The Technical Efficiency of Tunisian Ports: Comparing Data Envelopment Analysis and Stochastic Frontier Analysis Scores

Abstract Maritime transportation for Tunisia plays an important role in trade exchange with other countries. Therefore, the objective of this paper is to measure the efficiency scores of 7 seaports in Tunisia by applying the Stochastic Frontier Analysis (SFA) with Cobb-Douglas production function and Data envelopment analysis (DEA) with CCR and BCC models. The annual data collected cover the 2007-2017 period for each port. Thus, the sample size for the analysis comprises a total of 77 observations. The empirical result shows that the total average scores of operating efficiency scores were DEA-BCC (0.746) >SFACD (0.536)>DEA-CCR (0.334) from 2007 to 2017. Given these results, the port of Gabes can be considered as the best efficient port in the 3 models (DEA-BCC, DEA-CCR and SFA-CD).


INTRODUCTION
Maritime transport is the backbone of the world globalization and trade because 80 per cent of the volume of international trade in goods is carried by sea [2]. The maritime transport provides efficient and low-cost means of transporting goods, which help create prosperity among nations and peoples and facilitates trade. The advantage of seaway is safety, speed, comfort, and the ability to manage heavy traffic of goods and passengers at relatively low prices.
Efficiency is the success with which a Decision Making Unit (DMU) uses its inputs to produce outputs. In simple terms, efficiency can be simply defined as the ratio of output to input. Reference [20] proposed that the efficiency of a DMU consists of two components, technical efficiency, which reflects the ability and willingness of a firm to maximize its output from a given set of inputs and allocative efficiency which reflects the ability and willingness of the firm to use the inputs in optimal proportions for given factor prices. Economic efficiency or total efficiency is determined by the product of the technical and allocative efficiency.
A review of previous studies shows that the majority of the studies focused on the seaports in Europe [5,18,6,34] and Asia [11,28]. Nevertheless, none of these studies has focused on North Africa so far. Tunisia has 7 commercial ports (Bizerte, Goulette, Rades, Sousse, Sfax, Gabes and Zarzis). Their complementarity and exceptional location can accommodate various types of ships and treat all types of merchandise. Hence, it is important to study and evaluate the efficiency of the Tunisian ports as this country is witnessing significant development in port legislation and is setting many investment plans in port infrastructure like the new project of Enfidha port which is dedicated to receive panamax and post-panamax ships.
The objective of this paper is to investigate the technical efficiency of 7 ports in Tunisia by using two methodologies: the Data Envelopment Analysis (DEA) and the Stochastic Frontier Analysis (SFA). The analysis of technical efficiency in this research covers DEACCR [8], DEABCC [4] and SFACD (Cobb-Douglas function).
Moreover, we propose the input-oriented DEA model to minimize the inputs while the given current output remains the same if we look at the inefficiency in terms of excess inputs.
This study is organized as follows. In section 2, we present the of DEA and SFA methodologies. In section 3, we give a review of studies on measurement of port efficiency. We describe the data and present the results of empirical study in section 4. Finally, section 5 concludes this paper.

II. LITERATURE REVIEW
In the fast twenty years, a significant part of the literature on ports have focused on seaport efficiency. Most of the studies focused on seaports in Europe [ 24,5,6] and in Asia [26 , 28] but few dealt with the efficiency in the African and in the Middle East seaports. Thus, the majority of studies use both DEA and SFA methodologies to measure the efficiency of seaports.
A. Empirical port efficiency by using DEA The first researchers who attempted to use the DEA to analyze the seaport efficiency are [30]. They used cross-section data to estimate the efficiency of 20 seaports. Their work was limited to the application of the DEA-CCR, which is a standard DEA model.
Reference [24] classified 26 Spanish ports into three groups namely high, medium and low complexity ports. These authors examined the technical efficiency of these ports by using the DEA-CCR and DEA-BCC models. They conclude that high complexity seaports were associated with high efficiency.
Applying both DEA-CCR and DEA-additive models, reference [32] estimated the technical efficiency of four Australian and twelve international ports for the year 1996. He concludes that Melbourne, Rotterdam, Yokohama and Osaka are the most inefficient ports in the sample. By using a cross-sectional data for the year 1998, reference [35] applied the DEA-CCR model to determine the relationship between port efficiency with a particular type of ownership and organizational structure of 31 container seaports among the world's top 100 container seaports in 1998.
Reference [5] employed both DEA-CCR and DEA-BCC to estimate the efficiency of 4 Portuguese and 2 Greek seaports. The writers conclude that the majority of the seaports are efficient, with the sole exception of Thessaloniki.
By using DEA window analysis, reference [27] estimated the efficiency of 11 Korean container terminals for a period of three years 1999-2002. The data include the total quay length, the number of cranes, the size of yard areas, the size of the labour force, the size Lifts per Calls (LPC) storage, Net Berth Productivity(NBP) as inputs. The cargo throughput and the terminal capacity are used as outputs.
By using a cross-sectional data for the year 2002, reference [18] applied the DEA-CCR and DEA-BCC models to estimate the efficiency of 69 container terminals with an annual throughput of over 10,000 TEUs in Europe. The general conclusion is that the terminals are inefficient.
Regarding the research applied to Africa and the Middle East, reference [2] used the Standard Data Envelopment Analysis (DEA) and DEA Window Analysis to study the technical efficiency of seaports. Cross-sectional and panel data from 2000 to 2005 were collected for each of the twentytwo seaports in the Middle East and East African region. They reveal that the DEA-BCC model provides higher efficiency scores than the DEA-CCR model and they also conclude that the ports of Khor Fakkan and Djibouti are the most efficient.
Both DEA-CCR and DEA-CCR models were applied by [26] to analyze the technical efficiency of 69 container ports in the Asian region. They concluded that most of the efficient ports in Asia are located in Bangladesh, Philippines, China, Cambodia, India and Singapore.
Reference [28] has applied the Standard Data Envelopment Analysis (DEA) and DEA-Additive models to examine the technical efficiency of selected major ports in India for the period between 1993 and 2011. They concluded that the size is not a determinant factor for port efficiency i.e. bigger ports Jnpt, Mormugao and smaller ports Tuticorin and Ennore were proved to have efficient port operations all through.
Reference [22] applied the Standard Data Envelopment Analysis (DEA) of nine seaport in Saudi Arabian. They used two output and three inputs to measure of port performance for the year 2014. The writer concluded that Jazan port is considered inefficient plus most of the ports are also inefficient. Table 1 below presents the studies conducted using the DEA method. Among the applications of SFA to the port industry, reference [23] used the technical efficiency with a translog production function to test the hypothesis which states that the public sector ports are less efficient than private ones. A set of panel data relating to the outputs and inputs of 28 British ports over the 1983-1990 period was used.
The translog cost function was used by [14] to estimate the economic efficiency of 27 Spanish ports from 1985 to 1989. They concluded that smaller ports are more efficient. These authors claimed that this is not so much due to size, but to the level of autonomy: ports with smaller autonomy are considered to be highly efficient. By using the cross-sectional and panel data versions, reference [16] applied the SFA with Cobb-Douglas cost function to access the privatization achievement of 5 Korean and UK container terminals. For inputs, they took the managerial service, the employees' salaries, the capital cost of terminal operations, the net book value of mobile and cargo and handling equipment. For outputs, they took the turnover derived from the provision of container terminal services, but excluded property sales.
Reference [33] used the Cobb-Douglas production to measure the efficiency levels of 25 container ports/terminals and examine the relationship between port efficiency and port specific characteristics. They concluded that the private sector participation in the port industry can to some extent improve the port operation efficiency, which will in turn increase port competitiveness.
By using the translog cost function, reference [6] analyzed the extent of the technical change and technical efficiency in Portuguese seaport for the 1999-2000 period. His results showed an average score of inefficiency of 39.6%, denoting a high degree of waste in the management of seaports. The inputs include the price of labour and of capital. The outputs included the number of ships and the total cargo.
Applying the Cobb-Douglas production function, reference [31] estimated the efficiency of the container port production. Annual panel data from 1997 to 2005 have been collected for each of the eighty-three container terminal operators. Their inputs were the handling capacity between the ship and the quay, the handling capacity between the quay and the yard, the number of berths, the length of quay lines, the terminal area, the storage capacity of the port and the refers points while the cargo throughput was the output.
Using the cross-sectional data for 2002, reference [34] also used the Cobb-Douglas production function to analyze the technical efficiency of 22 European ports and estimate their legislation. They concluded that their analysis can't explain the factors that determine the level of port efficiency.
Reference [21] applied a translog production function with panel data for 9 Spanish ports from 1990 to 2002 to evaluate the technical efficiency evolution in transport infrastructure and analyze the impact of 90's port reforms. The results show that average technical efficiency has changed after the reforms.
By applying a panel data from 2002 to 2012, reference [7] analysed the impacts of cost and operational variables on major Chinese ports by means of a stochastic frontier model. Their inputs were the cost in Renminb, the price of labour, price of capital and price of intermediate consumption. conclude that there is considerable heterogeneity in China's seaports, affecting their cost efficiency estimation. Table 2 below shows the applications made by using the SFA method.

III. METHODOLOGY
We adopt two alternative approaches, DEA and SFA to quantify operational efficiency. The main difference between the two is that the former is a non-parametric technique and doesn't make accommodation for statistical noise, whereas the latter is a parametric technique and accounts for statistical noise. Both in the SFA and DEA analysis, a DMU's distance from the efficient frontier measures its relative inefficiency. The two approaches are presented in the next paragraphs.

A. Data envelopment analysis Approach
Data Envelopment Analysis (DEA) was proposed by [8] in 1978. The DEA is non-parametric technique for measuring the relative efficiencies on making units (DMUs) with multiple inputs and/or outputs. In case when there is no other DMU or a combination of DMUs which can produce at least the same amount of output with less of the same resources input and not more of any other resources, the DEA method states that a DMU is considered efficient. In general, a DMU is considered to be inefficient if it obtains a score of less than the unity where a score of unity implies that it is efficient.
Among the number of DEA models, we employ the two most used ones: DEA-CCR model [8] and DEA-BCC model [4]. The DEA-CCR model estimates constant returns to scale so that all the detected production combinations can be proportionally scaled up or down. Besides, the DEA-BCC model was developed by adding a convexity restriction to the DEA-CCR model envelope formulation, which leads to variable returns to scale. Besides, this model is an extreme point technique, noise (even symmetrical noise with zero mean) such as measurement error may cause significant problems.
In this study, we will adopt the input-oriented approach. Therefore, the dual mathematical formulation of the DEA-CCR model is: −Yo+λY ≥ 0 θXo -λX ≥ 0 λ≥ 0 Source : Reference [12] Where: θ : is a sought scalar (it represents the efficiency score of DMU i ), λ : vector of non-negative weights, Y: is the m × n matrix of outputs, X: is the k × n matrix of inputs.
Yo's and Xo's are the observed output and input values, respectively, of the DMUo, and the DMU to be evaluated. θ* is the input-oriented efficiency score of DMUo. If θ * is equal to the unity, then the current input levels cannot be reduced, indicating that DMUo is efficient. However, if θ * < 1, then DMUo is technically inefficient.
However, the DEA presents some drawbacks. The first drawbacks is that the DEA it ignores the statistical noise. So, one can apply the parametric Stochastic Frontier Approach (SFA) to resolve this problem.

B. Stochastic Frontier Approach
This approach was independently introduce by reference [1] and [25]. In fact, this paper uses the SFA model of Cobb-Douglas production function to analyze the efficiency of 7 Tunisian ports.The estimation of this model is allowed by the access to a panel of data which covers a nine year period 2007-2017. The specific functional formal tested are the following: (3) Source : Reference [13] Uit = ( Uiexp (-η (t-T))) (4) Source: Reference [13] Where: The variables are all deviations from the geometric mean and defined as follows: i=1,2,...,7; t=1,2,…,T; t: is a time trend; yit : is the volume of merchandise handled in port i during period t; x1it : is the area stored in port i during period t; x2it : is the number of stevedoring equipment used by port i in period t; x3it :is the number of employees in port i in period t; βk:is the unknown parameters to be estimated k = 0, 1,2, 3; Vit :are random variables which are assumed to bei.i.d N(0,σV 2 ), and independent of the Uit; Uit: are non-negative random variables representing technical inefficiency and are assumed to be i.i.d as half-normal distribution N (0, σU 2 ); η : is a parameter to be estimated; σV: is the variance parameter of noise term; σU: is the variance parameter of inefficiency term. Furthermore, we use the parameterization of [3]. They substitute σV 2 and σU 2 with σ 2 =σV 2 +σU 2 and γ=σU 2 / (σV 2 +σU 2 ), respectively. The parameter γ is between 0 and 1. If γ is close to one, it shows that the deviations from the frontier are due principally to the technical inefficiency. However, if γ is close to zero, it shows that the deviations from the frontier are due principally to noise.
The method of likelihood ratio-test is proposed to examine the presence of inefficiency effect (u it ) under both the null and alternate assumptions. This method is defined as: LR= -2 {ln[L(H0)]-ln[ L(H1)]} (7) Source: Reference [3] Where L (H0) and L (H1) are the values of the likelihood function under the null hypothesis (H0) and the alternative (H1), respectively. In this case, if H0 = 0 is true, this LR statistics, has an asymptotic distribution which is a mixture of chi-square distributions X².

IV.
EMPIRICAL RESULTS

A. Data
The available data are annual covering eleven years period, from 2007 to 2017, about 7 Tunisian ports (Bizerte, Goulette, Rades, Sousse, Sfax, Gabes and Zarzis). Thus, the sample of the analysis comprises a total of 77 observations. The data were obtained from the Merchant Marine and Port Office (OMMP) and the Tunisian Stevedoring and Handling Company (STAM). The measurement of the output is indicated for one element: • Throughput: Movements of general cargo (dry, liquids and containers) unload and load (tons). The measurement of the inputs is considered by the indicators: • Number of stevedoring equipment : Total number of reach stackers, straddle carriers, number of quayside cranes, mobile cranes, quay gantry, mobile gantry and the ship shore container gantry, • Number of employees : Total number of employees of the OMMP and of the STAM, • Area stores: Total area stores (m²).  Table 3 contains the descriptive statistics of the variables used in the study. They include the sample mean, the median, the standard deviation, the minimum and maximum value for each of the variables. Here, the largest traffic of throughput (i.e., 10319193 tons in 2017), the largest number of stevedoring equipment (i.e., 122 in 2014) and the largest number of employees (i.e., 709 in 2015) correspond to the port of Rades since it plays an important role in the national transport chain through its specialization in container traffic and rolling units (mainly trailer traffic). While the maximum Area stores (i.e., 35600 m² in 2014) correspond to the port of la Goulette.
On To estimate the efficiency scores, we used balanced panel data on Tunisian seaport authorities for the years 2007 to 2017. This number of observations allows the estimation of DEA with CCR and BCC models and a stochastic frontier model based on Cobb-Douglass production function.

B. Results and interpretation
FRONTIER Version 4.1 computer software is adopted for the calculation of the frontier for SFA with Cobb-Douglas function for the half-normal distribution (SFACD). Table 4 summarizes the maximumlikelihood estimation results, the test value calculated and the corresponding critical value of the X² distribution at 5% of significance. The estimated value of the variance parameter γ (0.971) is close to the unity, which suggests that deviations are due to technical inefficiency. The test refers to the evaluation of a Cobb-Douglas as a representation of production technology. The null hypothesis, β1 = β2 = β3= 0 test the joint significance of input parameters. LR values of SFACD (165.77722) are larger than the critical values (7.81) of X 2 distribution. This test suggests that we cannot reject this hypothesis and therefore the Cobb-Douglas function can be considered a good model to represent the production technology of the Tunisian port sector. Table 5 reports the technical efficiency of each port in Tunisia calculated by DEACCR, DEABCC and SFACD models within the observed period, between 2007 and 2017.
The scores raised by the application of the DEA models were calculated using the DEAP 2.1 program created by reference [12]. The input-oriented efficiency represents the degree to which a port could minimize its input use without altering its output. The DEA and SFA scores are between 0 and 1. DMUs with DEA and SFA scores equal to the unity are efficient. A DMU with a score of less than the unity is relatively inefficient.
Based on the DEABCC results, the ports of Rades, Gabes and Zarzis have achieved the best overall technical efficiency (score=1). However, the results for the port of Bizerte vary because it was inefficient in 2009.
Moreover, the results of DEABCC for the port of Sfax also vary in terms of efficiency as shown in Table  5. In fact, this port was inefficient along 2007, 2008, 2010, 2016 and 2017. On the other side, it was efficient during the rest of the study period.
When the DEACCR model capture the total technical efficiency and adequately discriminate the efficient DMUs. The results show that the port of Gabes was the only efficient port for this set of samples and showed efficiency scores of 1. This efficiency can be explained by its large production (this port is ranked second in Tunisia in terms of freight traffic) and by the optimal use of the infrastructure and the superstructure. The commercial port of Gabes, the activity of which is characterized by an industrial purpose, is mainly intended for the transit of chemical products on behalf of the neighboring factories located in the industrial zone of Gabes. This bulk traffic comprises above all sulphur and ammonia for import and phosphoric acid and phosphate fertilizer for export.
The results also showed that the ports of Bizerte, la Goulette, Rades, Sousse, Sfax and Zarzis were inefficient during the whole period of analysis. Those ports that invested from 2007 to 2017 found a general decline in efficiency scores, an element which could be explained by the time lag between the investment and the subsequent potential increase in container throughput.
Regarding the SFACD analysis, the results showed that none of the studied ports has high efficiency. However, the port of Rades can be considered as an efficient port during all the study period since its SFACD efficiency scores are always higher than 0.7193 while the SFACD scores for the other seaports are fluctuating.
The port of the La Goulette is the most inefficient, this inefficiency can be explained by its specilization in the passenger traffic and cruise. On the other hand, the port of Gabes is the most efficient by applying the 3 models. In 2016, this port represents 2 times of total traffic of port of Sousse and 3 times of total traffic of port of Zerzis.
We can conclude that the inefficiency of tunisian seaports is noticed in the decline of handling traffic, which corresponds to the results obtained by reference [28] regarding the Serbian ports case.

V. CONCLUSION
This study applies the two leading approaches to the efficiency measurement, DEA and SFA, on the same data set for the port industry in Tunisia and compares the efficiency derived from the two approaches.
The input data are composed of the storage area, the number of employees and the number of stevedoring equipment while the output data include the aggregated port throughput per year.
The analysis shows that the total average of operating efficiency scores of DEABCC (0.746)＞SFACD (0.536)＞DEACCR (0.334) between 2007 and 2017. Based on the DEABCC results, the ports of Rades, Gabes and Zarzis achieved the best overall technical efficiency of 1.0 over11 years of the observed periods. However, the port of Rades can be considered efficient during the whole period of analysis since its SFACD efficiency score has never fallen below 0.7193. Given these results, we can say that the port of Rades can be considered as the best efficient port in the 2 models (DEABCC, SFACD). Based on the DEACCR results, the port of Gabes is defined as the only efficient one for this set of samples, so we can conclude that the port of Gabes can be considered as the best efficient port by using the DEABCC, DEACCR and SFACD models.
We can conclude that there are two solutions to resolve the sources of inefficiencies. Firstly, all the most inefficient seaports are advised to increase the quantity of goods that can be transferred by attracting more clients. Secondly, these ports should rent their stevedoring equipment and storage area to other companies in order to reduce the use of considered inputs (number of stevedoring equipment, number of employees and storage area) in proportion to the achieved output (throughput) in these ports.