鐵路運輸之生產效率分析：DEA與SFA方法之比較

Measurement of Railways Productive Efficiency with Data Envelopment Analysis and Stochastic Frontier Analysis

本研究應用資料包絡分析法(DEA)及隨機前緣分析法(SFA)，衡量1999年世界上74家鐵路公司之生產技術效率。為與國外相關研究結果作比較，在資料的選取你以各鐵路公司之營運路線長度、車輛數、員工數為投入要素，以列車公里為產出，並採二階段作法先求算各鐵路公司之技術效率，再探討影響效率值之外在環境因素。採DEA法時分別嘗試CCR模式(假設固定規模報酬)與BCC模式(假設變動規模報酬)，採SFA法特則分別嘗試HN模式(假設衡量廠商生產技術無效率之隨機變數為半常態分配)與TN模式(假設衡量廠商生產技術無效率之隨機變數為截斷常態分配)。以上四種模式之實證結果顯示74家鐵路公司中，以荷蘭鐵路(NS)最有效率，其效率值在兩種DEA模式之排名均為第一，但在兩種SFA模式之排名均為第二，其他鐵路公司之效率排名隨分析方法或模式不同亦略有差異。整體而言，歐、美地區之鐵路生產效率值普遍高於亞、非地區，民主國家之效率值高於共產國家，民營公司之效率值高於公著公司。就各模式之平均效率值言，SFATN>SFAHN>DEABCC>DEAcCR。本研究亦發現，鐵路產業以Translog函數較能描述其生產行為，且不符合固定規模報酬之假設。就路線規模而言，以2,000至3,000公里之平均規模效率值較高。差額分析結果顯示，技術無效率廠商主要源、自過多車輛及人員之投入。Tobit迴歸發現，電氣化比例、路網密度、民營化你影響鐵路生產效率之正向顯著因素，而人口密度對效率之影響則不顯著。台織之效率值(DEAvRS)你以第一名之NS為標竿，排名19'其單位產出之路線長度為NS之1.26倍，但單位產出之車輛及人員使用量卻分別為NS之2.98與2.2倍，顯示以目前台鐵之路線規模及產出量而言，其車輛及人員之投入均過多，有大幅精簡之空間(相較於荷蘭鐵路)。為提升生產效率，台鐵宜在維持產出不變情況下縮減車輛及人員之投入要素量，或不增投入要素情況下擴增其產出，或兼採或投入要素及增加產出方式；引用更先進之生產與管理方式，當然亦是提升生產效率之作法。

This paper estimates the relative productive efficiency for 74 worldwide rail systems in 1999 by employing two methods--data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Following some previous studies, we select length of lines, number of locomotives and cars, and number of employees as input factors and train-kilometer as output. When applying DEA approach, we use the two-stage method, which involves estimating technical efficiency of each DMU based on CCR and BCC models, and then regressing efficiency scores on the environmental variables. When using SFA approach, both half-normal and truncated-normal distributions are specifìed on the inefficiency random variable. The empirical results show that among these 74 systems, both DEA models rank the Netherlands Railways (NS) as the most efficient firm, while both SFA models rank NS as the second efficient system. The relative efficiency rankings of the other rails also vary slightly with the methods or models used. The Tobit regression shows that percentage of line electrified, network density and operation entity (public or private) have significant influence on the efficiency scores, while population density is not statistically significant. In general, the efficiencies of forms in Europe and America are higher than those in Asia and Africa, democracy countries have higher productive efficiency than communism ones and private firms perform better than public ones. The empirical results show that the average technical efficiency of SFATN is the highest followed by SFATN, DEABcc, and then DEAcCR, Translog production function is more suitable than Cobb-Douglas to specify the relation between input and output of railway industry and the assumption of constant returns to scale does not apply to rail industry. The scale efficiency reveals that length size of 2,000 to 3,000 km is optimal for a rail system. The input slack analysis shows that productive inefficiency for the rail firms are mainly due to too many cars and labors being used. The efficiency score of DEABCC ranks Taiwan Railway Administration (TRA) as 19, which refers to NS as the peer company. Note that the operation line length of TRA per unit train-km is 126% as much as of NS the number of cars and labors per unit train-km, however, are 298% and 220% of NS, respectively. This implies that productive inefficiency of TRA mainly comes from too many cars and labors inputted. TRA can either raise its train-kilometers or curtail the rolling stock and employees or take both ways to increase its productive efficiency. Of course, untroducting innovative production and management is also an important means to enhance TRA's technical efficiency.