The applications of SFA to transit systems

The methods of measuring efficiency can be classified into two categories: non-parametric and parametric methods. Non-parametric method need no priori functional forms and number of parameters on the observations, while parametric method requires a specification of functional form for the relationship between inputs and outputs, and a distribution form for technical inefficiency. Since the parametric frontier method, or the Stochastic Frontier Analysis approach (SFA) is adopted in the current research, the review of some selected papers regarding applications of parametric frontier method to measuring efficiency for bus transit systems is presented as follows.

Many economists have employed parametric approaches to analyzing the efficiency of bus transit in the past decade. Studies of parametric approach to transportation efficiency have been employed in the following cases.

Gathon (1989) analyzed the performance, including indicators of partial productivity and technical efficiency, of urban transport companies using a deterministic translog production function. Data of 60 European bus firms in 1984 was adopted. The output variable was seat kilometers, while the inputs were total number of seats and total manpower employed. The

results showed that the ranking by degree of technical efficiency was independent of the size of the firm; and technical efficiency was positively affected by operational speed.

Filippini et al. (1992) measured the cost and scale efficiency for 62 Swiss regional bus companies by a deterministic translog cost function. A panel data for four years 1986, 87, 88 and 89 had been used for estimation. Output was measured in seat kilometers, while inputs were labor, energy and capital costs. The results showed that the majority of the Swiss bus companies operate at an inappropriately low scale and density level, and further showed that efficiency was positively and significantly correlated with compensation payments and the share of Cantons in subsidizing the deficit, and was negatively affected by Alpine regions.

Thiry and Tulkens (1992) identified and evaluated efficient versus inefficient observations numerically by the nonparametric FDH method. Next parametric production frontiers were obtained by means of estimating translog production functions through ordinary least square (OLS) applied to the subset of efficient observations only. Technical progress was included at both stages. Monthly data from three urban transit firms in Belgium (from 1977 to 1985, and from 1979 to 1985) were adopted. The output was measured by the number of seats kilometers, while inputs were labor, energy, and vehicles. The results showed widely varying degrees of efficiency over time and across firms. For STIB, the inefficiencies reached the bottom level of 79% in 1982; in the case of STIL, the worst case of inefficiency was 98.4% in 1985; in the case of STIC, the worst inefficiency level was 90.4% in 1983.

Bhattacharyya et al. (1995) estimated the determinants of cost inefficiency of several publicly operated passenger-bus transportation companies in India in terms of their ownership structure as well as other firm-specific characteristics. Inefficiency was specified in such a way that both its mean and variance are firm-and time-specific. A multi-step estimation procedure was adopted for the estimation of production technology and cost inefficiency: In the first step they estimated the translog cost system with heteroskedastic cost function without using any

distribution assumptions on the error terms. The second stage used the ML method to estimate the parameters associated with inefficiency, conditional on the parameter estimates obtained from the first stage. Finally, the residual of the cost function was decomposed to obtain firm-and time-specific measures of cost inefficiency, with ownership type and other firm-specific characteristics as explanatory variables. The study used a five-year unbalanced panel data of 32 state-run passenger-bus transportation units, operating in 18 states in India, over the period 1983 to 1987. The output variable was passenger-kilometer, and three input variables had been considered in this study, fuel, and two categories of labor: traffic and maintenance labor, and administrative labor. Apart from these variables inputs they have included two network variables:

fleet utilization and load factor. The result showed that the units directly run by the government transportation departments were most efficient, compared to the nationalized units and large transport corporations. The high inefficiency of the large transport corporations relative to the units run by the government departments was of significant interest. On the whole, it seemed to indicate that the large degree of administrative autonomy of the transport corporations allows them to be relatively more irresponsible and inefficient.

Jørgensen et al. (1997) estimated a stochastic cost frontier function based on data from 170 Norwegian subsidized bus companies in 1991 under two alternative presumptions regarding the distribution of the inefficiency among the bus operators. The output was total cost per vehicle-kms, while the inputs were number of vehicle kilometers, bus size and number of passengers. The results showed that when the inefficiency was assumed to be half-normally distributed, the average inefficiency in the industry was nearly halved when the exponential distribution was applied, while the ranking of the companies according to inefficiency was unchanged; it was also seen that inefficiency of the companies which negotiated with the public authorities over the subsidy amounts was slightly higher than the inefficiency of the companies which faced a subsidy policy based in cost norms. However, it was found no significant

difference in the efficiency between privately owned bus companies and publicly owned bus operators, and showed only minor economies of scale.

Sakano et al. (1997) studied the US urban transit system which received operating and capital subsidies from various levels of government using a stochastic translog production function. Both technical and allocative inefficiencies were calculated. The allocative inefficiencies were further decomposed among two sources, subsidies and factors internal to the firm. The output variable was vehicle-mile, and input variables included labor, fuel and capital.

In addition, there were two exogenous variables, route miles and population density, are added to the production function. The analysis revealed large allocative inefficiencies between labor, fuel, and capital. Furthermore, they found that subsidies lead to excess use of labor relative to capital and excess use of fuel relative to capital and labor. Also, most allocative inefficiencies in firms were due to internal factors and not subsidies, and the sizes of the inefficiencies varied substantially among transit firms.

Dalen and Gomez (2003) addressed a cost frontier model which was estimated for an eleven-year panel of Norwegian bus companies (1136 company-year observations) using the methodology proposed by Battese and Coelli (1995). The main objective of the paper was to investigate to what extent different type of regulatory contracts affect company performance.

Unobservable network or other time invariant characteristic of the operating environment could be controlled for by analyzing the dynamics of measured productivity across time for firms regulated under different types of contracts, rather than relying solely on variations across companies during one time period. The main result of the paper was that the adoption of a more high-powered scheme based on a yardstick type of regulation significantly reduced operating costs. The results contained in this paper thus confirmed theoretical predictions regarding the incentive properties of high powered incentive schemes and in particular the dynamic benefits of yardstick competition.

Table 2.1 summarizes the previous studies which apply the parametric frontier method for measuring the efficiency of bus transit system.

Table 2.1 Summarization of transit efficiency researches

Author Country Year Function Input variables Output variables

Gathon

Author Country Year Function Input variables Output variables

DEA and SFA are two common approaches for measuring efficiency of bus transportation companies. There have been large amount of bus efficiency studies using DEA approach in Taiwan, however, there haven’t been any applications using SFA methods to measuring efficiency for Taiwan’s bus transit industry.

In addition, from Table 2.1 one can see that most researchers choose labor, capital and fuel as input variables in bus efficiency measurement. As for output variables, vehicle-kilometer and passenger-kilometer are two distinct variables commonly used in previous studies. The former indicates essentially the level of capacity produced by bus transit companies and regarded as available output, while the latter indicates the level of output consumed by passengers and oftentimes regarded as revenue output. The current research attempts to measure technical or productive efficiency of Taipei bus transit systems and analyzes the effects of accident on efficiency measurement, thus vehicle-kilometer is selected as desirable output.