Ranking efficiency of Asian container ports: a bootstrapped frontier approach

Transcription

1 668 Int. J. Shipping and Transport Logistics, Vol. 5, No. 6, 2013 Ranking efficiency of Asian container ports: a bootstrapped frontier approach Susila Munisamy* Faculty of Economics and Administration, University of Malaya, Kuala Lumpur, Malaysia Fax: susila@um.edu.my *Corresponding author Wang Danxia Economics Research Unit, AmInvestment Management Sdn. Bhd., Level 10, Bangunan AmBank Group, 55 Jalan Raja Chulan, Kuala Lumpur, Malaysia Fax: danxiawong@alumni.nus.edu.sg Abstract: This paper employs a smoothed homogenous bootstrapped frontier approach to obtain data envelopment analysis (DEA) efficiency estimates for a more reliable efficiency ranking of Asian container ports. The paper applies desirable statistical properties to DEA efficiency estimates pertaining to consistency, unbiasedness, and estimation of confidence intervals. The paper uses a three-pronged analysis, first by identifying outliers using the log-ratio analysis; second, testing hypothesis with regard to global returns to scale employing a bootstrap methodology; and third, implementing the smooth homogenous bootstrap method to derive bias-corrected DEA efficiency estimates and to build confidence intervals. The results of the study enable individual ports to assess whether their production is efficient compared to their counterparts and indicate strategies for efficiency improvement. Keywords: data envelopment analysis; DEA; bootstrapped frontier; outlier detection; tests of global returns to scale; container ports. Reference to this paper should be made as follows: Munisamy, S. and Danxia, W. (2013) Ranking efficiency of Asian container ports: a bootstrapped frontier approach, Int. J. Shipping and Transport Logistics, Vol. 5, No. 6, pp Biographical notes: Susila Munisamy is an Associate Professor at the Faculty of Economics and Administration, University of Malaya, Malaysia. She received her PhD in Industrial and Business Studies from the University of Warwick, UK and MSC in Operations Research from University Putra Malaysia. She has an extensive research record and teaching experience in the area of statistics and operations research. Her research interests focus on performance evaluation and benchmarking. Copyright 2013 Inderscience Enterprises Ltd.

2 Ranking efficiency of Asian container ports 669 Wang Danxia is a Research Analyst with the Economics Research Unit at AmInvestment Management, Kuala Lumpur, a Malaysian fund management company. She attended the National University of Singapore where she received MSocSci in Economics, after graduating from University of Malaya with BBioMedEng. Her research covers macroeconomic surveillance and price movements across asset classes, econometrics analyses and performance management. This paper is a revised and expanded version of a paper entitled Non-parametric container port efficiency analysis using smooth homogenous bootstrap presented at Asia Pacific Productivity Conference (APPC 2010), Taipei, Taiwan, July Introduction In the 1960s when the main cargo type transported were in break-bulk and port operations were labour intensive, González and Trujillo (2009) observed that efficiency analysis began with interests in facilities-charge structures, capacity and investment policies, and the role of port infrastructure in economic activity. Since the 1980s, the thrust of globalisation propelled high and varied demands in international trade and spurred growth of the shipping industry. More than 90% of goods traded internationally are carried by sea transport and this amounts to 8.4 billion tonnes in 2010 (International Maritime Organization, 2012). The intensity of such demand popularised containerisation and prompted integrated logistic services. In addition, this has resulted in the growth of intermodal freight transport systems which involve quicker and lower cost of freight transportation under multiple modes such as rail, ship, and truck, using yard equipment. At the same time, container ports have evolved from being labour intensive to capital intensive in the race of acquiring sophisticated equipment to increase efficiency. Wang et al. (2005) observed that port service providers are obliged to adopt most sophisticated practices, ranging from high specification of quayside cranes, yard space optimisation systems, to automated transportation systems such as those used at the Euromax container terminal in Rotterdam. Due to the demand-derived nature of port services, incorporation of cutting-edge technology is deemed necessary to maintain competitiveness. The shipping industry plays an important role in the international supply chain especially crucial for development in Asia s export-oriented economies. As such, port competitiveness has a large influence on the region s economic growth. In this regard, it is not surprising that competition among neighbouring ports intensifies as sea-traffic rapidly increases (Cullinane and Wang, 2006). In the contemporary port industry, ports can no longer be considered monopolistic through means of concentrated sea-traffic or access to hinterland, bestowed by strategic geography. Rather, market structure has turned fiercely competitive through intermodal freight transportation systems. This highlight further the importance of proper management and operational policies, and this is where port efficiency studies come in. Container port efficiency can be evaluated through resource utilisation; and its strengths and weaknesses can be reflected by means of benchmarking against its peers. Such benchmarking, according to Wang et al. (2005), is advantageous to port operators in enabling them to act ex ante through proactive

3 670 S. Munisamy and W. Danxia operational enhancements, rather than ex post, where improvements are undertaken only upon shippers responses and suggestions. Data envelopment analysis (DEA) analysis in benchmarking container port efficiency was first proposed by Roll and Hayuth (1993), after which many empirical studies followed. However, many applied DEA studies within the container port literature have claimed DEA techniques as non-statistical. Simar and Wilson s (2000b) methodology of smoothed homogenous bootstrapped frontier model where observations are result of data-generating process (DGP) allows for statistical properties of efficiency estimates in a multiple input-output framework to be found. These include consistency, unbiasedness, and estimation of confidence intervals. The objective of this paper is to formally evaluate container port efficiency performance and rank the ports using statistically-founded DEA efficiency estimates. We propose a three-pronged analysis: first, outlier detection is conducted based on the log-ratio analysis following methods of Wilson (1993); second, a bootstrap methodology to test global returns to scale is employed along the lines suggested by Simar and Wilson (2002); and third, the smooth homogenous bootstrap frontier introduced by Simar and Wilson (1998, 2000b) is implemented to obtain biased-corrected DEA estimates. It is important to remove outliers and assess the technology of production before embarking on an efficiency study of ports to avoid measurement errors and flawed assumptions. Subsequently, the biased-corrected DEA estimates are used to rank the 69 major container ports in the Asian region. The paper is organised as follows. In the next section, we review the literature which encompasses theoretical developments in DEA and variations of DEA methods used in port efficiency analysis. In Section 3, we describe the main framework of our methodology. We discuss production dynamics of the container port and describe data variables in Section 4. Empirical results are given in Section 5. Finally, Section 6 concludes. 2 Literature review Within the literature of efficiency analysis, the parametric approach applies a functional form in estimating the production frontier. Strong assumptions on the probability distribution of residual terms are required, making the approach most restrictive. Although parametric estimators, such as the stochastic frontier analysis, are more efficient estimators, it relies on the assumption that the function is correctly specified. A non-parametric estimator, on the other hand, is based on the idea of data envelopment when estimating the production set, and usually involves mild assumptions. The work of Deprins et al. (1984) for instance, assumes free disposability on the observed data, leading to the free disposal hull (FDH) estimator. The DEA estimator was first used by Farrell (1957), but remained little known until Charnes et al. (1978) and Banker et al. (1984) popularised the idea. Charnes et al. (1978) imposed constant returns to scale (CRS) while Banker et al. (1984) imposed variable returns to scale (VRS) to the DEA estimator of the production set. While non-parametric estimators avoid the risk of misspecification, it usually involves more noise than parametric estimators. The discussion focuses on the port literature employing the non-parametric estimators. Wang and Cullinane (2006) produced by far the most extensive study on the efficiency of container terminals encompassing 104 European container terminals. Using

4 Ranking efficiency of Asian container ports 671 three inputs (terminal length, terminal area and equipment costs) and one output (container throughput), they revealed that the comparatively large sample size resulted in only 9% of fully efficient ports coupled with many less efficient ports under a VRS assumption. In Wu and Liang (2009), using the same output (container throughput) and capacity of cargo handling machines, number of berths, terminal area and storage capacity as inputs, 77 world container ports were analysed under an assumption of VRS. On the other hand, Rios and Maçada (2006) demonstrated that by using a smaller sample size of 23 units of South American container terminals, with five inputs (number of cranes, number of berths, terminal area, number of employees and number of yard equipment) and two outputs (cargo throughput and average cargo shipped) DEA analysis with VRS assumption yielded 70% of the container terminals studied to be fully efficient. Similarly, Kamble et al. (2010) found six out of 12 Indian ports were fully efficient in their study. Clearly, the latter studies indicate the curse of dimensionality small number of observations projected to a large number of orthogonal directions will yield many observations to lie on the boundary, causing low discrimination power. As such, any increase in the Euclidean space between observations must be compensated by an increase in the number observations, as mentioned by Tongzon (2001) and Bonilla et al. (2002). Whether the underlying technology exhibits CRS or VRS is an important question in studying efficiency. Due to a lack of robust statistical methods in returns to scale selection, as mentioned by Panayides et al. (2009), many authors including Wang et al. (2003), Park and De (2004) and Cullinane et al. (2006) employed both CRS and VRS DEA analyses in their papers. Cullinane and Wang (2006), on the other hand, tested for returns to scale using ANOVA and Spearman s rank test. Using ANOVA, they found that both analyses with CRS and VRS assumptions were not significantly different at the 5% level, while using Spearman s rank, they found that the rank of each DMU derived from applying both technologies are similar. Hence, they carried out two DEA analyses with both CRS and VRS impositions in their study. More recently, Carvalho and Marques (2012) underscored the importance of assessing the technology of production before embarking on an efficiency study of seaports. They applied a set of statistical tests suggested by Simar and Wilson (2002) to investigate the technology of production and found Iberian and some important world seaports to exhibit CRS. Few non-parametric tests of global returns to scale methods are available in the literature. Banker (1996) proposed three test statistics for testing the null hypotheses of CRS or non-increasing returns to scale (NIRS) against the alternative hypothesis of VRS. Monte Carlo simulation results in Kittelsen (1997) showed that Banker s (1996) tests performed poorly in terms of size and power. Simar and Wilson s (2002) bootstrap approach for testing hypothesis about returns to scale, on the other hand, has reasonable size and power properties evidenced from intensive Monte Carlo experiments. In more recent developments, Simar and Wilson (2011) introduced a general framework using a sub-sampling scheme that allows for heterogenity in the inefficiency process whilst being computationally efficient. Bootstrap pseudo-samples of size m drawn out of n observations are used to estimate critical values for tests of convexity and returns to scale. Bonilla et al. (2002) attempted to deal with the problem of outliers in DEA models by performing various sensitivity analyses and by deleting efficient observation until efficiency estimates stabilised. Wilson (1993) cautioned that this approach lacks strong statistical foundation and does not detect outliers that appear inefficient and suggested the

5 672 S. Munisamy and W. Danxia use of log-ratio analysis for outlier detection. This analysis proposed by Andrews and Pregibon s (1978) was expanded to a general case of multiple input-output setting by Wilson (1993). For applied research, Seaver and Triantis (1989) and Wilson (1993) recommends the use of more than one outlier detection scheme. In this paper, in addition to the log-ratio analysis for outlier detection, we also employ Pastor et al. s (1999) method of removing pairs of DMUs to detect influential observations, which could also be plausible outliers. Bonilla et al. (2002) also analysed port efficiencies using the method of naive bootstrap analysis. This is done by drawing pseudo-observations independently, uniformly and with replacement from the set of original observations to estimate the probability distribution function of the production set. As illustrated by Simar and Wilson (2000b), such an analysis will yield biased and inconsistent efficiency estimates in non-parametric frontier model such as DEA or FDH. To overcome the drawbacks of the naive bootstrap, modifications such as those in Löthgren and Tambour (1999a, 1999b), and Ferrier and Hirschberg (1997, 1999) have been introduced. Löthgren and Tambour (1999a, 1999b) measured distance from a random point to the estimated production frontier, thus producing a set of DEA estimates that has no correlation to the original DEA estimates. Meanwhile, Ferrier and Hirschberg (1997, 1999), through a modification on the naive bootstrap, produced a pseudo-probability distribution function that does not reflect any characteristics of the true distribution in the multiple input-output framework. In addition, both bootstrap methods produce estimates that are not statistically consistent (Simar and Wilson, 1999, 2000a). Simar and Wilson (2000b) developed a consistent smooth homogenous bootstrap method for inference about efficiency and confirmed consistency through Monte Carlo experiments. This paper extends the work of Bonilla et al. (2002) and Munisamy and Singh (2011). While Bonilla et al. (2002) used the method of naïve bootstrap which yield biased and inconsistent efficiency estimates, and Munisamy and Singh (2011) employed the conventional DEA method which does not generate any measure of error by which to gauge statistical confidence and are susceptible to bias from outliers. They also, do not test the nature of underlying technology before embarking on the efficiency study and assume constant returns to scale, though econometric evidence typically find economies of scale, as found below. Thus, this paper overcomes these drawbacks by identifying and removing outliers, testing returns to scale and implementing the smooth homogenous bootstrap frontier methodology developed by Simar and Wilson (1998, 2000b) to derive bias-corrected DEA efficiency estimates and to build confidence intervals. Thus, the statistically founded DEA estimates enable a more reliably ranking of the efficiency of Asian container ports. 3 Methodology In a framework based on the works of Koopmans (1951), Debreu (1951) and Farrell (1957), a container port production can be characterised by a set of observations on n ports, {(, )} n p S = xi y i i= 1 where each uses a set of x R + inputs to produce a set of outputs q y R +. Hence, the input and output vectors (x i, y i ) of physically attainable points makes a production possibility set of Ψ:

6 Ranking efficiency of Asian container ports 673 p+ q { x y R+ x y} Ψ = (, ) can produce. (1) The boundary of the production possibility set, Ψ, is known as the production frontier. We consider an output orientation approach in this paper, taking into account that the output factor, i.e., container throughput can be proportionally expanded without altering the input factors of berth length, terminal area, total reefer points, total quayside gantries, and total yard equipment. The output possibility set for all x Ψ is defined as follows: q { + } Y( x) = y R ( x, y) Ψ (2) which is bounded by { } Y ( x) = y y Y( x), λy Y( x) λ > 1. (3) The Farrell output-oriented efficiency measure, λ(x, y), of a port operating at the level p q ( x, y) R + + is defined as the reciprocal of the Shephard (1970) output distance function δ(x, y). Alternatively, λ(x, y) is also defined as the proportional output quantities that can be expanded without altering the input quantities. 1 { } { } λ( x, y) δ( x, y) sup λ > 0 ( x, λy) Ψ. (4) 3.1 Non-parametric frontier efficiency estimators Following the works of Farrell (1957), Charnes et al. (1978) and Banker et al. (1984), the output-oriented Farrell efficiency estimators of a container port can be arrived, depending on the type of hull applied onto the production frontier. While the estimator ˆΨ FDH is the n FDH of the observed samples of Sn = {( xi, y i)} i= 1, the estimator ˆΨ VRS is the convex hull of the estimated production frontier, allowing for VRS: p q { x y R+ + y y x x i n} ˆΨ = (, ),, = 1,, (5) ˆΨ FDH t i VRS n n p+ q ( x, y) R y γiyi; x γix + i i= 1 i= 1 = n such that γi = 1, γi 0, i = 1,, n i= 1 The output-oriented Farrell efficiency estimators can then be computed by taking the above hulls into consideration for the linear program: { } λ ˆ = sup λ > 0 λ y, x x, i = 1,, n (7) FDH y i i (6) λˆ VRS n n λ 0 λy γiyi; x γix i > i= 1 i= 1 = sup n such that γi = 1, γi 0, i = 1,, n i= 1 (8)

7 674 S. Munisamy and W. Danxia Since Ψ ˆ Ψ ˆ FDH VRS Ψ, and that Ψ ˆ Ψ ˆ Ψ ˆ VRS NIRS CRS, all FDH and DEA estimators are biased by construction. Hence, all output-oriented FDH and DEA scores are downward biased, with λ ˆ ˆ FDH λvrs λ, and λ ˆ ˆ ˆ VRS λnirs λcrs. While FDH estimate is consistent with or without the convexity assumption, the DEA estimates are only consistent when the convexity assumption is upheld. Korostelev et al. (1995a) proved the consistency of the input-oriented VRS estimates for the case of p 1 and q = 1. For the general multivariate case of p, q 1, Park et al. (2000, 2010) and Kneip et al. (1998) established the convergence rates of δ ˆ, ˆ and ˆ FDH δvrs δ CRS respectively and found that the speed of convergence follows: δ ˆ ˆ ˆ CRS > δvrs > δfdh. The faster convergence rate for the DEA (CRS) estimates is due to the fact that Ψˆ Ψˆ Ψ ˆ FDH VRS VRS. The convergence rates are highly dependent on the p and q parameters, reflecting the problem of curse of dimensionality higher values of p + q causes a slower convergence rate. For the general multivariate case, Park et al. (2000) and Kneip et al. (2008) derived asymptotic results for the input-oriented FDH and DEA efficiency estimators respectively. These results can be trivially extended to the output orientation. Wheelock and Wilson (2008) extended the Park et al. (2000) results to the hyperbolic framework, while Wilson (2011) extended the Kneip et al. (2008) results to the hyperbolic orientation. Asymptotic results for the FDH frontier estimator are due to Korostelev et al. (1995a), while corresponding results for the DEA frontier estimator are due to Korostelev et al. (1995b). Kneip et al. (2008) noted that the distribution function for DEA efficiency estimator has no closed analytical form, so that neither bias-correction nor confidence intervals can be built without going through complex calculations. As such, the bootstrap method is an appropriate technique to estimate distribution of the DEA efficiency estimator which allows confidence intervals to be constructed and assess its statistical significance (see Simar and Wilson, 1998, 2000b). Next, we briefly discuss theories behind outlier analysis, non-parametric tests of global returns to scale, and the smooth homogenous bootstrap methodology. 3.2 Outlier analysis Consider a set L, where L S, and L contains j observations: j {( i, i) } i= 1 L = x y (9) with j < n. Let X = x i and Y = y i. Following Andrews and Pregibon (1978), for the case of single output, the proportion of geometric volume of S L in the p + q space achieved S by deleting j observations is given by the following: 1 R X D X X X X (10) ( ) j ( ) ( j) * ( ) * * * * L L

8 Ranking efficiency of Asian container ports 675 ( j) * where X * = [XY]. The RL ( X ) statistic above can be simplified to reduce computation. One of the methods is by mentioning the statistic in terms of an idempotent matrix, and subsequently performing an orthogonal triangular. 2 j max ( j) * The values of RL ( X ) are computed, where j max is the largest subset to be j deleted, and the minimal value of ( j ) * RL ( X ) among these values is chosen for each ( j) possible subsets of L, i.e., R min. Identification of the outliers is done via a graphical analysis of log ratios, computed 2 j max for the subsets: j ( j) ( * R ) L X log for j 1,, j ( ) max. j = (11) Rmin Each significant separation between the smallest ratios indicates possible outliers. These ideas have been extended to the multivariate set-up in Wilson (1993) and implemented in the FEAR package (Wilson, 2008) that is used in the empirical part of this paper. 3.3 Non-parametric tests of global returns to scale The bootstrap methodology in Simar and Wilson (2002) is used to test for global returns to scale. Consider the Shephard s output distance function for an arbitrary point (x k, y k ) in the production possibility set Ψ. If δ(x k, y k ) > δ CRS, then Ψ = Ψ CRS, and Ψ does not exhibit CRS everywhere. On the other hand, if δ(x k, y k ) = δ CRS, we can say that only the point (x k, y k ) exhibits CRS, but not all other points. Therefore, it does not follow that Ψ = Ψ CRS. In this case, it could be that Ψ = Ψ NIRS by the same argument. Therefore, two hypothesis tests can be set up where it is possible to obtain a statistically significant test of returns to scale: Test #1 H0: Ψ is globally CRS H : Ψ is VRS. 1 If H 0 is rejected, then we perform the second less restrictive null hypothesis test, that is: Test #2 H0 : Ψ is globally NIRS H : Ψ is VRS. 1 We use the common mean of ratios, φ, as our test statistic. In each of the tests, if H 0 is true, φ = φ 0. Otherwise, φ < φ 0. The estimator of φ is φ ˆ. For test #1 where if Ψ exhibits CRS everywhere, φ ˆ = 1, but if Ψ does not exhibit CRS everywhere, φ ˆ < 1. Where Ψ does not exhibit CRS everywhere, we perform test #2. Again, we use the common mean

9 676 S. Munisamy and W. Danxia of ratios, where if Ψ exhibits NIRS everywhere φ ˆ = 1, but if Ψ does not exhibit NIRS everywhere, φ ˆ < 1: 1 δˆ ( x, y) 1 δˆ ( x, y) φˆ = = n δ ( x, y) δ ( x, y) (12) n CRS, i n NIRS, i and optionally, φˆ i= 1 ˆ i 1 ˆ VRS, i n = VRS, i * By performing B bootstrap replications for n observations, we obtain φ ˆb for b = 1,,B from PS ˆ( n ). For both tests 1 and 2, H 0 is rejected if φˆ φo c α, where for a test with size α, c α > 0 such that: ( φˆ φo c H0 ) Pr α = α. (13) From PS ˆ( n ), we are able to approximate the distribution of ( ˆ * φ φ) with ( φˆ φ); and approximate c α by c * α. We then have the following bootstrap approximation: * ( φˆ φ ˆ o c H0 P) Pr α, α (14) * where we reject H 0 if φˆ 1 c α, for a test of size α, given φ 0 = 1 under the null hypothesis. 3.4 Smooth homogenous bootstrap n From the original sample Sn = {( xi, y i)} i= 1, we can only estimate λ(x, y) with λ ˆ( x, y ), by applying the appropriate hull to estimate the production frontier. The statistical paradigm based on the work of Simar and Wilson (1998, 2000b) describes P, the true but unknown DGP that yields the set of Sn = {( xi, y i)} i n = 1 observations; and that for a set of crosssection data, it is reasonable to assume that the sampling process is independently drawn from the probability distribution defined in the DGP s probability model. Hence, following works of Kneip et al. (1998), Park et al. (2000) it is reasonable to define a set of assumptions on P as follows: Assumption 1 All observations are technically attainable, i.e., Prob((x i, y i ) Ψ) = 1. Assumption 2 Assumption 3 For all i = 1,,n, each (x i, y i ) sample observations are independently, identically distributed (iid) with the probability distribution function of f(x, y) in Ψ. Differentiability: The probability distribution function f(x, y) is strictly positive on Y (x) and continuous in all directions towards its interior. The above assumption is a regularity condition sufficient for proving the consistency of all non-parametric estimators. Assumption 4 Monotonicity: Every output must be produced by some inputs: i.e., (x, y) Ψ if x = 0 and y > 0.

10 Ranking efficiency of Asian container ports 677 Assumption 5 Free disposability: if (x, y) Ψ, then for any x xand y y, ( x, y ) Ψ. Assumption 6 Closedness: Ψ is a closed and bounded set. Assumption 7 Convexity: if (x 1, y 1 ), (x 2, y 2 ) Ψ, and for an γ [0, 1], (x, y) = γ(x 1, y 1 ) + (1 γ)(x 2, y 2 ) then (x, y) Ψ. This assumption is required for the consistency of DEA estimators. The smooth homogeneous bootstrap used in this paper was introduced by Simar and Wilson (1998, 2000b). In this framework of homogenous bootstrap, samples are drawn (with replacement) from a Gaussian Kernel function to generate bootstrap values of δ ˆ * ( x, y ) and to construct a pseudo dataset * { S n}. The pseudo dataset is then used to compute the bootstrap efficiency estimate of λ ˆ * VRS ( x, y ). The bootstrap simulations are used to estimate and correct bias and to construct confidence intervals for the efficiency estimate. Details of the full bootstrap algorithm can be found in Simar and Wilson (1998, 2000b). 4 Data description To decide on dataset, we first examine container ports in terms of functionality and transportation dynamics. Vis and de Koster (2003) defines a container port as a transshipment gateway through which containers are transferred from ships to barges, trucks and trains and vice versa. Apart from transportation, Meersman and de Voorde (2002) observed that port providers have extended facility provision services, for example, container storage. A typical unloading process at a container port with throughput greater than 100,000 TEUs a year, is as follows. The import container is taken off the ship using quayside cranes, and is then transferred to vehicles such as prime movers or trailers, which then takes the container to the stack served by gantry cranes. Alternatively, straddle carriers are used to transport containers from the quayside to the stack. After arrangements have been made by parties on the receiving end, the container at the stack is transported by vehicles to other transportation modes like barges, deep sea ships, trains, or is merely collected by trucks. An export container will encounter a reverse order of the above process. Generally, a container port with throughput less than 100,000 TEUs a year employs a smaller scale approach in its transshipment, by using mobile cranes instead of quayside cranes, reachstackers or toplifters instead of straddle carriers and gantry cranes and account to more use of utility trailers than prime movers. According to Vis and de Koster (2003), three planning and control levels in a container port s decision-making process make up an efficient terminal. They are the strategic, tactical and operational planning and control levels. The strategic level decides the layout, equipment required and its methods of operation implemented in the time frame of one to several years. An example of decision made at the strategic level for layout is the number of berths that should be made available at the quay. In the aspect of space utilisation at strategic planning levels, most container ports implemented the method of stacking from the ground instead of storing on chassis (where each container is

11 678 S. Munisamy and W. Danxia uniquely accessible) to maximise storage space. Storage is an important planning aspect as unplanned stacking and retrieval may cause unnecessary hold-up. As such, the efficiency in storage and retrievals can be achieved by strategic planning in the utilization of equipment such as straddle carriers, forklifts, reachstackers, and yard gantries. Tactical decisions are assigned to stow away specific containers to specific blocks such as refrigerated containers, or known as reefers. Noting the importance of facilities provided by the container ports, it is logical to infer that the container port operator s execution of the strategic, tactical and operation plans does affect the time taken for container ports to be transshipped. Furthermore, Wang et al. (2005) observed that better planning and execution will enable a port to transship more containers, resulting in higher container throughputs. Consequently, container throughput has been most appropriate and widely used output indicator. In this study, due to lack of information on labour, we assume that the total number of yard equipment reflect the number of workers required, i.e., the more the yard equipment, the more workers required. This is following Notteboom et al. (2000) who mentioned that expert analysis showed adequately stable, close relationship between the numbers of yard gantries with the number of dock workers in a container terminal. In line with this, Wang et al. (2005) found that the average number of workers per crane is six, comprising one crane operator, one supervisor, and four workers. Hence, we take the total yard equipment, i.e., sum of straddle carriers, yard gantries, reachstackers, front-end handlers, and forklifts, as an input factor. We enlist four other inputs including berth length, terminal area, total reefer points, and total quayside cranes (and/or mobile cranes) to reflect the capital inputs in the industry. Given that some ports may not reveal information through surveys due to operational confidentiality as reported by Tongzon (2001), and Wang et al. (2005); we obtain secondary data for 71 major Asian container ports from Containerisation International Yearbook This enlists ports from 17 countries, i.e., Bangladesh, Brunei, Cambodia, China, India, Indonesia, Japan, Hong Kong, Malaysia, Pakistan, Philippines, Singapore, South Korea, Sri Lanka, Taiwan, Thailand, and Vietnam. Table 1 contains the descriptive statistics for variables used to calculate the DEA efficiency estimates. Table 1 Descriptive statistics for inputs and outputs Berth length (m) Terminal area (m 2 ) Inputs Total reefer points Total quayside cranes Total yard equipment Output Total throughput (TEU) Min 100 3, ,700 Max 12,610 6,169,837 7, ,935,500 Mean 2, ,461 1, ,239, St. dev. 2, ,194, , ,690, Empirical results Each analysis in this section is performed using routines in the FEAR v1.12 package (see Wilson, 2008).

12 Ranking efficiency of Asian container ports Outlier detection Figure 1 shows graphical analysis for computing significance levels using the log ( j) * RL ( X ) ( j) ratios log ( j) as discussed in Section 3.2. Table 2 shows values of R min for Rmin j = 1,,16. Figure 1 Log-ratio plot for 71 major container ports in Asia Table 2 Outliers in 71 major container ports in Asia j Ports R min

13 680 S. Munisamy and W. Danxia From Figure 1, the separation between the smallest ratios indicates that there exist three groups of outliers. The first group, at j = 4, encompasses four ports, namely, Guangzhou (6), Hong Kong (7), Shanghai (11), and Singapore (known as PSA International) (60). From the figure, the first group can be said to be the most significant group of outliers j yielding a considerably low R min of At j = 7, the second group of outliers comprises of three ports, i.e., Qingdao (10), Yokohama (43) and Busan (61). At j = 11, separation between smallest ratios peaks again, yielding Port Klang (48), Manila (56), Bangkok (68), and LaemChabang (69) as the third group of outliers. We keep in view that for j = 15, there is a fourth group of rather insignificant outliers consisting Tianjin (14), Yantian (17), Ningbo (9) and Kaoshiung (65). As it is, let us consider for now that beyond j = 12, the separation in the log ratio plot stabilises. We use an additional approach suggested by Pastor et al. (1999), i.e., and eliminate observations in pairs to detect influential DMUs. We found that ports Ningbo and Zhangjiang are extremely influential and when removed individually is able to improve the average DEA (VRS) scores from 4.50 to 4.08 and to 3.03 respectively. Removing both simultaneously improves the average score dramatically to 2.74 and hence both the DMUs Ningbo and Zhangjiang are said to have masked each other. Furthermore, Ningbo is also one of the outliers in the graphical analysis. We also found that by removing the first four outliers Guangzhou, Hong Kong, Shanghai and Singapore simultaneously will deteriorate the mean efficiency scores marginally from 4.50 to The results are similar by removing the second and third group of outliers. As such, we remove the ports Ningbo, and Zhangjiang from our dataset. Although Guangzhou, Hong Kong, Shanghai, and Singapore are considered as significant outliers, it is of low probability that we find many such ports. Furthermore, in the process of elimination, the average efficiency scores do not change dramatically. Similarly, the second and third group of outliers may be considered to be outliers within the probability distribution, and hence are not removed from the dataset. 5.2 Non-parametric tests of global returns to scale In estimating the production technology we perform the non-parametric tests of global returns to scale using the smooth homogenous bootstrap procedure. In both tests #1 and #2 of returns to scale, we use 4,000 repetitions to acquire smooth homogenous bootstrap * values. From here, we find φ ˆb and obtain the one-tailed 95% confidence interval, based on equation (15). Based on the recommendations by Hyndman and Fan (1996), we use the median-unbiased quantiles which exhibits the most desirable properties of quantile estimators. For test #1, we obtain ˆ * φ = , and the value of 1 c α = Clearly, ˆ * φ 1 c, < α so we reject the H 0 that Ψ is globally constant returns to scale at 95% confidence level. Since the production frontier does not exhibit constant returns to scale, it could exhibit a non-increasing return to scale. We turn to test #2, and obtain φ ˆ = , and * * 1 c α to be Here, φˆ 1 c α, so H 0 that the Ψ is globally non-increasing returns to scale is rejected in favour of the alternative hypothesis of that Ψ exhibits global VRS at 95% confidence level. A VRS imposition in this context is valid following varying

14 Ranking efficiency of Asian container ports 681 sizes of container port production scale, i.e., container throughput. It is also plausible that the container ports studied adopt different capital, equipment and labour arrangements. 5.3 DEA efficiency estimates Wheelock and Wilson (2003) and Wilson (2004) have suggested that the FDH scores should be used as a diagnostic to check whether DEA estimators would be a reasonable application. When many of the observations lie on the boundary of ˆΨ FDH, it would be an indication of the problem of curse of dimensionality. Table 3 shows both FDH and DEA (VRS) estimates of the 69 Asian container ports. As many as 41 observations lie on the estimated ˆΨ FDH boundary, which makes 59.4% of the total observations. This result is similar to Wang et al. (2003) who analysed the efficiency of 57 top container ports or terminals in the world using two alternative techniques: DEA and FDH and found 63% to be efficient under the FDH frontier compared to 40% using the DEA frontier. Since more than half of the observations are classified as efficient using the FDH method in our study, this suggests problems due to curse of dimensionality. As this application uses five inputs and one output it is unlikely to obtain statistically meaningful estimates, given a total of 69 observations. Increasing dimensionality worsens the rate of convergence and by extension biasedness of the estimates (Simar and Wilson, 2000a). Next, using the DEA (VRS) estimator, we find 21 observations (30%) lie on the estimated ˆΨ VRS boundary. Although DEA (VRS) estimates guided by a faster convergence rate of n 2/7 are more efficient than FDH scores, this rate of convergence comes with considerable estimation error. As such, the result does not provide a meaningful basis to support the property that DEA (VRS) estimate is consistent. Even in cases where DEA (VRS) estimate s consistency property is satisfied, Kneip et al. (2008) showed no closed analytical form is available for DEA estimate s sampling distributions and this further highlights the need for proving the consistency of DEA estimates through the bootstrap approximation. Hence, the use of the smooth homogenous bootstrapping method is crucial to approximate the sampling distribution, to make inferences and to correct for estimation error. Table 4 presents the results arrived by applying Simar and Wilson s (2000b) method of homogenous bootstrap, which provides bias-corrected DEA (VRS) estimates and confidence interval estimates at the 95% level. Using the same set of 4,000 repetitions used in the tests of global returns to scale, we are able to produce a set of stable ranking. This is confirmed by the fact that a larger number of repetitions did not perturb the ranks and variability of confidence intervals is lowest possible (see Efron and Tibshirani, 1993). Note that the original DEA (VRS) estimates are subjected to substantial downward bias, as indicated in the fifth column of Table 4. Since the modulus of the estimated bias is greater than the estimated standard errors in each analysis, the bias-corrected estimates are preferred to the original scores, and hence the ports are ranked in a more reliable manner based on the bias-corrected DEA (VRS) estimates. With the bias correction, none of the resulting estimates are equal to one. This discrimination afforded by the bias-corrected estimates also addresses the issue of considerable number observations designated as fully efficient.

15 682 S. Munisamy and W. Danxia Table 3 Original DEA and FDH output efficiency estimates of 69 major container ports in Asia Obs. Port name DEA (VRS) FDH Obs. Port name DEA (VRS) FDH 1 Chittagong Osaka Muara Shimizu Sihanoukville Shimonoseki Dalian Tokyo Fuzhou Yokkaichi Guangzhou Yokohama Hong Kong Bintulu Lianyungang Kuantan Qingdao PasirGudang Shanghai Penang Shantou Port Klang Shekou TgPelepas Tianjin Karachi Xiamen Port Mohd b. Qasim Yantai Cebu Yantian Davao Chennai General Santos Jawaharlal Nehru Iloilo Kochi Manila Mumbai Subic Bay Mundra Zamboanga New Mangalore Jurong Pipavav Singapore Tuticorin Busan Visakhapatnam Inchon Belawan Kwangyang TgPriok Colombo Hakata Kaoshiung Kawasaki Keelung Kitakyushu Taichung Kobe Bangkok Mitajiri LaemChabang Mizushima Da Nang Nagoya Qui Nhon Niigata

16 Ranking efficiency of Asian container ports 683 Table 4 Output-oriented original DEA scores and bias-corrected DEA (VRS) estimates of 69 major container ports in Asia Rank Units Eff. scores DEA (VRS) Eff. bias-corrected DEA (VRS) BIAS std. error Lower bound Upper bound Local RTS 1 Qingdao DRS 2 Yantai IRS 3 Bintulu IRS 4 Guangzhou CRS 5 Tianjin CRS 6 Lianyungang CRS 7 Belawan IRS 8 Yantian CRS 9 Kaoshiung DRS 10 Shanghai DRS 11 Cebu IRS 12 Xiamen CRS 13 Singapore CRS 14 Sihanoukville CRS 15 Niigata IRS 16 Tuticorin IRS 17 New Mangalore IRS 18 Mitajiri IRS 19 Davao CRS 20 General Santos CRS 21 Shimonoseki IRS 22 Subic Bay IRS 23 Visakhapatnam IRS 24 Chittagong CRS 25 Zamboanga CRS 26 Mumbai CRS 27 Hong Kong DRS 28 Colombo DRS 29 Keelung DRS 30 Port Klang DRS 31 TgPelepas DRS 32 J. Nehru DRS 33 Inchon DRS 34 Busan DRS 35 TgPriok DRS 36 Qui Nhon IRS

17 684 S. Munisamy and W. Danxia Table 4 Output-oriented original DEA scores and bias-corrected DEA (VRS) estimates of 69 major container ports in Asia (continued) Rank Units Eff. scores DEA (VRS) Eff. bias-corrected DEA (VRS) BIAS std. error Lower bound Upper bound 37 PasirGudang IRS Local RTS 38 Tokyo DRS 39 Shekou DRS 40 Chennai IRS 41 Shantou IRS 42 Dalian DRS 43 Nagoya DRS 44 Karachi DRS 45 Fuzhou IRS 46 Port M. Qasim IRS 47 Kwangyang IRS 48 LaemChabang DRS 49 Mundra IRS 50 Mizushima IRS 51 Hakata IRS 52 Jurong IRS 53 Kitakyushu IRS 54 Yokohama DRS 55 Manila DRS 56 Penang IRS 57 Osaka DRS 58 Shimizu IRS 59 Kawasaki IRS 60 Bangkok DRS 61 Kobe DRS 62 Taichung IRS 63 Iloilo IRS 64 Kochi IRS 65 Pipavav IRS 66 Yokkaichi IRS 67 Kuantan IRS 68 Da Nang DRS 69 Muara IRS Geometric avg

18 Ranking efficiency of Asian container ports 685 The geometric average of the bias-corrected DEA (VRS) efficiency estimates of major ports in Asia is , 1 with a standard deviation of The metric suggests that given the inputs, the outputs can be expanded by 37%. The estimated 95% confidence interval for this set of ports suggests that outputs could have been increased by between 31.6 and 46.6%. The most efficient port is Qingdao of China with efficiency of , and the least efficient is port Muara of Brunei with efficiency of The Chinese container ports excluding Hong Kong appear to be amongst the most efficient ones with seven out of 11 Chinese ports ranked within the top ten. So et al. (2007) efficiency study on 19 major container ports in the Northeast Asia in 2004, found the Hong Kong port to be most efficient followed by Kaoshiung (Taiwan), and Qingdao was ranked at the 11th position. Many of the mainland Chinese ports have climbed to the top positions in Asia in our study, which could be attributed to China s emergence as the world s manufacturing powerhouse and consumer market (Cullinane et al., 2004) with increasing seaborne trade. In 2007, the total container throughput of the 11 ports in China is the highest, with a total of 77.9 million TEUs followed by Singapore yielding 27.9 million TEUs. China follows the global trend in concentrating liner services at ports, hence developing their ports into hubs, to cater for the rapid development of its hinterland economy as it emerges as the world s manufacturing powerhouse. In addition, the ports Yantian and Guangzhou received much expertise and technology transfer from Hong Kong due to entrepreneurial interests. Qingdao, the most efficient port in this study, is perceived to have a highly efficient and effective management, and its advantageous location at the Bay of Bohai can handle fifth generation container vessels. We also observe that for each of the ports in ranks 15 to 26, the bias-corrected estimates are very near to each other due to their similar distances to the estimated production frontier in the Euclidean space. Thus, the ports in this range must necessarily receive the same rank. The 95% confidence interval are structured from the bias-corrected bootstrap values {( δˆ xi, y i)} b B = 1 for i = 1,,n, and thus the original DEA (VRS) estimates do not fall within this range, due to its biasedness. The length of the confidence interval is considerably large attributing to noise in the original data. The last column of Table 4 indicates the local returns to scale of each port calculated based on the original DEA (VRS) estimates. Individual tests of returns to scale are similar to those of global returns to scale. Here, 33 ports (47.8%) show an increasing return to scale, 24 ports (34.8%) exhibits decreasing returns to scale, while the rest of the 12 ports exhibit constant returns to scale. It is evident that the majority of the container ports with throughput of one million TEUs and higher in a year tend to operate at a decreasing return to scale (DRS). On the other hand, smaller sized container ports with output below one million TEUs a year, exhibit either CRS or IRS. This outcome corresponds to the findings in Wang and Cullinane (2006) in their investigation of efficiency of 104 container terminals in Europe, where they found most of the container terminals under study to exhibit increasing returns to scale. In effect, the results here verify the conclusion from the non-parametric tests of global returns to scale in the previous section that ports operate at VRS technology. It is worth noting that in the case of container port industry, increasing returns to scale is expected when we consider containerisation and technological improvements. The spin-off effects induced increments in container throughput volumes and creation of hub ports which in turn, allows for the container ports to operate with increasing returns to scale (see Jones, 2005). Despite such advancements, many of the larger ports in this study