Introduction

Transportation is lifeline of economic development and also an important component of the support, services, and security system in sustainable and healthy development of national economy (Wang and Lu 2014). Since the seminal work by Marshall, Alfred (2006), when a company reduces costs and increases production volume, the internal economies of scale have been achieved. External economies of scale (EES) occur outside of the firm and within an industry. In fact, when an industry’s scope of operations expands (due to the creation of a better transportation network that resulting in a subsequent decrease in cost for a company working within that industry), the EES are said to have been achieved.

During the last decades, many scientific, analytical, and empirical works have attempted to study the findings of the economies of scale and density in the public road transport sector. In the seventies of the last century, these works were interested in the concept of the substitutability, their total productivity, and the relative concept to price elasticity and costing as well as economies of scale and density.

The previous main empirical works were based on cost estimates and production technology that can influence the charging structure in the transport sector. More precisely, these inputs were based on linear cost functions, the CobbDouglas functions, the Keller functions, and the Diwert second order translog arbitrary cost.

In this paper, we concern ourselves with Tunisian road transport, that is, with 12 road transport companies. In fact, this study seeks to broaden the knowledge in the impact of the economies of scale and density drawn in the road transport sector in Tunisia. This paper aims to grasp the possibility of a substitutability of the used production factors, in order to highlight the importance of the global productivity achieved in the operation of means of transport for the users and the community.

This paper contributes to the previous studies by using methodological developments and discussing policy recommendation about Tunisian transport.

The rest of this paper is organized as follows. Section “Previous Research Finding” focuses in the most relevant research finding in the literature. Section “Methodology and Proposed Approach” deals with the methodology and proposed approach used in the study. Section “The Descriptive Statistics” describes the data. Section “Results and Discussions” presents results and empirical findings. Section “Conclusion and Recommendations” gives some recommendations and concludes this study.

Previous Research Finding

Many researches were undertaken on road transport building on a sequence of function of trans-logarithmic cost (Ayadi and Hammami 2015a, 2015b). According to Viton (1981), on a sample of 54 urban and suburban American agglomerations for the year 1975, who estimated his function by the Sure-Zeller method (1962). The last drew that the American group bus network produces short-term and long-term rising economies of scale and density. Viton (1981) also noticed the existence of substitutability between the two factors of production, that is to say, the two inputs: work and energy (AES, \( \widehat{\nu} \) LF = 0.22), while stating that labor demand for urban small transport firms is inelastic to the price \( \left({\mu}_{LW}=-0.03\right) \), which is not the case for the large firms \( \left({\mu}_{LW}=-0.19\right) \). Besides, he concluded by maintaining that the energy demand is elastic to the price according to the various classifications of the different firms with \( \left(-0.19\le {\mu}_{FC}\le 0.57\right). \)

For their part, Karlaftis and Mccarthy (2002) estimated function of the variable trans-logarithmic cost from a sample of 256 urban and suburban group haulers in the period of time between 1986 and 1994 in the USA. Through their model, on the basis of the Sure-Zeller method, they used the cluster analysis, which allowed them to identify the gathering of individuals who shared the same attributes. Moreover, resorting to the variable (vehicles/miles) measuring the output in the road transport sector, they reached the following results: the existence of a common and increasing economy of scale and density with (ES = 1.28) and (ED = 1.33) where the two inputs work and energy are complementary (ύLF = −0.55). The demand of work and that of faintly elastic compared with their prices with \( \left({\mu}_{LW}=-0.17\right) \) and \( \left({\mu}_{FC}=-0.45\right) \). These results concern a common sample. On the other hand, when the sample was divided into six groups, the authors concerned affirmed the existence of an economy of scale and density between constant values evolving towards another one sharply increasing ES is for (0.99 to 11); ED is for (0.99 to 20).

As a result, the two inputs work and energy are at the same time substitutable and complementary, according to each group of haulers \( \left(0.63\le {\acute{\upsilon}}_{LF}\le -0.53\right) \), while the demand of work and that of energy are faintly elastic comparing to their price \( \left(-0.16\le {\eta}_{LW}\le 0.24\right) \) (\( -0.45\le {\mu}_{FC}\le -0.17 \) ).

Keho (2005) analyzed the contribution of the public investments to the private capital formation in Ivory Coast, using a co-integration test and an estimation of error correlation during the period 1965–2001. This analysis was concerned with the impact of the global public investment on the private investment which gave rise to a positive, significant relationship between the two variables. This analysis means that the first investment exerted a ratchet effect on the second one. The public capital was divided on six main components (education transport and communication, services, health, agriculture, mines, and industries). In fact, the public capital had a positive compact on the accumulation of the private capital with long-term elasticity varying between (0.54) and (0.80), and this is thanks to the contribution, especially, of the transport, communication and education sector, since the compact exerted by the other sectors is not significant. Keho (2005) concluded by stating that the politic of public investment in the economic infrastructure is in the transport and communication sector or in the formation of human capital. This analysis is an efficient instrument to stimulate growth and development of the private investment forming a fundamental factor for the attractiveness of the direct foreign investments.

Piacenza (2006) estimated a function of a variable trans-logarithmic cost by the maximum likelihood method using a cross-sectional database with a trend where its sample containing 45 transport company giving urban and suburban vehicles haulers during a period of 6 years from 1993 to 1999 in Italy. He used “place-vehicle/kilometers” as input variable and average speed as output variable. The chosen sample is heterogeneous, which encouraged him to work on a common sample and a classified one composed of various groups. He could draw the existence of an economy of short- and long-term growing density.

These authors chose, as inputs, two variables representing the work factor which corresponds to the number of half-time and full-time employees; the capital factor contains the number of used buses. Furthermore, they have also chosen two outputs: “Place/km and Vehicle/Kilometers.” They noticed in their studies that the economy of scale is increasing for small- and medium-size enterprises and that there is a small increase of the technical efficiency during the average of the period. There is also a low increase of the average efficiency due to additional constraints.

Starting from these analyses and empirical results which are coherent and pertinent as for the study of the existence of an economy of scale and density in the urban, suburban, and interurban road transport operation for certain developed and developing countries; starting from that, we are going to wonder if such situations exist or not in the Tunisian public road transport. In other words, does transport operation generate an economy of scale and density or not? In both cases, how to grasp these situations? The answers for these questions prompt us to undertake an empirical analysis.

For Tunisian context, some studies have been developed. In fact, Abdallah et al. (2013) studied causal links between indicators for sustainable energy development related to energy use from Tunisian road transport sector. Their investigation is made by using the co-integration test and the environmental Kuznets curve approach (EKC). They examined the nexus between road transport-related energy consumption, road infrastructure, transport value added, fuel price, and CO2 emissions from Tunisian transport sector. Their results show that road transport-related energy use, transport value added, road infrastructure, and transport CO2 emissions are mutually causal in the long run. Their results confirm also the presence of unidirectional links running from fuel price to road transport with no feedback in both the short and long runs. Therefore, the fuel price and the road infrastructure are important and significant in the causal chain. An important article by Haouas and Heshmati (2012) which analyzed the economies of scale in the Tunisian industries including the transport sector, in this article, electricity, transport, mechanical, and oil and gas industries show an increasing return to scale.

Ayadi and Hammami (2015a, 2015b) analyzed the cost structure of the public transport industry in Tunisia. They used a translog variable cost function to identify the firms’ technological features based on a sample of 12 Tunisian regional transport companies over the period 2000–2010. Their results show the critical productive situation of the Tunisian urban public transport system. This critical productive situation can be exemplified by the presence of a short- and long-term diseconomy of scale; in addition, the overall factor productivity is very low.

Methodology and Proposed Approach

We approximate the variable size of the network by the total length of lines reserved for the 12 regional transport companies in Tunisia. We also estimate the variable number of stops by the stop indicating the place where vehicles stop to pick up or drop the passengers which concern the collection center for captive transport. Furthermore, we determine the variable as the following. Vehicle park building on the acquired vehicles on the occasion of the creation or extension of the urban and interurban public transport service or the renewal of the used park for these services: buses, coaches, articulated buses, comfort coaches and minibuses, etc. This allows us to calculate the number of employees by the total number of the company employees which is composed of the administrative staff, the working staff, and the technical staff. Finally, we can estimate the production of the public transport service in the regional companies as a homogenous variable which is marked (Y). The production variable is calculated from the vehicle/kilometers traveled. This production gives a better representation not only of the average efficient capacity used to guarantee the service but also of the distance traveled by the vehicles simultaneously.

To study the economies of scale and density in the public road transport for the 12 regional Tunisian companies during the period 1995–2014 on annual frequency, we refer to an artificial econometric model. Historically, the economies of scale and density are expressed by the production of the public transport service of these regional companies. The production (Y) noted as endogenous variable for our database. In the other hand, the explanatory variables are the number of stops (NS), the size of network (SN), the fleet (F), the number of employees (NE), and the production (Y). Indeed, empirically speaking, the dynamic link between the economies of scale and density in the public road transport sector in Tunisia concerns the total length of lines reserved for the 12 regional transport companies (TR), the number of vehicle stops to pick up or drop the passengers (NS), the vehicle acquired on the occasion of the urban and interurban public transport service or the renewal of the fleet (F), and the number of employees (NE). In order to establish this dynamic link between these variables, we refer to the main works of Viton (1981), De Borger (1984), Obeng (1985), Thiry and Lawaree (1987), and Abbes and Bulteau (2003) to draw a base model which is presented in the form of the following Cobb–Douglass function:

$$ {Y}_{it}={A}_i{(SN)}_{it}^{\alpha_i}{(NS)}_{it}^{\beta_i}{(F)}_{it}^{\theta_i}{(NE)}_{it}^{\lambda_i}{e}^{\varepsilon_{it}}\kern4em \forall\ \mathrm{t}=1995\to 2014\kern0.5em \mathrm{e}\mathrm{t}\ \mathrm{i}=1,.......,12. $$

We use the logarithmic linear operation on the right and on the left to test the homogeneity of all the coefficients and constants of our reference model below and to give an exact specification to this model. After its transformation, our modal takes the following from:

$$ Log\left({Y}_{it}\right)= Log\left({A}_i\right)+{\alpha}_i Log{(SN)}_{it}+{\beta}_i Log{(NS)}_{it}+{\theta}_i Log{(F)}_{it}+{\lambda}_i Log{(NE)}_{it}+{\varepsilon}_{it}. $$

We use the Fisher homogeneity and heterogeneity tests to give an exact specification of the temporal-individual double dimension. Therefore, we adopt the two statistics of fisher (F1 and F3) to identify the common and different feature of all the parameters of our base model relating to the 12 regional public transport companies (SRT) in Tunisia for the period 1995–2014.

The Descriptive Statistics

The database was extracted from the directorate general research and planning of the ministry of transport and from regional public road transport company balance sheets (land transport directorate). The variables have a double dimension individual or spatial and temporal. The first corresponds to the 12 regional transport companies which are Beja, Bizerte, Gabes, Gafsa, Jendouba, Medenine, Nabeul, Kairouan, Kasserine, Kef, Sfax, and Sousse. The second represents during the period 1995–2014Footnote 1 based on annual basis.

The analysis of the economy of scale and density in the public transport sector requires the implementation of a road infrastructure and the use of production factors. The optimal allocation of these factors, that is to say the labor and the rolling stock, is the fundamental determinant of the total factor productivity.

The combination of these two production factors requires a dose of technology to achieve a certain level of output. The last represents the public transport service in our article. Our base for the temporary individual data concerns the explanatory and endogenous variables including the size of network (SN), the number of stops (NS), the fleet (F), the number of employees (NE), and the production (Y).

In this section, we are going to choose the indicators of positions, dispersions, and forms in order to study the normality, the adjustment, and the estimation quality of each component of our base model. So, Tables 1, 2, 3, and 4 correspond to a descriptive analysis of the explanatory variables and the endogenous variable during a period of study from 1995 to 2014 on annual frequency concerning the 12 regional transport companies.

Table 1 The indicators of positions
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Table 2 The indicators of dispersions
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Table 3 The indicators of forms
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Table 4 Total matrix correlation
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According to Table 1, we can conclude that on the one hand, the average for the five explanatory variables and the production of the companies transport services are a little high, since the values of these variables are quite strong median. This result shares the cumulated increasing frequency of each variable of our model which is grouped also into two and so strong for the explanatory variables and the endogenous variable of the base model. On the other hand, we must study the quality of estimation and the adjustment each component of this model by the indicators of absolute and relative dispersions. In order to achieve this, Table 2 corresponds to the dispersion criteria of these variables.

From the result of Table 2, we observe that the quality of estimation of these variables is very good since the variance of each variable below is too low. The linear adjustment of each previously mentioned variable is efficient because the standard deviations are low as well. Therefore, we can conclude that there is a good linear adjustment for the explanatory variables and the endogenous variables of our base model. Furthermore, it is necessary to study the normality of each variable of our reference model by the bias of the form indicators and the Jarque and Bera statistics presented in the Table 3.

Table 3 shows that all variables follow a normal law because the statistics of Jarque and Bera are two freedom degrees of lower than the critical value of Khi-two. In addition, all variables are asymmetric, since the statics of Kurtosis are greater than three. Thus, we conclude that all these variables have parabolic branches with asymptotic direction towards the abscissa axis but these statics of Skewness tend this to zero. We could conclude that the production, the size of network, and the number of stops are shifted to the left. However, the other variables are shifted to the right.

Results and Discussions

Causal and Correlation Relationships

The study of dependencies relationships between the explanatory variables and the production of public transport services for the 12 regional companies during a period of study from 1995 to 2014 on annual frequencies is given the total matrix correlation describing the interrelations between the variables of our model.

From this matrix, we can say that it is a positive dependency relationship between the endogenous variable and all the explanatory variables. Thus, there is a positive dependence between the production of public transport services for the regional companies, the size of the network, the number of stops, the vehicle fleet, and the number of employees. So it exists, by the end of the day, a positive correlation between the number of employees and the other explanatory variables. The vehicle fleet exerts positive influences on the production, the size of the network, and the number of employees. That is to say, the transport services provided by these companies are according to the vehicle park; the more we increase the number of vehicles in use, the more the available seats increase. We notice that the dependencies between the explicatory variables and the endogenous variable are very high. So, there is a strong correlation between the explanatory variables. Consequently, there will be a multi-collinearity problem between these explanatory variables.

Specification Tests

The estimation of the linear function, related to the logarithm of the productions of the public transport services according to explanatory variables in log for the 12 regional companies during a study period from 1995 to 2014 on annual frequencies, requires a first step, the homogenous or heterogeneous verification and specification of the generative process of individual-temporal data. Econometrically speaking, this comes down to test the equality of coefficients our theoretical model studied in its individual dimension. In addition, the specification tests amount to determine if we have the right to suppose that this production is perfectly identical for the 12 regional companies of Tunisian public road transport or, it is quite the reverse, that there are specificities which are peculiar to each company. Our theoretical model could be presented as follows:

$$ Log\left({Y}_{it}\right)= Log\left({A}_i\right)+{\alpha}_i Log{(SN)}_{it}+{\beta}_i Log{(NS)}_{it}+{\theta}_i Log{(F)}_{it}+{\lambda}_i Log{(NE)}_{it}+{\varepsilon}_{it}. $$

The innovations ε it are supposed to be “iid” with mean zero and variance of σ 2 ε , i ∈ [1, N]. Thus, we suppose that the constants Log(A i ) of our model can vary in the individualFootnote 2 dimension, but they are invariant in time. This model has many possible configurations (see Hurlin Christophe 2006).

Table 5 represents the tests of homogeneity and heterogeneity of the model parameters.

Table 5 The tests of homogeneities and heterogeneities
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From Table 5, we conclude that all the production coefficients of the public road transport services are identical for the 12 regional companies even though the invariant effects are heterogeneous among these companies. In view of that, our reference model is specified in the form of a panel with individual effects taking these following specifications:

$$ Log\left({Y}_{it}\right)= Log\left({A}_i\right)+\alpha Log{(SN)}_{it}+\beta Log{(NS)}_{it}+\theta Log{(F)}_{it}+\lambda Log{(NE)}_{it}+{\varepsilon}_{it}. $$

Static Estimate of the Production of the Public Road Transport Services in Tunisia

The specification tests show that our model can be formalized as a panel with individual effects. In order to estimate the production of the public transport services of the 12 Tunisia regional companies of road transport during the 1995–2014 period based on annual data using within and GLS techniques, Table 6 recapitulates these two estimation procedures. In fact, in the observation of the static relationship, what type links the production of the public transport services according to explanatory fundamental and behavioral variables?

Table 6 Static estimation
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According to Table 6, we could say that the estimation, using these two techniques, gives positive and significant results for all the explanatory variables of our reference model. The production of public transport services is elastic with respect to the size of network that means the growth of road networks has a big influence on the rise of this public production even on the presentation of the provided services. This result matches Hirshhausen and Cullmann’s work (2010) for collective public and private transport system in Germany. However, the production of public transport services is less sensitive but positive to the number of stops. This interpretation is in agreement with Hirshhausen and Cullman’s conclusion (2010) where the number of stops in Germany exerts a positive effect on the increase of production’s volumes of the public services. The vehicle park, also, and the number of employees have a positive impact on these volumes of transport production in Tunisia for both estimation procedures within and GLS.

Nevertheless, to arbitrate between the two estimation techniques, we must turn to Housman’s test (1979); Table 7 corresponds well to Housman’s test (1978) for the logarithm of the production of public road transport services.

Table 7 Hausman’s test (1978)
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Table 7 shows that the production of public transport services for the 12 regional companies is specified by a panel with random individual effects since Housman’s statistics is lower than Khi-two is four degrees of freedom below. This drives us to stick with the estimation results of this production using GLS techniques. The elasticity of the public transport production with respect to the explicatory variables are positive and significant, that means it exists or strong sensitivity between this production, the size of the network, the number of stops, the vehicle park, and the number of employees.

These results are expected because the accumulation of the production of the public transport services requires an innovation of lines. Such an innovation can have a positive effect for the existence of an economy of density in the management of Tunisian public road transport-concerned companies. The improvements of stops or stations for the used vehicles as well as a well-planned, efficient staff increase of the regional transport companies can have a positive impact on the management of these data. Table 8 corresponds to the constant estimation or the random individual effects for the 12 companies using the GLS technique.

Table 8 Estimation of random individual effects
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Finally, we can indicate that the estimation of individual effects by the generalized least-square method GLS gives expected and significant results. The estimated values of the constants are also very low; these ones mean that the average effects of the omitted variables are very low. Hence, it is a question of a good specification of the production of the public transport service with respect to the explanatory services since the unforeseen uncertainties are so low. We represent these random individual effects in Fig. 1.

Fig. 1
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Random individual effect

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Conclusion and Recommendations

This paper provides some important evidence on the impact of the economies of scale and density drawn in and by the road transport sector in Tunisia and the understanding of officials’ perceptions of the role of transport in facilitating city growth. The trans-logarithmic production function has been used in order to detect the relationship between the used variables. We have concentrated on the 12 regional transport companies which are Beja, Bizerte, Gabes, Gafsa, Jendouba, Kairouan, Kasserine, Kef, Medenine, Nabeul, Sfax, and Sousse during the period 1995–2014 with annual data. Results show a big interdependence between the production of public transport services for the regional companies, the size of the network, the number of stops, the vehicle fleet, and the number of employees. In fact, the principal findings of our study reveal the existence of a homogeneity in the total production of these companies which vary with the size of the networks, the number of stops, and the number of employees, although it exists a strong heterogeneity concern. Thus, despite of the shortage in staff and in rolling stock which are necessary for a proper operation of the public road transport run by the 12 regional companies, the focus of our study, we could affirm, considering our study on the urban, suburban, and interurban transport network, that the situation requires a strengthening not only in the field of infrastructure but also in the operation of the public road transport lines in Tunisia.

Further studies are needed to understand the full scope of integration of density and scale economies in the public road transport. What is the appropriate political economy of public transport pricing and what are the quality decisions in a sustainable urban transport? It is important to understand how to invest in this field. To get responses, we should deal with these issues in future research. The applications on the transport and economic time series have specific features in comparison with others; in order to address these issues, we will try with the non-linear and non-parametric models for the future extensions.