearl River Delta are shown in Table 1. Figure 2 and Figure 3 are the graphs of Figure 3. RCI of major ports in the Yangtze River Delta.On the whole, the RCI of the major port cities of the Yangtze River Delta in the past 10 years trends to 1, which indicates that the port-city relationship of these port cities trend to be coordinated, while the RCI of the major port cities of the Pearl River Delta has been fluctuating around 1 in recent years ,which means port-city relationship of the major port cities in Pearl River Delta is still in a state of uncoordinated, but we can see a slight trend of approaching 1 in Figure 4.

Gray Relational Analysis
Gray relational analysis is based on the microscopic or macroscopic geometric approximation of the sequence of behavioral factors to analyze and determine the degree of influence between factors or the factors that measure the contribution of the main behavior.Gray relational analysis is mainly on the development of changes in the situation analysis, that is, the dynamic development of the system quantitative analysis.The basic idea is to determine the relationship between the similarity of the sequence curve geometry, the closer the curve, the greater the correlation between the corresponding sequence, and vice versa.The gray relational analysis method makes up for the shortcomings caused by the system analysis of the mathematical statistics method.It does not have the requirement of the sample quantity and the regularity of the sample, and it is very easy to calculate.
Port system and urban economy system are gray systems.First, because the factors that reflect port development and urban economy development are too many and too complex, only limited indicators can be selected for analysis.
Second, the statistics of the various indicators are very limited, and the existing data mostly are gray, most of the data is not a typical probability distribution.
Thus, the analysis system has the characteristics of incomplete or "gray" information.This paper uses the gray relational analysis method to calculate the specific correlation between urban economy development and port development.

Calculation of Gray Correlation Degree
Let X k be the system factor, and its observation data on the serial number is x ki , , , is the behavior sequence of factor X k , which is the index number, x ki for the factor X k on the first k indicators of the observed data, ( ) ( ) ) When X i is an ascending sequence, 0 i s ≥ ; (ii) when X i is the descending column, 0 i s ≤ ; (iii) When X i is the oscillation sequence, the s i symbol is indefinite.
If the length of sequence X k and the sequence X m are the same, then is the gray absolute correlation degree of X k and X m .
Let the sequence X k , X m the same length, and the initial value is not equal to zero, then make and m X ′ are the values transformed by initialization.The gray correla- tion between k X ′ and m X ′ is the gray relative correlation degree of X k and X m , denoted as r km .
Let X k and X m have the same length and the initial value is different from zero, which means X k1 and X m1 are not zero, ε km and r km are gray absolute correlation degree and gray relative correlation degree of X k and X m respectively, and the resolution coefficient ρ is the gray comprehensive correlation degree of X k and X m .The gray comprehensive correlation degree not only reflects the similarity degree of the two sequences in the graph, but also reflects the degree of closeness of the two sequences relative to the starting point.It is a comprehensive indicator of whether the links are closely related.In general, the resolution coefficient is θ = 0.5, and if we are more concerned with the difference between the absolute quantities of the two sequences, θ can be larger; if we pay more attention to the difference in the rate of change between the two sequences relative to the starting point, θ can be made smaller.
In the gray correlation calculation of this paper, the original data is first transformed by initialization, and then the comprehensive gray correlation degree between the parent sequence and the subsequence is calculated, and the resolution coefficient θ = 0.5 is set.

The Selection of Indicators
Port system and urban economy system are complex systems and lots of indicators can reflect the situation of them.The focus of this paper is to study the inte-W.Chen raction between urban economy development and port development.Therefore, the port cargo throughput (Y 1 ), which is the most representative indicator of port system, is chosen to represent the port system.The urban economy system is more complex.GDP (X 1 ), fixed assets investment (X 2 ), import and export value (X 3 ), industrial output (X 4 ), freight volume (X 5 ) and premium income (

Calculation Results
Major cities of the Yangtze River Delta and the Pearl River Delta are selected for empirical analysis, Shanghai, Nantong, Suzhou, Zhenjiang, Nanjing, Ningbo, Zhoushan and Wenzhou are selected for the Yangtze River Delta; Guangzhou, Shenzhen, Zhuhai, Huizhou and Dongguan are selected for the Pearl River Delta.The port cargo throughput (Y 1 ) is set to be the parent sequence, GDP (X 1 ), fixed asset investment(X 2 ), import and export value (X 3 ), industrial output (X 4 ), freight volume (X 5 ) and premium income (X 6 ) are sub-sequences, then we can obtain the gray correlation coefficients of the two sequences.The correlation coefficients of parent sequence and sub-sequences are shown in Table 2.
In Table 2, it can be seen that in the urban economy system, the average gray correlation coefficient of GDP (X 1 ) and port cargo throughput (Y 1 ) is 0.750,and the average gray correlation coefficient of industrial output (X 4 ) and port cargo throughput (Y 1 ) is 0.764, while the other average gray correlation coefficients are small, all around 0.70.This shows that the port city's GDP is highly related to its port development, so port development should be referred to port city's GDP growth.The correlation coefficient between port cargo throughput (Y 1 ) and industrial output (X 4 ) is 0.764, which is the largest correlation coefficient between port index and urban economy index correlation coefficient.This is mainly because the industrial production needs to use coal, oil, steel and other raw materials which are big and heavy, and water transport is the best mode of transport; Second, the industrial production is mostly large quality and volume of products, water transport costs less.Therefore, in the process the port city's development of industry, we should pay more attention to the construction of port facilities.
W. Chen In order to analyze the differences of gray correlation coefficients between the Yangtze River Delta and the Pearl River Delta, the gray correlation coefficients of the two port groups are shown in Table 3 and Table 4 respectively.It can be seen from Table 3, in the Yangtze River Delta, the average correlation coefficient between GDP (X 1 ) and cargo port throughput (Y 1 ) is 0.789, the average correlation coefficient between industrial output (X 4 ) and port cargo throughput (Y 1 ) is 0.796, both of them are still high compared to other correlation coefficients, and the average port-city correlation coefficient is 0.742.In the Pearl River Delta, it can be seen in Table 4, only the average correlation coefficient of industrial output (X 4 ) and port cargo throughput (Y 1 ) exceeded 0.7, up to 0.713, the remaining correlation coefficient are below 0.7, the average port-city correlation coefficient is 0.685.Compared with the gray correlation coefficient between the Yangtze River Delta and the Pearl River Delta, it can be seen that the port-city correlation of the Yangtze River Delta is relatively high, while the port-city relationship of the Pearl River Delta is lower, indicating that compared with the Pearl River Delta, the port-city relationship of the Yangtze River Delta is more coordinated.

Impulse Response Analysis
In this section, the vector autoregressive (VAR) model is used to determine the extent of the impact of port development on port cities. Vector autoregressive (VAR) is a model based on statistical properties of data that can be used to correlate time series data [5].It is predicted that this method has been widely used in unstructured models in macroeconomic analysis in recent years.We have already found that GDP and industrial output have high correlation to the port W. Chen  cargo throughput both in the Yangtze River Delta and the Pearl River Delta, according to the measurement of the gray relational analysis.Therefore, in this section, we choose GDP and industrial output to represent the development of urban economy, which were recorded as GDP and I, the port development level is still measured by the port cargo throughput, recorded as T. The impulse response analysis of these three indexes is carried out, and the dynamic characteristics of the port-city relationship are obtained.

Vector Autoregressive (VAR) Model
In order to compare the impulse response analysis of the Pearl River Delta and the Yangtze River Delta, the GDP, industrial output and port cargo throughput of major port cities in the Yangtze River Delta and Pearl River Delta ports were summarized.The data ranges from 1998 to 2014.And then the analysis is shown in Table 5.
In order to eliminate the existence of collinearity and autocorrelation between indicators, the indicators are changed by natural logarithmic processing; the new sequences are recorded as lnGDP, lnI and lnT, and the timing diagram of them are shown in Figure 5 and Figure 6, respectively.It is easy to see, whether in the  Yangtze River Delta or the Pearl River Delta, sequences have generally consistent trends.
The maximum hysteresis order is required before vector autoregressive of the sequence.Table 6 and Table 7 are the results of the hysteresis order of the  According to the information criterion, the values of AIC, SC and HQ are the smallest in the lagged phase 3, so both the maximum hysteresis order of the Yangtze River Delta and the Pearl River Delta are 3. Then we can obtain the results of the VAR parameter estimation, which are shown in Table 8 and Table 9 respectively, the table consists of three parts: the parameter estimation results of the model, the estimated standard deviation of the coefficients (in the parenthesis below the coefficient estimates), and the t-test statistic values (in the square brackets below the coefficient estimates).
From Table 7  The Yangtze River Delta: The Pearl River Delta: where L = [LNGDP LNI LNT]', R 2 and the adjustment R 2 of the regression equation are more than 0.99, so the model of high degree of fit, indicating that the model is reasonable and stable.
The stationarity of the VAR model can be checked by the inverse roots of AR characteristic polynomial, in Figure 7, we can find that the reciprocal of the AR feature polynomial roots are all in the unit circle, which means the reciprocal absolute value of the eigenvalue is less than 1, indicating that the VAR satisfies the stationary condition.Inverse Roots of AR Characteristic Polynomial

Impulse Response Function
The most important role of the VAR model is to reflect the dynamic characteristics of the system, that is because the change of each endogenous variable not only affects itself, but also affects all other endogenous variables by increasing the standard deviation of the error term in the impulse response function (IRF) .
A change in the i-th endogenous variable not only directly affects the i-th variable, but also affects other endogenous variables through the dynamic structural features of the VAR model.The impulse response graph can visually reflect the trajectories of these effects; it can show how the variation of a variable affects all other variables through the model, and ultimately feedback to itself.In this paper, the lnGDP, lnI and lnT variables of the Yangtze River Delta and the Pearl River Delta are analyzed by Eviews 8.0 respectively.The impulse response graphs are shown in Figure 8 and Figure 9, respectively.
In the Yangtze River Delta, It can be seen from Figure 8(a) that the impact of the change of urban GDP on the port cargo throughput has shown a significant positive effect in the first four periods and has gradually increased, it begins to decline and gradually approaching zero from the fifth period.It can be seen from Figure 8(b), that the impact of the change of urban industrial output on the port cargo throughput in the Yangtze River Delta has shown a positive effect and gradually increased in the first two periods, and the effect begins to decrease from the third period and gradually approaches zero.From Figure 8(c) and Figure 8(d), it can be seen that the GDP and industrial output of port cities in the Yangtze River Delta have weaker positive impacts on the port cargo throughput in the short term, but then there is a negative effect, in the long term, the negative effect gradually approaches zero.
In the Pearl River Delta, it can be seen from Figure 9

Variance Decomposition
The impulse response function reflects the dynamic influence of an endogenous variable on other endogenous variables.The variance decomposition divides the variance of a variable in the VAR model system into the perturbation terms [6].
The main idea is that the variation of each endogenous variable in the system is decomposed according to its origin, so that the degree of influence of other endogenous variables can be visually observed [7].

The Impact of Urban Economy Development on Port Development
The results of variance decomposition of LNT of the Yangtze River Delta and the Pearl River Delta are shown in Figure 10 and Figure 11 respectively.
From Figure 10, it can be seen that the contribution of GDP to port cargo throughput (T) in the Yangtze River Delta decreased from 35% to 21% in the first two periods, but begins to rise sharply from the third period, and it finally stabilized around 75%, while the contribution of industrial output(I) to port cargo throughput (T) increased from 12% to 53% in the first two periods, but declined sharply from the third period and finally stabilized around 16%.As can be seen from Figure 11, the contribution of GDP to port cargo throughput (T) in the Pearl River Delta decreased from 80% to 43% in the first two periods, but it began to increase from the third period, and finally it is close to 60%, while the contribution of industrial output (I) to port cargo throughput increased from 6% to 38% in the first two periods, but it decreased weakly from the third period and finally stabilized around 26%.

The Impact of Port Development on Urban Economy Development
The results of variance decomposition of LNGDP and LNI of the Yangtze River Delta and the Pearl River Delta are shown in Figure 12 and Figure 13 respectively.
As can be seen from Figure 12, port cargo throughput (T) has maintained a low contribution (less than 7%) to GDP and industrial output over the study period for the Yangtze River Delta.In contrast, in the Pearl River Delta, the contribution of port cargo throughput (T) to port city GDP increased from 0 to 8% in the first two periods, and gradually stabilized around 10% from the third pe- Overall, both in the Yangtze River Delta and the Pearl River Delta, GDP and industrial output have high contribution to the port cargo throughput, and the contribution of GDP is slightly higher than the contribution of industrial output.
The port cargo throughput in the Yangtze River Delta has little contribution to the growth of GDP and industrial output, while in the Pearl River Delta, and port cargo throughput has a certain contribution to GDP and industrial output.
This result is consistent with the result of the impulse response graph.

Concluding Remarks
In this paper, we measure the relative size of port to the size of urban economy In order to analyze the specific relevance between the port system and the urban economy system, we measure the port-city relationship of major port cities of the two major port groups by the gray relational analysis method.We found that GDP and industrial output have high relationship with the port cargo throughput, which indicates that port development is highly related to the city's GDP and industry.Therefore, the port needs to determine its speed of development according to the scale of its urban economy and industry.Whereas, the financial industry, fixed asset investment and foreign trade do not have high relationship with port development.The correlation coefficient in the Yangtze River Delta is higher than that of the Pearl River Delta, which indicates that the port-city connection of the Yangtze River Delta is closer.
Based on the gray relational analysis, the dynamic influence mechanism of urban economy so as to fully absorb the demand created by urban economy.The effect in the Yangtze River Delta is higher than that in the Pearl River Delta, so port city in the Yangtze River Delta needs to pay more attention to the construction of port facilities.On the other hand, the development of the port has small effect on GDP and industrial output, indicating that the current port-city interaction mechanism is mainly unilateral.
Although the port development has small effect on GDP and industrial output, we found that in the Pearl River Delta port development has a certain role in promoting urban economy and industry by variance diagram, that is mainly because the Pearl River Delta has higher dependence on foreign trade, then the development of the port can effectively promote the development of foreign trade of the city, which finally affects urban economy and industry.Therefore, port development needs to consider the economic type of its city, for city with more foreign trade; it needs to pay more attention to port development.
We have studied the port-city relationship of the port cities in the Yangtze River Delta and the Pearl River Delta, but China has many port cities, so the sample needs to be expanded in the future research.What's more, the specific impact mechanism is not studied in this paper, which is worth to be studied in the future.

Figure 1 and
Figure 1 and Figure 2 show the changes in GDP and port cargo throughput

Figure 1 .
Figure 1.Changes of GDP and port cargo throughput in Shanghai Data Source: Yearbook of Each City.

Figure 2 .
Figure 2. Changes of GDP and port cargo throughput in Guangzhou.Data Source: Yearbook of Each City.

Figure 4 .
Figure 4. RCI of major ports in the Pearl River Delta.

X 6 )
are chosen to reflect the degree of development of the urban economy.GDP is obviously the most representative indicator of urban economy.Fixed assets investment mainly includes capital construction, renovation, real estate development and other economic activities, in which process the port plays an important role.Import and export value can reflect the degree of demand of a city to the port.The quality of raw materials and finished products used in the industrial production process are mostly transported by ship, and gross industrial output is the best indicator of industrial development.Port is an important infrastructure for urban transport, freight volume (X 5 ) can directly reflect city's demand for the port.The financial industry is at the core of the modern economy and the insurance industry is an important branch of the financial industry, the change of the premium income (X 6 ) can indirectly reflect the development of the financial industry.

Figure 5 .
Figure 5. Timing diagram of the Yangtze River Delta.

Figure 6 .
Figure 6.Timing diagram of the Pearl River Delta.

Figure 7 .
Figure 7.The inverse roots of AR characteristic polynomial.

Figure 8 .
Figure 8. Impulse response graphs of the Yangtze River Delta.

Figure 9 .
Figure 9. Impulse response graphs of the Pearl River Delta.

Figure 10 .Figure 11 .
Figure 10.Variance decomposition of LNT of the Yangtze River Delta.

Figure 12 .
Figure 12.Variance decomposition of LNGDP and LNI of the Yangtze River Delta.

Figure 13 .
Figure 13.Variance decomposition of LNGDP and LNI of the Pearl River Delta.
GDP and industrial output with port cargo throughput is studied by impulse response analysis.The results show that GDP and industrial output have obvious positive effects on the development of the port development in the short term.Therefore, the port construction needs to cooperate with the development of

Table 1 .
RCI of major port cities in Yangtze River Delta and the Pearl River Delta.

Table 2 .
Gray correlation coefficients of the two port groups.
Source: Yearbook of Each City.

Table 3 .
Gray correlation coefficients of the Yangtze River Delta.

Table 4 .
Gray correlation coefficients of the Pearl River Delta.
Source: Yearbook of Each City.

Table 5 .
Data of the Yangtze River Delta and Pearl River Delta.

Table 6 .
Hysteresis results of the Yangtze River Delta.

Table 7 .
Hysteresis results of the Pearl River Delta.

Table 8 .
Estimates of VAR model parameters for the Yangtze River Delta.
and Table8, the vector autoregressive equations of the Yangtze River Delta and the Pearl River Delta can be obtained respectively.The parameters are in matrix form.The specific equations are as follows:

Table 9 .
Estimates of VAR model parameters for the Pearl River Delta.
port has little effect on the development of the urban GDP and industrial output in the Yangtze River Delta, but the development of port in the Pearl River Delta has a positive impact on the urban GDP and industrial output.