SHAO Yanbo()， PAN Baofeng ()

1 College of Economics and Management， China Jiliang University， Hangzhou 310014， China2 Graduate School， Korea Maritime and Ocean University， Busan 49112， Korea

Abstract： The efficiency of the seaport has been variously studied utilizing either data envelopment analysis (DEA) or stochastic Frontier analysis (SFA). Given the strengths and weaknesses associated with these two approaches， applying both models to compute efficiency estimates for the 11 seaports of the China and Korea from 2012-2016 and comparing the results obtained. Main finding facts of this paper are as follows： (i) there are some differences among relative efficiency levels， but almost no differences among efficiency ranks in DEA and SFA results. (ii) The tendency of VRS is stronger in Chinese coastal seaports during the past several years. (iii)The values among seaports in SFA model are relatively smaller than those in the DEA models. The results show that the efficiency of major seaports in Korea is far lower than that of ports in China.

Key words： data envelopment analysis (DEA); stochastic Frontier approach (SFA); seaports efficiency; China; Korea

Introduction

Seaport， as a combination of land and sea for two large geographical regions， has become one of the most dynamic economic entities and powerful engine of urban， regional and national development[1]. With the process of rapid economic globalization， all over the world， where most of the trade is done by sea， they gradually realize the importance of ports in promoting the economic development of the region. Over the past years， the Eastern Asia has become an important market in world shipping network. Container throughput of China ports like Shanghai and Qingdao shows a significant expansion. Similarly， Korea ports’ container throughput has been on the rise， although the growth trend has recently slowed down[2]. Therefore， competition among the main ports in Eastern Asia is becoming inevitable. Especially competition between ports of Korea and China will be unavoidable mainly due to their close geographical positions[3]. The study of Chinese and Korean seaports’ efficiency is not only a way to know the economic performance of theses seaports， but also a pass through to understand the economic situation and to forecast the future development of the seaports.

A large number of researches concerning port efficiency evaluation began in the 1970s， using various methodologies. The data envelopment analysis (DEA) with mathematical programming techniques has applied to the measurement of port efficiency for hypothetical port date by Roll and Hayuth[4]. Ravelo[5]applied BCC model to assess global efficiencies of 26 Spain ports using 5 observations for each port from 1993 to 1997, and to examine efficiency evolution of individual port. Lietal.[6]applied CCR-BCC model to evaluate the efficiency of 16 seaports in Northeast Asia. Stochastic Frontier analysis(SFA) is based on the quantitative economy theory that has been applied to the measurement of technical efficiency by Liu[7]for 28 Britain ports during 1983-1990. Culliance and Song[8]assessed the success achieved by Korea’s port privatization policies in increasing the productive efficiency of its container terminals. Ai[9]studied the efficiency of container terminals in the Pearl River Delta region of China by SFA.

However， previous studies on port efficiency evaluation of different countries were merely focusing on their ports. They have not touched comparison on container ports efficiency among two or more countries. In this paper， after selecting container ports within major ports in China and Korea， we try to compare and analyze their relative efficiency. It is intended to find problems presented in the port operation and to derive implications required for efficiency improvement and operation level enhancement.

1 Methodology

DEA can be roughly defined as a nonparametric method of measuring the efficiency of a decision making unit (DMU) with multiple inputs and/or multiple outputs[10]. This is achieved by constructing a single ‘virtual’ output to a single ‘virtual’ input without pre-defining a production function. The DEA CCR model was first proposed by Charnesetal.[11]， which assume constant returns to scale(CRS). We call it DEA-CRS model. The DEA CCR was first proposed by Bankeretal.[12]， which assumes VRS (variable returns to scale). We call it DEA-VRS model.

Assume that there areNports (DMUs)， each producingJdifferent outputs employingIdifferent inputs. Also， assuming thatxirepresents the amount of input employed andyirepresents the amount of output produced by thei-th ports. Thus， the data of all ports in the sample are represented byJ×Noutput matrix，YandI×Ninput matrix，X. Since there areNports， the linear programming problem is solvedNtimes， once for each port in the sample.

The Technical Efficiency DEA CRS (DEA CRS Model)： To simplify the problem， let’s consider that theseNports， operate under the CRS and employ three inputs (Xi，i=1， 2， 3) to produce single output (Y). The formal problem for the technical efficiency (TE) can conveniently be expressed as

MinTE， wTEi

Xj·wi≤TEi·xi，j=1， 2， 3，wi≥0

(1)

whereTEiis a scalar and represents the technical efficiency measure (index) for thei-th port.wijis the 1 ×Nvector of intensity weights defining the linear combination of efficient ports to be compared withi-th port. The inequality (Y·wi≥yi) implies that the observed outputs must be less or equal to a linear combination of outputs of the ports forming the efficient frontier. The inequality(Xj·wi≥TEi·xi) assures that the use of inputs at the linear combination of the efficient ports must be less or equal to the use of inputs of thei-th port. The formulation will show thatTEi≤1. According to Farrell[13]， an index value of 1 refers to a point on the frontier and thus to a technically efficient port.

The technical efficiency VRS (DEA VRS Model)： the CRS assumption will be incorrect if all poets are not operating at an optimal scale[14]. In this case， the CRS specification will bias the estimation of the technical efficiency by confounding scale effects. However， the substitution of the CRS with VRS assumption brings about the estimation of the pure technical (PTE)，i.e.，TEdevoid of the scale effects. This can be achieved by adding a convexity constraint (N1×wi=1) to Formula(1) which allows VRS as demonstrated below.

MinTE， wTEi

Xj·wi≤TEi·xi，j=1， 2， 3，N1×wi=1，

wi≥0，

(2)

whereN1is a 1×Nvector of ones. The VRS frontier obtained this way envelops the data more tightly than the CRS frontier and thus generates technical efficiency scores which are greater than or equal to those obtained from the CRS frontier.

SFA is a method of economic modeling. It has the starting point in the stochastic production frontier models simultaneously introduced by Aigneretal[15].

The SFA Model： in order to estimate the technical efficiency of seaport production by SFA， we assume Cobb-Douglas production frontier function， which is estimated by using Maximum likelihood techniques to examine factors influencing the output of seaport production. The stochastic production frontier can be written as

(3)

whereYiis output ofDMUi，xijis thejinput used byDMUi. The essential idea behind the stochastic frontier model is thatεiis a “composed” error term. The error term (εi) is now defined as

εi=vi-ui,i=1， 2， …，N,

(4)

whereviis two-sided (-∞

2 Empirical Results

2.1 The data

In this paper we assume two inputs and single output. Output is the volume of seaport’s cargo handling， and inputs are the number of productive Berths and the yard area. The selected samples are 11 seaports from China and Korea. Because these ports are China and Korea famous ports， so their efficiency could reflect the overall efficiency of China and Korea seaports. We collected all the data from the Statistical Yearbooks’ and the Shipping Statistics Handbooks， some dates provided by the Ministry of Korean National Territory and Maritime Affairs.

Table 1 Introduction of the selected 11 seaports

The summary of the information on the input and output variable is given in Table 2. The sample seems to combine appropriate different-sized DMUs as shown by the coefficients of variation (C.V.).

Table 2 Summary for the input and output variables

Note： S. D. means standard deviation

2.2 DEA and SFA results

Using the DEAP 2.1 and FRONTIER 4.1 software， 11 seaports in China and Korea were selected with a span of the years 2012-2016， after processing the raw data according to the design of the index system of the indicators of efficiency values.

Table 3 and Figs. 1-2 show the efficiency levels which are measured from the assumptions of CRS and VRS by using input-oriented DEA methods. The average efficiency of DMU10 is the highest in both CRS and VRS models. DMU5 is the second highest in both models.The average efficiency of DMU6 and DMU8 are relative lower in both models. In DMU2 and DMU11 the difference between CRS and VRS model is relatively large. DMU5 and DMU10 show almost the similar results in both CRS and VRS models.

The efficiency measures of VRS are higher than those of CRS， which can be evident from the definition of VRS. The efficiency of DMU4 has been rapidly increasing over time.

Table 3 Efficiency levels of input-oriented DEA CRS and

Fig.1 DEA CRS efficiency level trends of eleven seaports

Fig.2 DEA VRS efficiency level trends of eleven seaports

Table 4 shows maximum likelihood estimation (MLE) results from SFA methods. We estimated parameters using FRONTIER 4.1， which is considering half-normal and truncated-normal distributions aboutμi’s. All coefficients are significant at the 1% or 5% significance level of T are positive， which means output-increasing effects of factors， which is consistent with economic theory.

The LR(test of the one-sided error) values of SFA are 127.7， which is large than the critical value 5.02 ofx2distribution at the 5% two-sided hypothesis test. It means thatH0：λ=0 is rejected. So there exists some technical inefficiency effect.

Table 4 Parameter estimation of the stochastic frontier production function model

Note： ***， **， * are the significance at 1%， 5%， 10% level, repectwely

Table 5 and Fig. 3 show the efficiency levels of SFA’s model. In terms of the efficiency levels of SFA, DMU1， DMU2 and DMU10’s average values are comparatively higher than other values， but the efficiencies of DMU4， DMU6， DMU7， DMU8， DMU9 and DMU11 are relative low. Especially， DMU as the first seaport in Korea， whatever DEA or SFA， the efficiency appears comparatively low with other seaports. Overall， whatever Chinese seaports or Korean seaports， the efficiency is not the most efficient， namely 1.000.

Table 5 Efficiency levels of SFA model

Fig. 3 SFA efficiency level trends of eleven seaports

2.3 Comparison of DEA and SFA in efficiency measurement

Efficiency value of the DEA to calculate the 11 ports with the SFA method to calculate the efficiency scores and rankings were compared， as shown in Table 6. The differences among seaports in SFA model are relatively smaller than those in the DEA models. Because econometric method permits error terms， it can exclude some irregular fluctuation from dependent variable. Therefore the differences of SFA model seem to be smaller than those of DEA models.

It can be seen from Table 6， the DMU2， performance rankings vary greatly， the efficiency of two methods， respectively， and a difference of 7. The differences among Ningbo-Zhoushan port in SFA model are relatively smaller than those in the DEA models. The reason that DEA methods approaches are different methods from SFA approaches. DEA methods don’t permit any randomness of variables and measurement errors， while SFA methods are econometric methods to measure the efficiency levels permitting some errors. Furthermore， we may also need more time series data of Ningbo-Zhoushan port to fine more accurate reasons of this difference. Taking the data in Table 6 as the basis， and using the SPSS21.0 software to carry on the descriptive statistics to the sample， the results are as follows.

Table 6 Comparison between DEA and SFA results

Table 7 is descriptive statistical results of the paired samples. It can be seen that the mean value of the DEA efficiency is 0.651， and the mean value of the SFA efficiency is 0.564， SFA efficiency values significantly are lower than the value of DEA efficiency.

Table 7 Descriptive statistics of the paired samples

Taking the data in Table 6 as the basis again， efficiency values measured by two methods using paired two-sample means t-test， to look at whether the significant differences， the results are shown in Table 8.

Table 8 Paired sample t-text value analysis

From Table 8， it can be seen， to the 11 seaports， the mean value of the DEA efficiency is 0.651， and the mean value of the SFA efficiency is 0.564， SFA efficiency values significantly lower than the value of DEA Efficiency， the difference is 0.087. Two-tailed T-test significant probability P value of only 0.023<0.05， which means that the DEA efficiency value and the value of the SFA efficiency significant difference in the probability of making mistakes is only 0.018， which is a small probability， namely， there are significant differences between the DEA efficiency value and the value of the SFA efficiency. We compare the two results of DEA and SFA， based on ranking and value of the relative performance of the two methods， carrying on the relevant examination.

According to the reference described by Snedecor and Cochran[16]， Spearman rank correlation coefficient is

rs=1-6∑D2/ [n(n2-1)],

whereDis the same port to different measure of the relative performance ranking difference， andnis the number of samples. The relatively higher coefficient represents the similarity of relative performance ranking between the two methods.

From these results of DEA and SFA， based on above formula， we can calculate the correlation between the two methods. The correlation between DEA and SFA efficiency is 0.60. It shows that the performance of these two methods has higher correlations consistency.

Using SPSS 21.0 software to conduct the Spearman correlation test， the correlation coefficient results are the 0.637 overall valid values of 11 ports， the Spearman correlation test， and significant results in the 95% confidence level. The result is shown in Table 9.

These results suggest that ranking the relative performance of these two methods the value and efficiency of the hypothesis test， indicating that although the two methods to measure the existence of significant differences in the efficiency values， but significant correlation and good agreement between the sort of efficiency values sex. It also verified the DEA and SFA model is reasonable in Port Performance Evaluation.

Table 9 Efficiency related test derived from DEA and SFA

3 Conclusions

In this paper， we apply two methods to Chinese and Korean seaports and compare the results. Importance implications are presented in the following. First， there are some differences among relative efficiency levels， but almost no differences among efficiency ranks in DEA and SFA results. Second， the tendency of VRS is stronger in Chinese coastal seaports during the past several years. Third， VRS model’s values are higher than CRS. Fourth， the values among seaports in SFA model are relatively smaller than the in the DEA models. In addition， DEA results are highly correlated with SFA results， and DEA method shows upper trends close to one， but SFA methods shows lower trends close to zero.

From the years 2012 to 2016， the growth of China ports largely depended hinterland economic development and government’s support rather than other factors. This was because China ports got many benefits from the growth China’s economy and government policy’s support， which both made import-export volume and port productivity rapidly. And the factors named free trade zone area， berth length; direct-call line played an important role in container throughput. From the standpoint of China ports， in order to raise port efficiency， on one hand all the ports should put emphasis on attracting more transshipment through improving competition advantage， for example providing lower tariff， service and so on.

Since seaside operations have impact on the overall production efficiency of container terminal， adequate distribution of seaside resources to vessels benefit both the terminal and clients a lot[16]. China ports also should make unremitting efforts to develop other new profits models from now.

In order to find the influence factors to port efficiency more clearly and effectively， future research may be required to collect and analyze more data of more ports over a long period.