Econometric analysis and applications

¶ … economic analysis of the operating cost that are incurred in the running of a metro station. The paper also reveals the variables that are tied to the cost efficiency of the whole process of running a metro station. The cost of operating the stations is however grouped under the semi-fixed costs that are involved. This is because these costs do not vary proportionately with the output of the metro business. This paper seeks to shed light on some of the main factors that affect these costs. Empirical analysis reveals that very strong system specific factors influences costs but it is worth mentioning that there are other station specific details that also influences the costs. These include the number of platforms in the station, the length of the passageways, the interchange demand, availability of toilet facilities etc.We also discover that presence of air-conditioning has a great effect in the propulsion of the expected station operating cost by over forty percent.

Introduction

The study of the cost structure of the railway transportation industry has receives a considerable chunk of academic literature attention. For example Caves et al. 1980,1981a,1981b.1985;Freeman et al. 1985;Dodgson et al. 1985;Wunch 1996;Oum et al. 1999; Cantos et al. 1999.All these pieces of literature focused on the study of the running and operation of railway systems. Through the years, research work has demonstrated the very large variation in the cost efficiency or productivity that is usually present within a selected sample of railway companies. The factors underlining this variance have also been developed in terms of the cost and production function viewpoint.

In the rail way efficiency literature, it is noted that a prominent theme that is most discussed is the subject of return to scale (RTS).TRS is also referred to as return to density (RTD).Return to density is used to describe the correlation between all the aspects of inputs and the summation of all the firms operations. Such operations would normally include elements such as the total output and the entire network size. The RTS component is used in describing the relationship that exists between the input component of the railway network and the output components while the railway network itself is held fixed.Circumstancial evidence in the literature reveal that RTS are as a result of the existence of fixed costs in the railway business. It can also be attributed to the existence of a certain range of semi-fixed costs that do not bear a direct correlation with the industry's input. Several other less consistent evidence exists to support the notion of the existence of elements of economies of scale. However the running of a railway service is always undertaken under a constant return to scale.

The operation in the railway stations may provide a vital source of increasing the level of RDS in Metro operations. It is critical to ensure that the station is continuously staffed and in proper operation with all the energy and other elements running at all times. Several factors however may cause a variation in the running cost of one metro station to another. Such factors include the type of engineering, the station's depth, the size and the dimensions of station, the nature and degree of technology rolled and many other factors. The cost of a running a railway station can be conceived to be semifixed and can be considered to not to be varying proportionately with the system output. This fact makes the cost to be of paramount importance in the process of increasing the RTD.

In this paper, we come up with an econometric model to study and analyze all the variances in the cost of operating a metro station. An econometric model then becomes paramount in the process of determining the effects of certain characteristics of the station on its cost of running and other more factors that also affect the running cost in other ways. It is worth noting that it is almost impossible to deduce from historical data the effects of certain factor in the running of a metro station. We analyze data from a total of 83 stations and 13 metro systems from various cities of the world. From the analysis we try to zero in on the major drivers of cost by way of approximation. The result presented is then used in the estimation and the discussion of the model description.

Model description

The data used in our analysis describes the total sum of each metro station's operating cost and the various metro station characteristics that are unique to the 13 metro stations. The metro stations that were considered in this study include the following:Buernos Aires, Hong Kong MTR., Hong Kong KCR, Dublin, Lisbon, Montreal, London, Taipei, Singapore, Sao Paulo, Toronto, Glasgow and Naples. In the subsequent analysis, we consider a regression of the total cost of operating a metro station against the characteristics of the station in order to determine the role of these characteristics in the various variances in the cost of running the metros.

In this study we do not adopt the usual cost function approach in the analysis. The cost function cannot be determined in this study since we do not possess the data on the prices factor. The reason for dropping the cost factor is because the operating cost of an individual station cannot be used as the appropriate measure or unit against which the cost decisions are based. For example, the operation of the metro stations does not require factor inputs at the level of the station in relation to the costs and operations for the railway system in general.

In addition, it would be erroneous to associate any particular behavior to be peculiar to an individual station. Such behavior would include items or elements of cost minimizing behavior. It is usual for a metro system not to adopt a certain level of operational efficiency by allowing a certain controlled amount of discrepancies in efficiency in order to realize a broader goal and/or objective that is associated with a certain reasonable level of system output that is reflected in the subsequent overall cost of running the metro.

In light of the above mentioned factor, what is of real importance in our analysis is the way and the extent to which the metro station characteristics serve to bring an influence on the total overall costs. It is worth mentioning once again that there is an absence of the factor price data as this is definitely important in the determination of the station costs. In order to gain control over these omitted variables, we must estimate the operating costs of the metro station by use of certain set of dummy variables. These dummy variables must be representative of the 13 metro station systems. The assumption that we must hold with the use the deployment of these dummy variables is that they will aid in the capture of certain unobservable system-specific effects such as the factor prices.

In coming up with the model to represent the factors that influence the operating cost of a metro station, we use a log linear model below:

(1)

Where

Represent the total operating cost of a certain metro station

Represent a vector (kx1) that is for continuous explanatory variables in nature and utilized in the description of Station i's characteristics.

Represents a vector (mx1) used for the dummy variables that are associated with the metro stations

Represents white noise

Represents the yet to be estimated kx1 vector of parameters

Represents the yet to be estimated mx1 vector of parameters.

The analysis is based on a log linear scale since it reduces possibility of multicollinearity and therefore presents a more direct and straightforward parameter estimates for the present elesticities.In this analysis, the dependent variable is taken to be the annual operating cost of the metro station. This cost is made up of several other sub-costs that are either related to the money spent on the staff and other utilities such as water and electricity. Other forms of utilities that make up the cost are the costs associated with the repair of lifts, and the cost incurred in the maintenance of several other integral systems e.g air conditioning. Building maintainence, CCTV and the ticketing system.

The equation (1) will be used in coming up with two econometric models. The first model is estimated without the metro system-specific dummy variables and then the second econometric model is estimated using the metro system-specific dummies in order to have a direct control over the country-specific effects on the operating cost of the metro stations

The following is the list of the explanatory variables which are used in the description of the station's characteristics and the corresponding hypotheses that we seek to test with the variables.

Age of the metro station -- the age of the metro station is considered in terms of the number of years taken from the time the station was first opened. An average is taken in case the station was opened in different stages. The hypothesis drawn here is that the older the station, the higher is the costs incurred in the maintenance of the ststion.Newer station therefore incur far less costs in regard to the maintenance.

The number of lifts and escalators -- the operating cost of a metro station is influenced to certain extent by the number of lifts and escalators. This is because of the cost incurred in the daily operation and the maintenance of the equipment.

The total number of ticket offices/ticket machines/entrance and exits-

In the process of establishing the absolute cost associated with the running of a railway system. It becomes mandatory to consider the total number of ticket machines which by this definition includes only the machines that are utilized by the public to buy or to validate their tickets. The number of ticketing offices is this context means the total area in the station where the actual ticket selling occurs. The number of the sold tickets or rather the ticket sales windows correlates directly with the total number of staffed positions that are used by the staff who run the metro in selling the tickets to the passengers. Our hypothesis is that these factors all influence the cost of staffing the metro station

The number of hours the station is operational per day: We consider utilize this variable as an average number of hours in which the metro is open per day. The hypothesis that is associated with this variable is that the longer the hours of operation of the metro, the higher the costs incurred.

Frequency of service: There exists two types of service frequency variables.These are the peak frequency and then the off-peak frequency. Any particular frequency is calculated as the average number of metro trains per hour (one way) during the peak moments (peak frequency) or the average number of trains per hour (each way) during number off peak periods. By including these variables, we are enabled to test the effects of frequency on the cost of running the metros.

The length of the trains: The length of the trains is evaluated as the summation of the total length of the carriages of the train that are part of the metro station system.

The dimension of the platform: This is evaluated as the summation of all the carriages of a particular train network that are using the station. The averages of a station with multiple lines is considered and used.

The length of the platforms: This variable is considered to be of equal value to platform length in the case of an underground metro system. However, in the case of an et-grade and elevated stations there are certain areas that alone are part of the platform. These parts may be draped with a canopy, roof or a shelter of sorts. The use of this variable is to gauge the extent to which variations in the maintenance that are related with the overall length of the roof has on the total cost of running the station.

The total length of the passageways.-This variable is evaluated by considering the total passageways' length. This length takes into account the length of various items and components such as the length of escalator shafts -- an important dimension in metros since it indicates by proxy the amount of cleaning and building maintenance that ought to be carried out. There is no taking into consideration any form of variations in the total length of the passageways. It would have been better to consider the total floor area instead. But this method is however dropped since it is nit reflective of the amount of walls and the ceilings that are needed in the for the maintenance and cleaning to take place seamlessly. This method too is discarded on the basis of its difficulty in the estimation stage of the metros.

The demand of the station variables: These are several variables affecting this element of the railway system. However there exist two main demand variables that are considered. These two are the interchange demand variables and the entry demand variables. The station demand variables are is considered to be the sum of all the passengers who enter the station in a period of one year. This number includes the passengers who are changing their modes of transportation and also those passengers who are entering from the main rail way line or bus stations. Also included in this bracket are those passengers who are also just starting their journey locally and are entering into the station while on foot.

On the other hand, interchange demand refers to those passengers who are switching their metro lines at the concerned metro station. There are however other two secondary variable in operation at this particular stage. These variables are the peak demand together with the peak interchange variables. The peak interchange variable is evaluated as the total number of interchange passengers at the busiest of hour during the course of a standard week. This variable is designed in order to test whether peak demand at entry drives the capacity of the station and therefore the cost or rather the total demand has a direct influence in driving the level of staffing and therefore the cost.

The type of metro station: The type and nature of the dummy variables deployed reflects the category of metros in terms of certain smaller factors. These factors that categories the various types of metros cluster them into at-grade metros, elevated metros, subsurface metros or deep tube. It is possible to manage At-grade and subsurface metro stations without using lifts and escalators for the vertical movement/travel of the passengers. The type of metros that require this equipment are the elevated type and the deep tube type of metros. This equipment adds greatly to the costs as they are major consumers of electricity.

Several other variables: Other variables such as the installation of the air conditioning systems, public and private toilets, screen doors for the platforms and even shops are taken care of in the modeling of the costs. This is done by the use of dummy variables too.

Results

Before the process of fitting the model, several statistical tests were done in order to determine the behavior of the data. As an illustration, it is possible to observe that the explanatory variables can be correlated with one another so as to achieve the effect of collinearity.The data can also be shown to exhibit elements of heteroskedasticity (an effect of nonconstant variance).

It is worth noting that indirect multicollinearity does not go against the assumptions of the basic model, its present in very little form can result in the biasing, inefficiency and even erroneous estimates. A very high value of the goodness of fit R2 coupled with just a few explanatory variables which are very different from 0 and a certain level of high pair-wise correlations of the regressors, then the possibility of multicollinearity is manifested. In this analysis we employ the Variance Inflation factor (VIF) that is suggested by Chatterjee (2000) to be able to determine the existence of multicollinearity. The number of tickets sale for example is found to bear a heavy correlation to the entry demand at the metro stations. While pinning our basis on the VIF test, we realize that the heavily correlated variables are not included in the pool of variable variables that are utilized later in the construction of the final model. It therefore becomes mandatory to address the problem of Omitted Variable Bias (OVB) in the usual way the going through the proxy variables and then manipulating the fixed effects in order to control the unobserved variables that are metro system-specific. We however do not possess any evidence to ascertain that multicollinearity affect the estimates of the parameter.

It is however important to point out that data from the London metro stations were not included in the final model since the operating costs were not easily obtainable as compared to the other metros. The total number of observations are therefore reduced to 83.Despite all this, we still have to come up with estimates of more than 30 parameters which are correlated with one another. Several explanatory variables which include the entry and the interchange demand, escalators and lifts are therefore combined in order to reduce the number of parameters to be estimated. The presence of the lifts and escalators in the model are represented by way of dummy variables. These dummies take the values of 1 in case of any lifts or escalators in the station and the value 0 in the otherwise scenario. The statistics of the summary are shown in the Table 1.

One of the classical assumptions made in the modeling of classical linear regression is that the disturbances that are present in the regression function are homoskedastistic.The heteroskedasticity problem is inherently common in the cross sectional analysis since the data involved is usually derived from the observation of units that by themselves are heterogenous.An example in this case is the data from the stations from different metros.Heteroskedasticity is therefore an expected behavior if the data being analyzed is fetched from the small, the medium and the large metro stations. The Park Test reveals (Park1966) that our data are never characterized by their heteroskedasticity.The main cause of this could be due to the use of a model that runs on a log linear scale. This has the effect of reducing significantly, the variances that exists among the variables.

The table 2 is used in displaying our results. In this case we make use of two models. The first model is based on the metro dummies while the second model does not use the metro dummies. In the second model metro-specific effects are used in order to manipulate the heterogeneous environments. The selection of the better model is achieved by employing the Ramsey RESET test. The Ramsey's RESET test is also known as the F-test and is deployed in order to select the better model.

Ramsey's test shows that the increase or rather the addition of the dummies that control the metro station increases with a lot of significance, the model's goodness of fit. The interpretation of the results is therefore carried out by means of a model having metro station dummies. The table 1 shows the comparison that exists between the cost observed and the cost that is predicted. There is a mean prediction error that is evaluated to stand at roughly 2.4%. It is however worthwhile to mention that the table excludes the name of the stations in order to maintain confidentiality.

The table 2 is used to display the number of statistically significant effects on the operating cost of the metros. These effects come up after having the unobservable metro system-specific effects under tight control. It is however worth mentioning that the metro station's age is found to negatively impact the operating cost of the station. This is particularly observable at about the 90% level of confidence. This in deed is a surprise since we would normally anticipate the older stations to consume a higher amount of money in terms of maintenance. The explanation for this peculiar behavior would be that the more recent metro stations such as the Hong Kong KCR usually tend to be more spacious and with larger floor areas. This in turn results in the need for more high quality facilities which also demand a higher level of maintenance.