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Journal of Transport Economics and Policy, Volume 40, Part 3, September 2006, pp. 383–408

Performance Measurement for Railway Transport: Stochastic Distance Functions with Inefficiency and Ineffectiveness Effects Lawrence W. Lan and Erwin T. J. Lin

Address for correspondence: Lawrence W. Lan, Emeritus Professor, Institute of Traffic and Transportation, National Chiao Tung University, 4F, 114 Sec. 1, Chung-Hsiao W. Rd., Taipei, Taiwan 10012 ([email protected]). Erwin T. J. Lin is Deputy Division Director, Bureau of High Speed Rail, Ministry of Transportation and Communications, Taiwan. The authors wish to thank the constructive comments and suggestions from two anonymous referees.

Abstract To scrutinise the plausible sources of poor performance for non-storable transport services, it is necessary to distinguish technical inefficiency from service ineffectiveness. This paper attempts to measure the performance of railways that produce passenger and freight services by two stochastic distance function approaches. A stochastic input distance function with an inefficiency effect is defined to evaluate technical efficiency; whereas a stochastic consumption distance function with an ineffectiveness effect is introduced to assess service effectiveness. The empirical analysis examines 39 worldwide railway systems over eight years (1995–2002) where inputs contain number of passenger cars, number of freight cars, and number of employees, while outputs contain passenger train-kilometres and freight train-kilometres, and consumptions contain passenger-kilometres and tonkilometres. The findings show that railways’ technical inefficiency and service ineffectiveness are negatively influenced by gross national income per capita, percentage of electrified lines, and line density. Overall, the railways in West Europe perform more efficiently and effectively than those in East Europe and Non-European regions. Strategies for ameliorating the operation of less-efficient and/or less-effective railways are proposed.

Date of receipt of final manuscript: October 2005 383

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1.0 Introduction Many railways in the world have been facing keen competition from highway carriers over past decades. Some railways have even suffered from a major decline in the market share and failed to adopt effective strategies to correct the situation. Taking freight transport as an example, the market share (ton-km) for European Union (EU) rails has declined from 32 per cent in 1970 to 12 per cent by 1999 (Lewis et al. 2001). As Fleming (1999) pointed out, truckers can deliver furniture from Lyon, France, to Milan, Italy, in eight hours, while railways need forty-eight hours. The decline of the railway market could be attributed to the relatively high level-of-service of other modes or to rail’s poor performance in technical efficiency and/or service effectiveness. Without in-depth examination, one cannot gain insights into the main causes for the decline or the main sources of poor performance. In addition, enhancing technical efficiency and service effectiveness should always be viewed as essential for railway transport to remain sustainable in the market. If one could scrutinise the sources of inefficiency and ineffectiveness by making a clear distinction between efficiency and effectiveness, it would perhaps be possible to propose more practical strategies to ameliorate the problems of the operation of rail transport. Many studies have dealt with railway transport performance evaluation. They mainly focused on efficiency and productivity measurements. The methodologies were generally classified into four categories: index number, least squares, data envelopment analysis (DEA) and stochastic frontier analysis (SFA) (Coelli et al., 1998; Oum et al., 1999). For example, Freeman et al. (1985) applied the index number method to measuring and comparing the total factor productivity of Canadian Pacific (CP) and Canadian National (CN) railways over the period of 1956–81. Tretheway et al. (1997) also employed the same method but extended the data to 1991. They found that although CP and CN sustained modest productivity growth throughout the period of 1956– 91, their performance slipped over the next decade. Caves et al. (1981) adopted the least squares method to develop definitions of productivity growth for more general structures of production. Friedlaender et al. (1993) used the least squares method to estimate the short-run variable cost function of US Class I railroads. They concluded that the institutional barriers to capital adjustment might be substantial. McGeehan (1993) also employed the least squares method to estimating the cost functions of Irish railways and found that the Cobb–Douglas functional form would not be appropriate in describing the production structure. 384

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Chapin and Schmidt (1999) used the DEA approach to measure the efficiency of US Class I railroad companies since deregulation. By regression analysis, they found that their efficiency had been improved since deregulation, but not because of mergers. Cowie (1999) also applied the DEA method to compare the efficiency of Swiss public and private railways by constructing technical and managerial efficiency frontiers and then measuring both efficiencies. Private railways were found to have 13 per cent higher technical efficiency than the public ones (89 versus 76 per cent). Fa¨re and Grosskopf (2000) further introduced a network data envelopment analysis (NDEA) for the multiple-stage production efficiency measurement. Lan and Lin (2003a) employed different DEA approaches to measure the technical efficiency and service effectiveness of worldwide railways. Lan and Lin (2005) further developed a four-stage DEA approach to evaluate railway performance with the adjustment of environmental effects, data noise, and slacks. Cantos and Maudos (2000) estimated productivity, efficiency, and technical change for 15 European railways by using the SFA approach. The results showed that the most efficient companies were those with higher degrees of autonomy. Cantos and Maudos (2001) also employed SFA to estimate both cost efficiency and revenue efficiency for 16 European railways, concluding that the existence of inefficiency could be explained by the strong policy of regulation and intervention. Lan and Lin (2003a) compared the relative productive efficiency of worldwide rail systems with DEA and SFA approaches. They found a translog production function more suitable than Cobb– Douglas for specifying the relation between inputs and outputs, and variable returns to scale more relevant than constant returns to scale for the rail transport industry. When applying econometric approaches to estimate efficiency and/or effectiveness, it is necessary to specify a suitable functional form. Production function and cost function are the two conventional approaches used in previous studies. However, when dealing with the multiple-output nature of railway transport (passenger and freight services), the production function has the disadvantage that only a single output can be appropriately modelled. Although the cost function approach can overcome this problem by allowing the modelling of a multiple-input and multipleoutput production technology, its drawback is that it requires data on input prices and total cost, which are very difficult to collect in the international context. Another model that can be utilised in dealing with multiple-input and multiple-output production technology is the distance function, which was initially introduced by Shephard (1970). However, it was not used in measuring the efficiency of railways until Bosco (1996), who developed an input distance function to estimate the excess-input 385


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expenditure for four European public railways over the period of 1971–87. Coelli and Perelman (1999) introduced both parametric and nonparametric distance functions to estimate the efficiency of European railways. They suggested that a combination of technical efficiency scores obtained by different methods could be used as the preferred set of scores. Coelli and Perelman (2000) further estimated the technical efficiency of European railways using a distance function approach. The results indicated that the technical efficiencies of European railways differed substantially from country to country. More recently, Kennedy and Smith (2004) proposed an internal benchmarking approach to assess the cost efficiency of Britain’s rail network based on seven geographical zones within Railtrack. Their internal benchmarking approach was essentially the input distance function proposed by Coelli and Perelman (1999). The models specified by Coelli and Perelman (1999, 2000) did not consider random error terms, which were attributed to a deterministic distance function approach. This paper attempts to evaluate railway transport performance by employing stochastic distance function approaches including consideration of the random error terms. Corresponding to a certain level of output, a railway firm is presumed to minimise the input factors (cost) and/or to maximise the sales (revenue). Therefore, we specify the stochastic input distance function to measure technical efficiency, whereas to estimate service effectiveness we specify the stochastic consumption distance function. Moreover, in order to scrutinise the plausible sources of less-efficient and/or less-ineffective firms, our stochastic distance functions further incorporate inefficiency/ineffectiveness effects. The paper is structured as follows. Section 2 elucidates the rationale for the distinction of efficiency and effectiveness measurements for nonstorable commodities. Section 3 defines the stochastic input (consumption) distance functions with inefficiency (ineffectiveness) effects. Section 4 conducts the empirical analysis and scrutinises the sources of inefficiency and ineffectiveness. Section 5 addresses the policy implications and discusses the strategies for ameliorating problems in less-efficient and/or less-effective firms.

2.0 Distinction of Efficiency and Effectiveness Measurements We define technical efficiency as a transformation of outputs from inputs, sale effectiveness as a transformation of consumptions from outputs, and technical effectiveness as a transformation of consumptions from inputs. 386


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For ordinary commodities, measures of technical efficiency and technical effectiveness are essentially the same because the commodities, once produced, can be stockpiled for consumption. Nothing will be lost throughout the transformation from outputs to consumptions if one assumes that all the stockpiles are eventually sold out (that is, conventional measures for ordinary commodities assume perfect sale effectiveness). For non-storable commodities, however, when commodities are produced and a portion of them are not consumed straight away (that is, imperfect sale effectiveness), the technical effectiveness, a combined effect of technical efficiency and sale effectiveness, would be less than the technical efficiency. Transport infrastructures and services are typical non-storable commodities because one can never store the surplus service capacity at low demands (off-peak hours) for use at high demands (peak hours). Taking passenger transport as an example, once the transport outputs (in terms of seat-miles) are transformed from such inputs as vehicle, fuel and labour, the seat-miles must be consumed immediately by the passengers, otherwise they are exhausted and wasted. Both technical efficiency and technical effectiveness for passenger transport services represent two different measurements and thus should be evaluated separately considering the fact that not all the seat-miles are fully utilised in practice. Technical effectiveness depends not only on how well the outputs (seat-miles) are transformed from the inputs, but also on how well the consumptions (passenger-miles) are transformed from the outputs. In summary, to assess the system performance for non-storable commodities, it would be more informative if one could separate the efficiency measurement (transforming the inputs into outputs) from the effectiveness measurement (transforming the outputs into consumptions). To explain this concept, Fielding et al. (1985) introduced three performance measures for a transit system: cost efficiency, service effectiveness, and cost effectiveness. They defined cost-efficiency as the ratio of outputs to inputs, service-effectiveness as the ratio of consumptions to outputs, and cost-effectiveness as the ratio of consumptions to inputs. It should be noted that if the input factor prices are not known, one cannot measure cost efficiency or cost effectiveness. Nonetheless, one can still measure technical efficiency or technical effectiveness. Similarly, if sale prices are not known, one cannot measure revenue-related effectiveness; but one can measure service or technical effectiveness. Figure 1 uses rail transport as an example to depict the concept of distinctive performance measurements of technical effectiveness, technical efficiency, and service effectiveness for non-storable commodities. This figure suggests that any poor performance in transport services can be attributed to either poor technical efficiency or poor service effectiveness or a combination of both. Without the separation 387


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Figure 1 Distinctive Performance Measurements for Non-Storable Commodities (Rail Transport as an Example) Inputs • Labour • Vehicle • Energy

Technical effectiveness measurement

Technical efficiency measurement

Outputs • Passenger-train-km • Freight-train-km • Affiliated business

Consumptions

Service effectiveness measurement

• Passenger-km • Ton-km • Passenger-revenue • Freight-revenue • Affiliated-revenue

of technical efficiency and service effectiveness measurements, it is difficult to discover the sources of poor performance. Most previous studies related to performance evaluation mainly focused on technical efficiency or technical effectiveness measures (Orea et al., 2004). To the best of the authors’ knowledge, little has been devoted to service (or sale) effectiveness measures for non-storable commodities.

3.0 Methodologies 3.1 Deterministic distance functions To define a production technology, let x denote a non-negative input vector and y denote a non-negative output vector. We use PðxÞ to represent all output sets y, which can be produced by using the input vector x. That is PðxÞ ¼ y 2 RM þ : x can produce y : Following Fa¨re and Primont (1995), PðxÞ is assumed to satisfy: (1) (2)

388

0 2 PðxÞ; Non-zero output levels cannot be produced from a zero level of inputs;

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(3) (4) (5) (6) (7)

PðxÞ satisfies strong disposability of outputs; that is, if y 2 PðxÞ and y 4 y, then y 2 PðxÞ; PðxÞ satisfies strong disposability of inputs; that is, if y can be produced from x then y can be produced from any x 5 x; PðxÞ is closed; PðxÞ is bounded; PðxÞ is convex.

The output distance function is then defined on the output set, PðxÞ, as dO ðx; yÞ ¼ minfy: ðy=yÞ 2 PðxÞg; where PðxÞ ¼ fy 2 RM þ : x can produce yg;

Lovell et al. (1994) have pointed out that (1) (2) (3) (4)

dO ðx; yÞ is non-decreasing in y and non-increasing in x; dO ðx; yÞ is linearly homogeneous and convex in y; dO ðx; yÞ 4 1; if y 2 PðxÞ; = PðxÞ; o > 1g. dO ðx; yÞ ¼ 1; if y 2 IsoqPðxÞ ¼ f y: y 2 PðxÞ; o y 2

In summary, a firm is efficient if it lies on the frontier or isoquant. Conversely, a firm is inefficient if it is located inside the frontier. From linear homogeneity, we can obtain dO ðx; o yÞ ¼ o dO ðx; yÞ, for any o > 0. One can arbitrarily choose one of the outputs (for example, the Mth output) and set o ¼ 1=yM . Then dO ðx; y=yM Þ ¼ dO ðx; yÞ=yM . Thus, if we adopt the standard flexible translog form, the deterministic output distance function can be written as: lnðdOi =yM Þ ¼ a0 þ

M 1 X

am ln ymi þ

m¼1

þ

K X

bk ln xki þ

k¼1

þ

K M 1 X X

1 M 1 X X 1M a ln ymi ln yni 2 m ¼ 1 n ¼ 1 mn

K X K 1X b ln xki ln xli 2 k ¼ 1 l ¼ 1 kl

rkm ln xki ln ymi ;

ð1Þ

i ¼ 1; 2; . . . ; N;

k¼1 m¼1

where ym ¼ ym =yM . Let lnðdOi =yMi Þ ¼ TLðxi ; ymi =yMi ; a; b; rÞ;

i ¼ 1; 2; . . . ; N:

Or, lnðdOi Þ lnðyMi Þ ¼ TLðxi ; ymi =yMi ; a; b; rÞ;

i ¼ 1; 2; . . . ; N:

Hence, lnðyMi Þ ¼ TLðxi ; ymi =yMi ; a; b; rÞ lnðdOi Þ;

i ¼ 1; 2; . . . ; N:

ð2Þ

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Similarly, the input distance function can be defined on the input set, LðyÞ, as dI ðx; yÞ ¼ maxfl: ðx=lÞ 2 LðyÞg; where LðyÞ ¼ fx 2 RK þ : x can produce yg:

Lovell et al. (1994) also point out that (1) (2) (3) (4)

dI ðx; yÞ is non-decreasing in x and non-increasing in y; dI ðx; yÞ is positively linearly homogeneous and concave in x; dI ðx; yÞ 5 1, if x 2 LðyÞ; dI ðx; yÞ ¼ 1, if x 2 IsoqLðyÞ ¼ fx: x 2 LðyÞg.

From linear homogeneity, we obtain dI ðox; yÞ ¼ odI ðx; yÞ, for any o > 0. One can arbitrarily choose one of the inputs, say the Kth input, and set o ¼ 1=xK , then dI ðx=xK ; yÞ ¼ dI ðx; yÞ=xK . Thus, a translog form of deterministic input distance function becomes lnðdIi =xKi Þ ¼ a0 þ

M X

am ln ymi þ

m¼1

þ

K 1 X

bk ln xki þ

k¼1

þ

K 1 X

M X

M X M 1X a ln ymi ln yni 2 m ¼ 1 n ¼ 1 mn

1 K 1 X 1 KX b ln xki ln xli 2 k ¼ 1 l ¼ 1 kl

rkm ln xki ln ymi ;

ð3Þ

i ¼ 1; 2; . . . ; N;

k¼1 m¼1

where xki ¼ xki =xKi . Let lnðdIi =xKi Þ ¼ TLðyi ; xki =xKi ; a; b; rÞ;

i ¼ 1; 2; . . . ; N:

Or, lnðdIi Þ lnðxKi Þ ¼ TLðyi ; xki =xKi ; a; b; rÞ;

i ¼ 1; 2; . . . ; N:

Hence, lnðxKi Þ ¼ TLðyi ; xki =xKi ; a; b; rÞ þ lnðdIi Þ;

i ¼ 1; 2; . . . ; N:

ð4Þ

In equation (2), lnðdOi Þ can be viewed as residual. We can regress lnðyMi Þ on TLðJÞ by using the ordinary least squares (OLS) method and correct each residual by adding the largest negative residual. To estimate the service effectiveness of each firm, we simply find the exponent of each corrected residual. Similarly, to estimate technical efficiency, we regress lnðxKi Þ on TLðJÞ in equation (4) and follow the same procedure as in effectiveness estimation. 390


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3.2 Stochastic distance functions The output and input distance functions described in 3.1 are all deterministic because they do not account for random errors. To account for statistical noise, Aigner, Lovell and Schmidt (1977) proposed a composite error model, called the stochastic production frontier model, defined as yi ¼ f ðxi ; bÞ expðvi Þ expðui Þ ¼ f ðxi ; bÞ expðvi Þ TEi ;

ð5Þ

where yi is the output of ith firm, vi is symmetric random error term. Aigner et al. (1977) assumed that vi follows a normal distribution with zero mean and constant variance, and ui is non-negative independently and identically distributed (iid ) random variable, which counts the technical inefficiency of firms. The technical efficiency of firms (TEi ) is defined as TEi ¼ expðui Þ ¼

yi ; f ðxi ; bÞ expðvi Þ

i ¼ 1; 2; . . . ; N:

ð6Þ

In order to estimate ui , one has to impose a distribution form (for example, half-normal, truncated-normal, gamma, and so on) on the model. Taking half-normal distribution as an example, following Kumbhakar and Lovell (2000), one can assume that (1) (2) (3)

vi iid Nð0; s2v Þ; ui iid N þ ð0; s2u Þ; Both vi and ui are independently and identically distributed.

Because vi is independent of ui , the joint probability density function of ui and vi is ! 2 el e2 2 e el f ðeÞ ¼ pffiffiffiffiffiffi exp 1 exp 2 ¼ f ; ð7Þ s s s s 2s s 2p where e ¼ v u, s ¼ ðs2u þ s2v Þ1=2 , l ¼ su =sv , fðÞ and ðÞ are respectively the standard normal cumulative distribution function and probability density function. The log likelihood function of f ðeÞ is N N X ei l 1 X ln e2i : ð8Þ ln L ¼ const N ln s þ 2 s 2s i¼1 i¼1 One can estimate equation (8) by using maximum likelihood estimation method. Jondrow et al. (1982) have derived fðmi =s Þ fðei l=sÞ ei l Ehui jei i ¼ mi þ s ; ¼ s 1 ðmi =s Þ 1 ðei l=sÞ s ð9Þ

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where mi ¼ ðes2u =s2 Þ, s2 ¼ ðs2u s2v =s2 Þ. The technical efficiency of firms then becomes ui Þ ¼ expðEhui jei iÞ: TEi ¼ expð^

ð10Þ

Battese and Coelli (1988) proposed another point estimator for TEi as follows: 1 ðs mi =s Þ TEi ¼ E½exphui jei i ¼ expðmi þ 12 s2 Þ: ð11Þ 1 ðmi =s Þ For any nonlinear function gðxÞ, E½gðxÞ is not equal to gðE½xÞ. In this case, Kumbhakar and Lovell (2000) indicate that equation (11) is preferred to equation (10). One can define stochastic output and input distance functions by simply adding symmetric error term vi to the deterministic models as shown in equations (2) and (4). The models become equations (12) and (13), respectively. It should be noted that in equation (12) ui represents inefficiency due to insufficient outputs, while in equation (13) ui stands for inefficiency due to excess inputs. lnðyMi Þ ¼ TLðxi ; ymi =yMi ; a; b; rÞ þ vi ui ; lnðxKi Þ ¼ TLðyi ; xki =xKi ; a; b; rÞ þ vi þ ui ;

i ¼ 1; 2; . . . ; N; i ¼ 1; 2; . . . ; N:

ð12Þ ð13Þ

3.3 Incorporation with inefficiency/ineffectiveness effects To investigate further the factors causing the inefficiency of firms, a number of researchers have developed models incorporating inefficiency effects into stochastic production functions (Kumbhakar et al., 1991; Reifschneider and Stevenson, 1991; Huang and Liu, 1994; and Battese and Coelli, 1995). For instance, Battese and Coelli (1995) proposed a model incorporating technical inefficiency effects into a stochastic frontier production model. They assumed that the inefficiency effects were stochastic and their model permitted the estimation of technical efficiency in the stochastic frontier and the determinants of technical inefficiencies. In this paper, we adopt the concept proposed by Battese and Coelli (1995) and define the stochastic consumption distance function with an ineffectiveness effect as follows (hereinafter named the SCDF model): lnðyMit Þ ¼ TLðxkit ; ymit =yMit ; a; b; rÞ þ vit uit ; i ¼ 1; 2; . . . ; N;

t ¼ 1; 2; . . . ; T:

ð14Þ

We define uit as a vector of non-negative random variables associated with service ineffectiveness, which are assumed to be independently distributed, such that: uit is obtained by truncation (at zero) of the normal distribution 392


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with mean zit d and variance s2 ; zit is a vector of explanatory variables associated with service ineffectiveness of firms over time; and d is a vector of unknown coefficients to be estimated. Thus, the service ineffectiveness effect, uit , in equation (14) can be specified as uit ¼ zit d þ Wit ;

ð15Þ

the random variable Wit is defined by the truncation of the normal distribution with zero mean and variance s2 . Similarly, we define the stochastic input distance function with an inefficiency effect as follows (hereinafter named the SIDF model): lnðxKit Þ ¼ TLðyit ; xit =xkit ; a; b; rÞ þ vit þ uit ; i ¼ 1; 2; . . . ; N; t ¼ 1; 2; . . . ; T:

ð16Þ

The associated technical inefficiency effect could also be specified as in equation (15).

4.0 Empirical Analysis 4.1 Data This study focuses on multi-product railways that provide both passenger and freight services. The single-product railways providing only passenger or freight service are not considered in the empirical analysis. Since we also conduct in-depth analysis on how external factors affect efficiency (effectiveness) measures, those railways with incomplete data sets within the eight-year study horizon are also excluded. Our complete data set, drawn from International Railway Statistics published by the International Union of Railways (UIC), contains 312 panel data composed of 39 railways over the period of 1995–2002. In order to investigate whether efficiency and effectiveness vary significantly among regions, we further classify the samples into three regions: West Europe (WE), East Europe (EE) and Non-Europe (NE). Previous studies used the number of employees, length of lines, and the sum of freight wagons and coach cars as inputs (for example, Coelli and Perelman, 1999; Cowie, 1999). For a multiple-output railway system that provides passenger and freight services, it seems more reasonable to separate those inputs for passenger and freight services. Thus, we separate freight-car from passenger-car rolling stock in the input data set, and separate freight-train-kilometres from passenger-train-kilometres in the output data set. However, such factors as staff are not exactly divided between both services; we directly use the total number of employees as 393


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another input. Because we measure the short-term performance of railways, we discard length of lines as an input, which is in general attributed to a fixed cost category. For simplicity, we do not account for such external factors as public/private ownership and regulatory differences across the firms. Our panel data contain five data sets including two consumptions (passenger-kilometres and ton-kilometres), two outputs (passenger trainkilometres and freight train-kilometres), three inputs (number of passenger cars, number of freight cars, and number of employees), two environmental variables (per capita gross national income and population density), and two variables characterising the railways (percentage of electrified line and line density). Table 1 summarises the descriptive statistics of the data. Note that the data in different regions are somewhat heterogeneous.

4.2 Estimation results Previous studies may have used input-oriented comparison (measuring the relative inputs under the same output level) or output-oriented comparison (measuring the relative outputs under the same input level) in assessing technical efficiency. Whether a company is output-oriented or inputoriented is a question that depends on many factors. If companies have restrictions on the inputs they use, the output distance function would be the appropriate approach. If companies have restrictions on the quantities of outputs, the input distance function would be appropriate. For the ease of comparison among different railways, we presume that firms minimise the input factors (cost) and maximise the sales (revenue) associated with a given level of output. Thus, when measuring the relative technical efficiency we specify a stochastic input distance function (SIDF) model with inefficiency effect as shown in equation (16); whereas to estimate relative service effectiveness, we specify a stochastic consumption distance function (SCDF) with an ineffectiveness effect as shown in equation (14). Note that the estimated parameters of stochastic distance functions may violate the monotonicity assumption. To avoid violation, some studies estimated the parameters by imposing monotonic constraint on the specified functional form (for example, O’Donnell and Coelli, 2005; and Griffiths et al., 2000). In order to maintain the flexibility of the specified distance functions, we do not impose this restriction; instead, we check monotonicity after estimation. The FRONTIER 4.1 software, developed by Coelli (1996), is applied to estimate both models. Table 2 reports the estimation results. We find that most of the parameters (a; b; r) are statistically significant at the 5 per cent significance level. s2v are significant in both models, supporting the theory that stochastic distance functions, rather than deterministic ones, 394

195,762 265 22,587 42,699

40,628 438 8,787 10,314

East Europe Max. 63,752 Min. 104 Mean 7,888 Std. dev. 13,461

Non-Europe Max. 251,723 Min. 74 Mean 28,865 Std. dev. 72,726 739,800 562 89,542 158,711

698,160 562 87,039 206,065

175,696 840 47,550 52,771

739,800 5,647 136,322 182,344

pax train-km (103 )

225,500 832 28,785 42,972

85,905 1,367 15,734 22,945

110,109 832 24,592 29,874

225,500 920 42,599 59,229

freight train-km (103 )

Outputs

26,150 40 3,801 5,731

26,150 99 3,449 7,505

15,781 40 2,993 3,445

21,723 146 4,917 6,095

pax cars

266,245 142 28,941 45,759

30,286 677 9,200 6,720

266,245 142 41,517 55,740

205,431 146 29,566 45,291

freight cars

Inputs

421,010 1,212 54,663 78,739

192,456 1,212 32,084 47,953

421,010 1,792 71,326 99,038

294,911 1,438 52,938 67,438

No. of employees

45,060 200 13,496 12,940

35,610 200 9,816 10,901

10,060 390 3,554 2,231

45,060 10,840 26,776 9,202

GNI

622.13 2.42 139.40 130.84

622.13 2.42 198.54 206.15

130.42 6.43 88.42 30.84

389.01 11.45 151.78 105.89

PD

Environmental variables

1.000 0.000 0.409 0.283

0.611 0.000 0.261 0.253

1.000 0.000 0.328 0.205

1.000 0.000 0.600 0.273

ELEC (%)

0.120 0.001 0.043 0.032

0.053 0.001 0.019 0.016

0.120 0.002 0.048 0.030

0.117 0.006 0.054 0.035

LD (km/km2 )

Characteristics of railways

Note: GNI denotes per capita gross national income (US dollar) and PD denotes population density (persons per square kilometre) of the country to which the railway belongs. ELEC represents the percentages of electrified lines. LD denotes line density, the ratio of length of lines to the area of a country.

Total Max. Min. Mean Std. dev.

195,762 265 16,436 30,160

76,815 357 15,310 20,831

West Europe Max. 74,387 Min. 268 Mean 17,876 Std. dev. 22,819

251,723 74 16,852 40,832

ton-km (106 )

Statistics

pax-km (106 )

Consumptions

Table 1 Descriptive Statistics of the Decision Making Units (39 Railways over 8 Years: 1995–2002)

Performance Measurement for Railway Transport Lan and Lin

395

396 a0 a1 a2 a11 a22 a12 b1 b2 b3 b11 b22 b12 r11 r12 r21 r22 d0 d1 d2 d3 d4 D1 D2 s2v g

25.4717 6.2850

3.7260 0.7982 0.2018 0.0090 1.0286 0.5366 0.1230 0.4012 0.2995 0.0409 0.1630

1.7768 0.1599 0.0248 0.6574 15.7592 0.7769 0.0026 0.1323 0.9602

Constant ln y1 ln y2 lnð y1 =y2 Þ2 ln x1 ln x2 ln x21 ln x1 ln x2 ln x22 ln x1 lnð y1 =y2 Þ ln x2 lnð y1 =y2 Þ

Constant ln(GNI/1000) ln(PD) ELEC LD Region Region Variance Variance ratio

a0 a1 a2 a11 b1 b2 b11 b12 b22 r11 r21

d0 d1 d2 d3 d4 D1 D2 s2v g

Constant ln y1 ln y2 ln y21 ln y22 ln y1 ln y2 ln x1 ln x2 ln x3 lnðx1 =x3 Þ2 lnðx2 =x3 Þ2 lnðx1 =x3 Þ lnðx2 =x3 Þ ln y1 lnðx1 =x3 Þ ln y1 lnðx2 =x3 Þ ln y2 lnðx1 =x3 Þ ln y2 lnðx2 =x3 Þ Constant ln(GNI/1000) ln(PD) ELEC LD Region Region Variance Variance ratio

variables 3.3368 0.2835 0.5557 0.1772 0.0803 0.1224 0.4616 0.1291 0.4093 0.0258 0.0008 0.0094 0.0050 0.0229 0.0043 0.0313 0.5452 0.4615 0.1199 0.1275 2.7882 0.3108 0.0414 0.0420 0.8508

coefficient

Efficiency (SIDF) model

2.9605 0.2530 3.0675 0.1963 1.9627 0.1621 2.4080 3.6497 19.1562 1.5629 4.2635 3.8158 4.3392 0.8329 9.2617 14.1537

4.7839 1.8907 2.5532 3.0103 1.2738 2.1669 4.2160 2.9608

t-ratio

Note: denotes significance at the 5 per cent significant level (two tailed). a2 and b3 are calculated by homogeneity conditions. Two dummy variables are introduced: D1 ¼ 1 for West Europe, D1 ¼ 0 for elsewhere; D2 ¼ 1 for East Europe, D2 ¼ 0 for elsewhere.

10.2252 5.6655 0.6474 4.8052 6.3563 4.6472 0.0342 7.3704 71.0177

0.1430 6.2938 3.2983 1.0963 3.7785 2.7411 0.4837 2.0547

parameters

t-ratio

coefficient

variables

parameters

Effectiveness (SCDF) model

Table 2 Estimation Results of SCDF and SIDF Models

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are appropriate. Moreover, g are significant in both models indicating the importance of ineffectiveness and inefficiency effects for the performance measurements. To scrutinise the plausible sources of inefficiency and ineffectiveness, Table 2 further provides useful information as we can express the service ineffectiveness and technical inefficiency effects by the following two models, respectively. ¼ 1:777 0:160z1 0:025z2 0:657z3 15:759z4 uineffectiveness it 0:777D1 0:003D2 þ Wit ; uinefficiency ¼ 0:545 0:462z1 0:120z2 0:128z3 2:788z4 it 0:311D1 þ 0:041D2 þ Wit ; where z1 is ln(GNI/1000), z2 is ln(PD), z3 is ELEC, z4 is LD, and D1 and D2 are two dummy variables of region. The estimated coefficients in these two models are of particular interest to this study. Note that, except for z2 and D2 , the coefficients z1 , z3 and z4 of both the ineffectiveness and inefficiency models are all negative and significant. This indicates that a higher gross national income per capita, a higher percentage of electrified lines, and a higher line density will significantly lead to less ineffectiveness and less inefficiency in railway transport services. Moreover, the negative coefficient of D1 indicates that the service effectiveness and technical efficiency of railways in West Europe are significantly greater than the other two regions. However, D2 is not statistically significant in both models, suggesting that inefficiency and ineffectiveness have no significant difference between East Europe and Non-Europe regions. The technical efficiency and service effectiveness scores for each DMU over eight years are reported in Appendices 1 and 2, respectively. The distributions of both efficiency and effectiveness scores are summarised in Table 3. The mean efficiency and effectiveness scores are 0.637 and 0.640, respectively, indicating that there is considerable technical inefficiency and service ineffectiveness in the railway transport industry. Both appendices also show that, in general, the levels of railways technical effectiveness and service efficiency are either stable over time or present smooth changes, as anticipated. The only exceptions appear in less developed countries (such as Mozambique) or in transition economies (such as Hungary). 4.3 Statistical testing In the following, we conduct some statistical tests, including testing for inefficiency and ineffectiveness effects, checking for the monotonicity of the distance functions, testing for the shifts of efficiency and effectiveness 397

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Table 3 Distributions of Effectiveness and Efficiency Scores (Total Number of DMUs ¼ 312) No. of DMUs (per cent) Score

Effectiveness

Efficiency

Greater or equal to 0.900 0.800–0.899 0.700–0.799 0.600–0.699 0.500–0.599 0.400–0.499 Less than 0.400 Min. Max. Mean St. dev.

85 (27.2%) 57 (18.3%) 17 (5.4%) 15 (4.8%) 22 (7.1%) 23 (7.4%) 93 (29.8%) 0.087 0.977 0.639 0.281

62 (19.9%) 50 (16.0%) 32 (10.3%) 28 (9.0%) 39 (12.5%) 37 (11.9%) 64 (20.5%) 0.144 0.981 0.637 0.243

frontiers over time, and testing for the differences of inefficiency and ineffectiveness among regions. 4.3.1 Testing for inefficiency/ineffectiveness effects Since we estimate parameters and efficiency/effectiveness by using maximum likelihood estimation, we conduct a one-sided generalised likelihood-ratio test for the null hypothesis H0 : s2u ¼ 0. For the SCDF model, it is found that LR ¼ 2fln½LðH0 Þ ln½LðH1 Þg ¼ 2½137:56 ð43:03Þ ¼ 189:06; which is greater than the 5 per cent critical chi-square value of 14.853; hence we reject H0 . That is, s2u 6¼ 0, indicating that significant service ineffectiveness exists. Similarly, for the SIDF model, LR ¼ 2ð94:32 108:07Þ ¼ 404:78; which is also greater than 14.853, indicating that technical inefficiency exists significantly. These test results concur with the significant results for g in Table 2. Thus we conclude that both inefficiency and ineffectiveness effects are significant in the railway transport industry over the period of 1995– 2002. 4.3.2 Checking for monotonicity The stochastic consumption distance function is non-decreasing in y and non-increasing in x. Non-decreasing in y means that partial derivatives of 398

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Table 4 Elasticities of SCDF and SIDF Models Elasticities of variables passenger-km ton-km passenger-train-km freight-train-km no. of passenger cars no. of freight cars no. of employees

Effectiveness (SCDF) model

Efficiency (SIDF) model

0.5247 0.4753 0.7161 0.4516

0.5590 0.3550 0.1405 0.2331 0.6264

the dO with respect to y must be greater than or equal to zero. For a Cobb– Douglas specification, bi 5 0 ensures global monotonicity. However, for a translog specification, it is more complicated and we may only check local monotonicity: @dO =@ym ¼ @ ln dO =@ ln ym dO =ym 5 0, or equivalently @ ln dO =@ ln ym 5 0 and @ ln dO =@ ln xk 4 0. Based on the estimated results in Table 2, the SCDF is ln y2 ¼ 3:726 þ 0:798 ln y þ 12 0:009ðln y Þ2 1:029 ln x1 0:537 ln x2 þ 12 ½0:123ðln x1 Þ2 þ 0:3ðln x2 Þ2 0:401 ln x1 ln x2 þ 0:041 ln x1 ln y 0:163 ln x2 ln y þ vit uit where y ¼ y1 =y2 and uit are defined in equation (15). The first derivatives of the SCDF with respect to y1 and y2 should be greater than or equal to zero, and the first derivatives of the SCDF with respect to x1 and x2 should be less than or equal to zero. By substituting observation data into the above first derivatives, we obtain the elasticity of each variable for the SCDF model (Table 4). Similarly, we can calculate the elasticity of each variable for the SIDF model (also reported in Table 4). An increase in each consumption variable or a decrease in each output variable, on average, will level up the service effectiveness. The results are consistent with what we anticipated because we define the consumption distance function as the direct measure for service effectiveness. In contrast, a decrease in each input variable or an increase in each output variable will raise technical efficiency. The results also agree with what we expected as we define the reciprocal of input distance function as the measure for technical efficiency. 4.3.3 Testing for changes in efficiency and effectiveness frontiers Our panel data cover the years from 1995 to 2002, so it is necessary to test whether there are frontier shifts during this period. We adopt a 399

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Kruskal–Wallis rank test (Sueyoshi and Aoki, 2001) with the following statistic: " # X Tj2 12 H¼ 3ðN þ 1Þ; NðN þ 1Þ j nj where Tj is the sum of ranks for group j, nj is the number of group j and N is total number of samples (Hays, 1973). In our case, nj is 39, j is 8, and N is 312. We estimate both efficiency and effectiveness by using equations (16) and (14) associated with equation (15). All the efficiency (effectiveness) scores are ranked in a single series, and by eliminating the effect of ties the efficiency and effectiveness statistics (H) are 5.13 and 0.062, respectively, both less than the critical value of w2 (¼ 14.07, with d.o.f. ¼ 7 and Pr ¼ 0.05). The null hypotheses that both efficiency and effectiveness frontiers do not shift during the observed period cannot be rejected; thus, changes in technical efficiency and service effectiveness frontiers do not occur during the period 1995–2002. This finding is particularly important to justify the pooling of eight-year sampling data in the same model. 4.3.4 Testing for differences of efficiency/effectiveness among regions A Kruskal–Wallis rank test can also be used to examine whether scores vary among regions or not. Our samples are divided into three regions: West Europe, East Europe and Non-Europe. After eliminating the effect of ties, we obtain Heffi ¼ 126:57 and Heffe ¼ 126:39, both significantly greater than the critical value of w2 (¼ 5.99, with d.o.f. ¼ 2 and Pr ¼ 0.05). Therefore, we reject the null hypothesis that the efficiency (effectiveness) scores do not vary across regions. The testing results are consistent with the dummy variables D1 in both the SCDF and SIDF models being negative and significant, indicating that railways in West Europe are less inefficient and ineffective than those in other regions. Table 5 reports the details of the efficiency and effectiveness scores in the three regions. On average, Table 5 Comparison of Effectiveness and Efficiency Scores among Regions Effectiveness score

Efficiency score

Statistics West Europe East Europe Non-Europe West Europe East Europe Non-Europe Max Min Mean St. dev.

400

0.966 0.586 0.875 0.103

0.936 0.210 0.572 0.259

0.889 0.172 0.412 0.254

0.961 0.604 0.828 0.109

0.825 0.180 0.497 0.165

0.961 0.196 0.586 0.285

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railways in West Europe are more efficient and effective than those in the other two regions. It could be due to greater technological sophistication in West Europe compared with the other two regions. Higher gross national income per capita, higher percentages of electrified lines, and higher line density in West European countries could also explain the results.

5.0 Policy Implications and Discussion Based on the results of two stochastic distance functions, a performance matrix is established in Figure 2, in which each firm’s efficiency and effectiveness scores are indicated. Since we adopt input and consumption distance functions to measure railways’ technical efficiency and service effectiveness respectively, the results should be explained as input savings and consumption augments for each DMU in order to attain the efficient and effective frontiers. Those firms in the upper-left matrix with relatively low efficiency but high effectiveness, such as DMU16 (Croatia, HZ), DMU17 (Crech, CD), DMU20 (Hungary, MAVRt), DMU23 (Poland, PKP) and DMU25 (Slovakia, ZSSK) should focus on curtailing excess Figure 2 Performance Matrix for 39 Railways 1.0

1716 20

2 7

.8

5 8 14 1 9 11 4 12 37 26 1336 10 6

25

Effectiveness

23 3

24 15

.6

35

29 34

.4

27 33 .2

0.0

0.0

.2

22 32 28

21

18

19

39 30

31

38

.4

.6

.8

1.0

Efficiency

401


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inputs; whereas those in the lower-right matrix with relatively high efficiency but low effectiveness, such as DMU19 (Hungary, GySEV), DMU30 (Israel, IsR), DMU35 (South Korea, KORAIL) and DMU39 (Australia, QR) should put more emphasis on attracting more passengers and/or freight. Those firms in the lower-left matrix with relatively low efficiency and low effectiveness, in particular DMU 27 (Moldova, CFM(E)), DMU 33 (Mozambique, CFM), DMU 28 (Ukraine, UZ), and DMU 38 (Turkmenistan, TRK), should consider both directions to improve poor performance. In general, introducing innovative production and marketing techniques are always important for any rail firm to enhance efficiency and effectiveness so as to remain sustainable in competitive transport markets. In Table 4, the elasticity of the input distance function with respect to the number of employees (¼ 0.6264) is greater than that with respect to the other two inputs (freight-car ¼ 0.2331 and passenger-car ¼ 0.1405), implying that overstaffing is critical in the railway transport industry. Thus, reducing the number of employees should be viewed as the imperative strategy to enhance technical efficiency. This strategy can be explained as the result of restructuring of some DMUs. For instance, DMU 14 (Switzerland, CFF) and DMU 6 (Ireland, CIE), both companies have enhanced technical efficiency due to a considerable reduction of the number of employees after 1997 and 1998, respectively. Table 2 shows that the percentage of electrified lines and line density are two internal factors significantly affecting efficiency. The policy implications of this suggest that railway firms should increase the percentage of electrified lines as well as enlarge the network to improve technical efficiency. The elasticity of the consumption distance function in Table 4 with respect to passenger service (¼ 0.5247) is only slightly greater than that with respect to freight service (¼ 0.4753), suggesting that the provision of passenger as well as freight services could be equally important for a railway company to enhance its service effectiveness. Table 2 also shows that gross national income per capita is an important external factor affecting railways’ effectiveness and efficiency. On the one hand, higher gross national income per capita generally leads to intensive transport demands for passenger and freight services due to strong socio-economic activities. On the other hand, higher income countries normally possess more innovative technologies and advanced management knowledge. Railway operators cannot control such external factors as gross national income per capita and population density to improve effectiveness. Nor can they impose any restriction on the use of private vehicles. However, operators can concentrate on enhancing service quality, such as raising the punctuality rate, introducing more high-speed rails, replacing 402


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over-aged assets (tracks and rolling stock), and reducing total loading and unloading time at stations (particularly for freight), to attract more passengers from private cars and/or more freight from trucks. More importantly, because the demands for transport are derived and transport services are non-storable, rescheduling trains so as optimally to match the demands for passenger and freight services should be considered. Certainly, improving the booking system, developing the prepaid ticketing system, and providing discounts to loyal customers, frequent users, or group travelers, are also potential good strategies for promoting railway effectiveness. It is worth noting that rail is the most important mode in long-distance land haul, particularly for low-value bulk commodities including raw materials, intermediate, and final products. Rail freight transport is very labour-intensive and time-consuming, especially at the terminals where loading and unloading take place. Hence, expediting the processing of freight at terminals by introducing fast loading and unloading facilities in association with the intelligent transport technologies might make a rail service more compatible with a trucking service. Intercity passenger trains or high-speed trains can also consider providing line-haul service for high-value compact goods, if the logistics can be well integrated with local pickup and delivery services. Note that distance function approaches are parametric methods. Efficiency and/or effectiveness measures can also be evaluated by nonparametric methods (such as data envelopment analysis). A comparison of technical efficiency and service effectiveness for rail transport between parametric and non-parametric methods deserves further exploration. In this study, we did not account for such external factors as public/private ownership and regulatory differences across the firms. As pointed out by Pittman (2004), countries throughout the world are in the process of abandoning the centralised, monopolistic, and state-owned model of rail in favour of models that create competition. For example, with the privatisation of British Rail (BR) between 1994 and 1997, the British government intended to transfer to the private sector the main responsibility of operating and funding rail transport. A structural reform, with vertical and horizontal separation of track and trains, was therefore introduced. The ownership and operation of the entire track network was transferred to a private infrastructure company (Railtrack), while passenger rail services were horizontally separated into 25 operations consisting of a bundle of services over various train-paths under an ‘open access competition’ franchise mechanism. Once the operator had been assigned a franchise, access to the track for the provision of the service in the assigned area was obtained from Railtrack at a regulated price. However, this ‘open 403


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access’ project was suspended as the British government felt necessary to move towards more integration rather than pursuing further separation (Affuso, 2003). A similar vertical separation of rail infrastructure from service operation was also established in Italy in 2002. The train paths were allocated by means of an auction mechanism. The potential operators participating in the auction were required to specify the paths they demanded including details of the services they intended to run. The outcome of the competition was then based on the quality of the service offered rather than the price (which was regulated). The bidders could decide the type of services to offer given the price that was automatically supplied by the infrastructure manager for each potential bid (see http://www.rfi.it). More recently, a multinational intermodal PolCorridor project was announced in 2002 to create a new trans-European freight supply network. The northern part of the corridor will consist of sea-land connections from Sweden, Finland, and Norway to an intermodal hub in Poland. From there, the corridor will be connected via a regularly scheduled block train (Blue Shuttle Train) to an intermodal terminal in Vienna. The southern part of the corridor will involve the utilisation of existing land connections to destinations in most of central and southeastern Europe. Through collaboration with various transport and logistics organisations, a comprehensive feeder network will be established to supply cargo by truck, train, and ferry to one of the PolCorridor logistical canters. From there, cargo will be redistributed to the Blue Shuttle Train, which will carry it faster, cheaper, and more securely than current transport alternatives (see http://www.toi.no). The outcome and effectiveness of the above-mentioned recent changes in the rail sector (vertical and horizontal separation, different mechanisms to introduce more competition such as auction systems, and multinational intermodal integration) will be of great interest. Such changes may invite more competition and introduce important modifications in the performance of the rail sector, but the results have yet to be empirically tested. It would be interesting to examine differences in technical efficiency and service effectiveness resulting from these institutional and restructuring changes in the rail sector in a future study.

References Affuso, L. (2003): ‘Auctions of Rail Capacity?’ Utilities Policy, 11, 43–46. Aigner, D. J., C. A. K. Lovell, and P. Schmidt (1977): ‘Formulation and Estimation of Stochastic Frontier Production Function Models’, Journal of Econometrics, 6, 21–37.

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Battese, G. E. and T. J. Coelli (1988): ‘Prediction of Firm-level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data’, Journal of Econometrics, 38, 387–99. Battese, G. E. and T. J. Coelli (1995): ‘A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data’, Empirical Economics, 20, 325–32. Bosco, B. (1996): ‘Excess-input Expenditure Estimated by Means of an Input Distance Function: The Case of Public Railways’, Applied Economics, 28, 491–7. Cantos, P. and J. Maudos (2000): ‘Efficiency, Technical Change and Productivity in the European Rail Sector: A Stochastic Frontier Approach’, International Journal of Transport Economics, 27, 55–76. Cantos, P. and J. Maudos (2001): ‘Regulation and Efficiency: The Case of European Railways’, Transportation Research, 35A, 459–72. Caves, D. W., L. R. Christensen, and J. A. Swanson (1981): ‘Productivity Growth, Scale Economies, and Capacity Utilization in U.S. Railroads, 1955–74’, The American Economic Review, 71, 994–1002. Chapin, A. and S. Schmidt (1999): ‘Do Mergers Improve Efficiency?’ Journal of Transport Economics and Policy, 33, 147–62. Coelli, T. J. (1996): ‘A Guide to FRONTIER Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation’, CEPA Working Papers, No. 7/96, Department of Econometrics, University of New England. Coelli, T. J., D. S. P. Rao, and G. Battese (1998): An Introduction to Efficiency and Productivity Analysis, Kluwer Academic Publishers. Coelli, T. J. and S. Perelman (1999): ‘A Comparison of Parametric and Non-parametric Distance Functions: With Application to European Railways’, European Journal of Operational Research, 117, 326–29. Coelli, T. J. and S. Perelman (2000): ‘Technical Efficiency of European Railways: A Distance Function Approach’, Applied Economics, 32, 1967–76. Cowie, J. (1999): ‘The Technical Efficiency of Public and Private Ownership in the Rail Industry’, Journal of Transport Economics and Policy, 33, 241–52. Fa¨re, R. and S. Grosskopf (2000): ‘Network DEA’, Socio-Economic Planning Sciences, 34, 35–50. Fa¨re, R. and D. Primont (1995): Multi-output Production and Duality: Theory and Applications, Kluwer Academic Publishers. Fielding, G. J., T. T. Babitsky, and M. E. Brenner (1985): ‘Performance Evaluation for Bus Transit’, Transportation Research, 19A, 73–82. Fleming, C. (1999): ‘Train Drain: in the Unified Europe Shipping Freight by Rail is a Journey into the Past’, The Wall Street Journal, 29 March, A1–A8. Freeman, K. D., T. H. Oum, M. W. Tretheway, and W. G. Waters II (1985): ‘The Total Factor Productivity of the Canadian Class I Railways: 1956–1981’, The Logistics and Transportation Review, 21, 249–76. Friedlaender, A. F., E. R. Berndt, J. S. Wang Chiang, M. Showalter, and C. A. Vellturo (1993): ‘Rail Cost and Capital Adjustments in a Quasi-Regulated Environment’, Journal of Transport Economics and Policy, 27, 131–52. Gathon, H. J. and S. Perelman (1992): ‘Measuring Technical Efficiency in European Railways: A Panel Data Approach’, Journal of Productivity Analysis, 3, 135–51. Griffiths, W. E., C. J. O’Donnell, and A. Tan Cruz (2000): ‘Imposing Regularity Conditions on a System of Cost and Factor Share Equations’, The Australian Journal of Agricultural and Resource Economics, 44, 107–27. Hays, W. L. (1973): Statistics, Holt, Rinehart and Winston. Huang, C. J. and J. T. Liu (1994): ‘Estimation of a Non-neutral Stochastic Frontier Production Function’, Journal of Productivity Analysis, 5, 171–80.

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Jondrow, J., C. A. K. Lovell, I. S. Materov, and P. Schmidt (1982): ‘On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model’, Journal of Econometrics, 19, 233–8. Kennedy, J. and A. S. J. Smith (2004): ‘Assessing the Efficient Cost of Sustaining Britain’s Rail Network: Perspectives based on Zonal Comparisons’, Journal of Transport Economics and Policy, 38, 157–90. Kumbhakar, S. C. and C. A. K. Lovell (2000): Stochastic Frontier Analysis, Cambridge University Press. Kumbhakar, S. C., S. Ghosh, and J. T. McGuckin (1991): ‘A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms’, Journal of Business and Economic Statistics, 9, 279–86. Lan, L. W. and E. T. J. Lin (2003a): ‘Measurement of Railways Productive Efficiency with Data Envelopment Analysis and Stochastic Frontier Analysis’, Journal of the Chinese Institute of Transportation, 15, 49–78. Lan, L. W. and E. T. J. Lin (2003b): ‘Technical Efficiency and Service Effectiveness for Railways Industry: DEA Approaches’, Journal of the Eastern Asia Society for Transportation Studies, 5, 2932–47. Lan, L. W. and E. T. J. Lin (2005): ‘Measuring Railway Performance with Adjustment of Environmental Effects, Data Noise and Slacks’, Transportmetrica, 1, 161–89. Lewis, I., J. Semeijn, and D. B. Vellenga (2001): ‘Issues and Initiatives Surrounding Rail Freight Transportation in Europe’, Transportation Journal, 41, 23–31. Lovell, C. A. K., S. Richardson, P. Travers, and L. L. Wood (1994): ‘Resources and Functionings: A New View of Inequality in Australia’, in W. Eichhorn (ed.), Models and Measurement of Welfare and Inequality, Berlin, Springer-Verlag. McGeehan, H. (1993): ‘Railway Costs and Productivity Growth: The Case of the Republic of Ireland, 1973–1983’, Journal of Transport Economics and Policy, 27, 19–32. O’Donnell, C. J. and T. J. Coelli (2005): ‘A Bayesian Approach to Imposing Curvature on Distance Function’, Journal of Econometrics, 126, 493–523. Orea, L., D. Roibas, and A. Wall (2004): ‘Choosing the Technical Efficiency Orientation to Analyze Firms Technology: A Model Selection Test Approach’, Journal of Productivity Analysis, 22, 51–71. Oum, T. H., W. G. Waters II, and C. Yu (1999): ‘A Survey of Productivity and Efficiency Measurement in Rail Transport’, Journal of Transport Economics and Policy, 33, 9–42. Pittman, R. (2004): ‘Chinese Railway Reform and Competition: Lessons from the Experience in Other Countries’, Journal of Transport Economics and Policy, 38, 309–32. Reifschneider, D. and R. Stevenson (1991): ‘Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency’, International Economic Review, 32, 715–23. Shephard, R. W. (1970): Theory of Cost and Production Functions, Princeton University Press. Sueyoshi, T. and S. Aoki (2001): ‘A Use of a Nonparametric Statistic for DEA Frontier Shift: the Kruskal and Wallis Rank Test’, OMEGA International Journal of Management Science, 29, 1–18. Tretheway, M. W., W. G. Waters II, and A. K. Fok (1997): ‘The Total Factor Productivity of the Canadian Class I Railways: 1956–91’, Journal of Transport Economics and Policy, 31, 93–113. UIC (1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002): International Railway Statistics, Paris.

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Appendix 1 The Service Effectiveness Scores Measured by SCDF Model (Ranked by Average Score within Each Region) Region

Average DMU score no.

Country

Railways 1995 1996 1997 1998 1999 2000 2001 2002

WestEurope

0.966 0.952 0.946 0.931 0.931 0.925 0.911 0.906 0.897 0.856 0.842 0.803 0.803 0.586

5 8 1 9 11 14 2 4 12 7 13 6 10 3

Germany Luxembourg Austria Netherlands Spain Switzerland Belgium French Norway Italy Switzerland Ireland Portugal Finland

DBAG CFL OBB NSNV RENFE CFF SNCB SNCF NSB FS Spa BLS CIE CP VR

0.977 0.961 0.943 0.961 0.956 0.944 0.893 0.936 0.932 0.863 0.860 0.713 0.672 0.566

0.975 0.960 0.897 0.945 0.945 0.959 0.898 0.837 0.940 0.881 0.836 0.849 0.739 0.568

0.960 0.967 0.954 0.938 0.959 0.932 0.931 0.928 0.943 0.900 0.894 0.839 0.885 0.571

0.958 0.968 0.969 0.924 0.923 0.910 0.910 0.910 0.945 0.885 0.918 0.850 0.936 0.585

0.968 0.969 0.973 0.942 0.946 0.897 0.944 0.917 0.861 0.868 0.818 0.802 0.771 0.583

0.969 0.939 0.963 0.937 0.935 0.882 0.932 0.898 0.864 0.844 0.875 0.786 0.872 0.580

0.956 0.896 0.942 0.904 0.894 0.923 0.893 0.907 0.848 0.786 0.828 0.847 0.787 0.604

0.968 0.960 0.927 0.893 0.888 0.952 0.884 0.912 0.844 0.821 0.708 0.738 0.763 0.630

EastEurope

0.936 0.932 0.923 0.885 0.738 0.653 0.574 0.564 0.466 0.391 0.375 0.346 0.331 0.257 0.210

16 17 20 26 25 23 24 15 29 22 18 21 19 27 28

Croatia Crech Rep. Hungary Slovenia Slovakia Poland Romania Bulgaria Turkey Lithuania Estonia Latvia Hungary Moldova Ukraine

HZ CD MAVRt SZ ZSSK PKP CFR BDZ TCDD LG EVR LDZ GySEV CFM(E) UZ

0.920 0.923 0.945 0.905 0.660 0.622 0.506 0.341 0.462 0.386 0.404 0.355 0.339 0.247 0.214

0.955 0.910 0.938 0.925 0.699 0.631 0.506 0.536 0.489 0.406 0.418 0.353 0.234 0.253 0.215

0.968 0.910 0.912 0.913 0.763 0.629 0.556 0.507 0.472 0.399 0.435 0.353 0.222 0.205 0.214

0.968 0.939 0.902 0.882 0.742 0.646 0.582 0.523 0.459 0.403 0.432 0.350 0.292 0.221 0.212

0.963 0.952 0.949 0.903 0.794 0.657 0.597 0.619 0.455 0.378 0.367 0.340 0.235 0.318 0.212

0.869 0.945 0.923 0.872 0.746 0.648 0.570 0.570 0.483 0.402 0.364 0.373 0.436 0.284 0.204

0.957 0.929 0.915 0.861 0.756 0.722 0.592 0.681 0.458 0.392 0.317 0.341 0.378 0.274 0.206

0.886 0.950 0.904 0.821 0.746 0.669 0.683 0.733 0.453 0.359 0.265 0.303 0.511 0.251 0.204

NonEurope

0.889 0.830 0.487 0.409 0.314 0.299 0.257 0.237 0.222 0.172

37 36 35 34 39 32 30 33 31 38

Taiwan TRA 0.817 0.857 0.883 0.877 0.876 0.898 0.945 Japan JR 0.837 0.814 0.824 0.844 0.841 0.814 0.836 South Korea KORAIL 0.419 0.432 0.460 0.484 0.534 0.526 0.500 Azerbaidjan AZ 0.381 0.462 0.478 0.419 0.393 0.399 0.391 Australia QR 0.304 0.326 0.342 0.332 0.329 0.311 0.280 Syria CFS 0.347 0.306 0.327 0.302 0.279 0.334 0.245 Israel IsR 0.230 0.240 0.236 0.241 0.273 0.258 0.272 Mozambique CFM 0.097 0.087 0.131 0.288 0.310 0.382 0.378 Morocco ONCFM 0.241 0.224 0.212 0.221 0.220 0.220 0.220 Turkmenistan TRK 0.156 0.144 0.202 0.198 0.213 0.166 0.150

0.963 0.827 0.543 0.346 0.286 0.256 0.304 0.227 0.218 0.151

Mean

0.640

0.621 0.630 0.645 0.650 0.648 0.648 0.641 0.635

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Appendix 2 The Technical Efficiency Scores Measured by SIDF Model (Ranked by Average Score within Each Region) Region

Average DMU score no.

Country

Railways 1995 1996 1997 1998 1999 2000 2001 2002

WestEurope

0.961 0.939 0.924 0.902 0.899 0.878 0.868 0.845 0.812 0.794 0.774 0.765 0.624 0.604

12 3 8 13 11 5 9 1 14 6 4 10 2 7

Norway Finland Luxembourg Switzerland Spain Germany Netherlands Austria Switzerland Ireland French Portugal Belgium Italy

NSB VR CFL BLS RENFE DBAG NSNV OBB CFF CIE SNCF CP SNCB FS Spa

0.954 0.909 0.933 0.832 0.824 0.858 0.921 0.752 0.667 0.661 0.635 0.687 0.617 0.552

0.978 0.916 0.928 0.771 0.831 0.890 0.850 0.778 0.745 0.711 0.787 0.677 0.629 0.592

0.979 0.943 0.911 0.907 0.902 0.891 0.885 0.811 0.765 0.717 0.805 0.831 0.619 0.619

0.981 0.950 0.929 0.942 0.904 0.886 0.880 0.861 0.910 0.710 0.715 0.815 0.625 0.603

0.944 0.948 0.941 0.963 0.916 0.861 0.846 0.864 0.825 0.952 0.741 0.613 0.628 0.583

0.961 0.948 0.928 0.907 0.913 0.853 0.877 0.878 0.862 0.841 0.761 0.686 0.620 0.605

0.946 0.948 0.916 0.920 0.954 0.868 0.853 0.909 0.846 0.926 0.861 0.902 0.625 0.613

0.944 0.954 0.907 0.972 0.952 0.913 0.833 0.904 0.877 0.832 0.886 0.907 0.628 0.663

EastEurope

0.825 0.756 0.614 0.542 0.533 0.529 0.505 0.504 0.497 0.489 0.484 0.381 0.321 0.290 0.180

26 19 18 21 20 16 17 29 23 25 22 15 24 28 27

Slovenia Hungary Estonia Latvia Hungary Croatia Crech Rep. Turkey Poland Slovakia Lithuania Bulgaria Romania Ukraine Moldova

SZ GySEV EVR LDZ MAVRt HZ CD TCDD PKP ZSSK LG BDZ CFR UZ CFM(E)

0.775 0.718 0.405 0.393 0.470 0.444 0.493 0.483 0.487 0.473 0.457 0.390 0.377 0.269 0.207

0.783 0.623 0.404 0.464 0.491 0.471 0.512 0.505 0.455 0.458 0.487 0.382 0.342 0.265 0.202

0.810 0.651 0.541 0.528 0.527 0.496 0.485 0.533 0.469 0.485 0.492 0.390 0.333 0.294 0.188

0.817 0.715 0.572 0.507 0.533 0.503 0.466 0.516 0.491 0.472 0.476 0.346 0.318 0.293 0.180

0.838 0.754 0.718 0.609 0.565 0.534 0.473 0.501 0.516 0.471 0.461 0.356 0.233 0.291 0.156

0.859 0.887 0.755 0.663 0.557 0.573 0.515 0.507 0.526 0.473 0.494 0.351 0.310 0.297 0.150

0.855 0.792 0.670 0.576 0.586 0.572 0.546 0.494 0.514 0.536 0.482 0.402 0.313 0.291 0.169

0.861 0.906 0.848 0.594 0.534 0.635 0.554 0.494 0.518 0.539 0.527 0.428 0.346 0.318 0.190

NonEurope

0.961 0.931 0.849 0.767 0.735 0.493 0.338 0.328 0.212 0.196

39 36 30 37 35 31 38 32 33 34

Australia QR 0.926 0.941 0.965 0.967 0.969 Japan JR 0.894 0.934 0.945 0.905 0.944 Israel IsR 0.927 0.838 0.849 0.834 0.763 Taiwan TRA 0.860 0.821 0.758 0.721 0.714 South Korea KORAIL 0.690 0.714 0.704 0.672 0.733 Morocco ONCFM 0.383 0.441 0.448 0.493 0.508 Turkmenistan TRK 0.365 0.335 0.344 0.311 0.338 Syria CFS 0.390 0.327 0.321 0.290 0.287 Mozambique CFM 0.170 0.183 0.224 0.186 0.190 Azerbaidjan AZ 0.144 0.162 0.167 0.185 0.214

0.971 0.937 0.861 0.749 0.743 0.513 0.321 0.312 0.221 0.220

0.974 0.948 0.880 0.752 0.874 0.565 0.342 0.314 0.220 0.236

0.976 0.943 0.841 0.757 0.747 0.592 0.347 0.381 0.306 0.240

Mean

0.637

408

0.600 0.606 0.629 0.628 0.635 0.651 0.666 0.682