where L = [LNGDP LNI LNT]’, R2 and the adjustment R2 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.

Figure 7. The inverse roots of AR characteristic polynomial.

4.2. 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(a) that the impact of the change of urban GDP on the port cargo throughput is obvious in the first two periods, but the positive effect gradually decreases and approaches zero, then the positive effects are gradually strengthened and stabilized around zero. It can be seen from Figure 9(b) that the impact of the change of urban industrial output on the port cargo throughput has shown a significant increasing positive impact in the first two periods, but the positive impact begins to weaken and gradually approaches zero from the third period. As can be seen from Figure 9(c), the impact of the port cargo throughput change on port cities has shown an increasing positive impact on GDP in the first two periods, then the impact trends to be stabilized. It can be seen from Figure 9(d) that the impact of the change of urban industrial output on the port cargo throughput has shown a positive effect in the first two periods, and it tends to be stabilized from the third period.

Compared with impulse response maps of the Yangtze River Delta and the Pearl River Delta, it can be found that in both areas, the growth of GDP and industrial output can aggregate the development of port in the short term, and the impact approaches zero in the long term. However, the impacts of the development of the urban GDP and industrial output in the Yangtze River Delta are greater than that in the Pearl River Delta. At the same time, the development of

(a)(b)(c)(d)

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

(a)(b)(c)(d)

Figure 9. Impulse response graphs of 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.

4.3. 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] .

4.3.1. 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

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

Figure 11. Variance decomposition of LNT of the Pearl River Delta.

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%.

4.3.2. 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 period. And the contribution of port cargo throughput (T) to industrial output (I)

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

increased from 0 to 19% in the first two periods, and gradually stabilized at around 19% of the contribution.

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.

5. Concluding Remarks

In this paper, we measure the relative size of port to the size of urban economy through improved relative concentration index (RCI), and the results show that the port-city relationship of the Yangtze River Delta is approaching coordination in the past ten years, while the port-city relationship of the Pearl River Delta is still in a state of incoordination, but it has begun to show the trend of coordination. In general, due to the favorable geographical conditions of the Yangtze River Delta, the economy is more developed, and the port system is more perfect,

Figure 13. Variance decomposition of LNGDP and LNI of the Pearl River Delta.

and the economy hinterland is also more open, and the port-city relationship of the Yangtze River Delta is more coordinated than the Pearl River Delta.

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 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 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.

Conflicts of Interest

The authors declare no conflicts of interest.

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