State road transport undertakingsin India: technical efficiency

and its determinantsSunil Kumar

Faculty of Economics, South Asian University, New Delhi, India

Abstract

Purpose – The purpose of this paper is not only to gauge the extent of technical efficiency in 31 stateroad transport undertakings (SRTUs) operating in India but also to explore the most influential factorsexplaining its variations across SRTUs.

Design/methodology/approach – Three popular data envelopment analysis (DEA) models,namely CCR, BCC and Andersen and Petersen’s super-efficiency models, have been utilized to computevarious efficiency scores for individual SRTUs. A censored Tobit analysis is conducted to see whichfactors significantly explain the inter-SRTU variations in efficiency.

Findings – The key findings of the DEA analysis are only five SRTUs define the efficient frontier,and the remaining 26 inefficient undertakings have a scope of inputs reduction, albeit by the differentmagnitude; the extent of average overall technical inefficiency (OTIE) in these SRTUs is to the tune of22.8 percent, indicating that the sample SRTUs are wasting about one-fourth of their resources in theproduction operations; managerial inefficiency (as captured by the pure technical inefficiency) is arelatively more dominant source of OTIE; and operation in the zone of increasing returns-to-scale is acommon feature for most of the undertakings. The multivariate regression analysis usingTobit analysis highlights that the occupancy ratio is the most significant determinant for all theefficiency measures, and bears a positive relationship with overall technical, pure technical and scaleefficiencies. Further, scale efficiency is also impacted positively by the staff productivity.

Practical implications – The results of this paper can be applied from management’s perspective.The managers can assess the relative efficiency of their SRTUs in the industry and take correctivemeasures to improve efficiency by altering input-output mix.

Originality/value – This paper provides more robust estimates of relative efficiency of theSRTUs and highlights the key determinants of overall technical efficiency.

Keywords Data envelopment analysis (DEA), Tobit analysis, State road transport undertakings,Returns-to-scale, Road transport, Process efficiency

Paper type Research paper

1. IntroductionThe present study aims to analyze:

. the technical efficiency differences across state road transport undertakings(SRTUs) operating in India; and

. the significant determinants explaining the observed efficiency differences.

SRTUs are public owned bus operators which play gargantuan role in enhancing thepassenger mobility in diverse terrains throughout the country, and thus lay aconsiderable impact on the life of masses. There is no doubt that an analysis of thesources and determinants of operational efficiency would be a valuable aid to the policyformulators in designing appropriate policies aiming to improve the overall healthand competitiveness of these undertakings. However, in Indian context, the analysis

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of efficiency of SRTUs has not received considerable attention from the scholars, andthere are only a handful of studies on the subject matter in the academic journals (seeSection 3 for details). Our study intends to enrich the scant literature, and in particular,endeavours to gauge the extent of overall technical, pure technical and scale efficienciesin SRTUs using a non-parametric, data driven, deterministic and non-statisticaltechnique known as data envelopment analysis (DEA). The choice of DEA over itsarchrival stochastic frontier analysis (SFA) in the present context is directed by itsintrinsic advantages such as:

. DEA does not entail any incorrect functional form of the production function;

. DEA provides a scalar measure of technical efficiency in case of productiontechnology with multiple inputs and outputs;

. DEA is competent to investigate the changes in efficiency resulting from inputssaving, and can also assess whether the reasons for such changes areimprovements in scale (i.e. scale efficiency (SE)) or management practices(i.e. pure technical efficiency (PTE)) (Topuz et al., 2005); and

. DEA has proved to be particularly useful for analyzing production in the publicsector where there is market failure or outputs are not traded using market prices(Ganley and Cubbin, 1992).

In recent years, a growing interest in the DEA methodology for analyzing the efficiencyof bus transport services sector has been noticed (Chang and Kao, 1992; Nolan, 1996;Levaggi, 1994; Viton, 1997; Cowie and Asenova, 1999; Nolan et al., 2001; Odeck andAlkadi, 2001; Pina and Torres, 2001; Karlaftis, 2003, 2004; Boame, 2004; Sheth et al.,2007; Lin and Lan, 2009). In addition, DEA has gained tremendous popularity as arelative efficiency measurement technique in other major areas of transport sector likeairports (Gillen and Lal, 1997; Milo et al., 1998; Sarkis, 2000; Martin and Roman, 2001;Pels et al., 2001; Adlar and Golany, 2001; Adlar and Berchman, 2001; Fernandes andPacheco, 2002; Pels et al., 2003; Bazargan and Vasigh, 2003; Pacheco and Fernades,2003; Yu, 2004; Sarkis and Talluri, 2004; Scheraga, 2004; Bowlin, 2004; Capobianco andFernandes, 2004; Lin and Hong, 2006; Pacheco et al., 2006; Chiou and Chen, 2006; Greer,2008, etc.), ports (Tongzon, 2001; Turner et al., 2004; Cullinane et al., 2005, etc.) andrailways (Caves et al., 1980; Caves et al., 1981; Freeman et al., 1985; Dodgson, 1985;McGeeham, 1993; Wunsch, 1996; Tretheway et al., 1997; Oum et al., 1999; Cantos et al.,1999; Babalik-Sutcliffe, 2003; Graham, 2008, etc.). In fact, the applications of DEA intransport sector are voluminous. Nevertheless, the research on the efficiency of IndianSRTUs using DEA and other frontier efficiency measurement techniques is still in thestage of infancy. The available literature reviewed by us does not provide even a singlestudy which detected the presence of outliers in efficiency measurement, and examinedthe factors determining technically inefficiency using Tobit regression analysis.The present study is an endeavour in this direction, and particularly aims to:

. rank the SRTUs on the basis of super-efficiency scores obtained from Andersenand Petersen’s (1993) DEA model;

. decompose the measure of overall technical efficiency (OTE) into its components,namely PTE and SE;

. set the targets for the inefficient SRTUs so that they can become efficient byadjusting their inputs and outputs; and

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. explain the significant factors affecting OTE, PTE and SE of SRTUs by usingTobit regression analysis.

The remainder of the paper is structured as follows. Section 2 provides an overview ofSRTUs in India. Section 3 reviews the relevant literature on the subject matter. Section4 presents the DEA models used for efficiency measurement. The data used and issuesof measurement of inputs and outputs are discussed in Section 5. The empirical resultsare presented in Section 6, and conclusions are drawn in the final section.

2. SRTUs in India: an overviewPrior to independence in 1947, the passenger road transport sector in India wasdominated by the private players, and there was unhealthy competition amongstoperators who concentrated on the more remunerative routes. A consensus, however, hasemerged that controlled monopoly is the only answer to the evils of unhindered andselfish competition. Following the recommendations of some high-powered committeesset up in the 1930s, the Motor Vehicle Act of 1939 has been enacted with the purpose toregulate road transport on the basis of healthy competition in the industry itself. In thepost-independence era, the idea of nationalization of passenger road transport gainedmomentum so as to provide as an affordable, safe and reliable passenger services topeople. Eventually, the Road Transport Corporation Act of 1950 has been enacted with aclear objective to meet the social obligations. This paved the way of nationalization ofstate carriages in five states, namely Andhra Pradesh, Gujarat, Haryana, Maharashtraand Punjab. However, in the rest of the country such services have been provided both bythe public and private sectors, but in varying degree. The government, therefore, becamenot only the regulator of the road transport but also an operator in some states exclusivelyand in others alongside several other small operators. Currently, bus transport servicesare provided by both private bus operators as well as publicly owned SRTUs. Although,the private sector has an effective participation in the passenger mobility, yet itsoperational activities are very much disaggregated and unorganized. One the other hand,the operational activities of public transport sector are well regulated and organized.

In the past few decades, the share of bus transportation in total surface trafficmovement in India has grown by leaps and bounds. A significant change in the share ofbus transport sector has been observed relative to its closest alternative railway transport.The bus transport sector is estimated to be handling around 80 percent of passengermovements and 60 percent of freight movements as compared to its estimated share of20 and 11 percent, respectively, in passenger and freight in the early 1950s (Sriraman,2002). At present, there are 47 SRTUs operating in the country, out of which, 23 arecorporations formed under the Road Transport Act of 1950, eight are governmentcompanies which have been formed under the Companies Act of 1956, eight aregovernment departments controlled by the state governments, and eight are municipalundertakings operating owned and controlled by municipal corporations. These SRTUsare operating with more than a hundred thousand of vehicles and eight hundred thousandof workers. The total effective kilometers operated by the SRTUs are more than ten billion,the number of passengers carried are more than a 23 billion and the volume of operationhave crossed 450 billion passenger-kms mark. These undertakings operate 1,200 millionpassenger kilometers and carrying 245 million passengers daily. These undertakingsprovide direct employment to 0.73 million people (Government of India, 2007).

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In the Indian context, the SRTUs, over a period of time, have occupied a pivtol role byvirtue of certain inherent advantages like its affordability, flexibility, door-to-dooroperations, timely deliveries and linking remote and hill areas with rest of the country.But, over the years, most of these SRTUs have moved from profit-making areas toloss-incurring zones due to trade-off between the commercial objectives and socialresponsibility, controlled fares and greater share of old buses in total fleet size, etc(Saxena et al., 2003). Moreover, the SRTUs have twisted to serve the political objectivesof the state governments, both as a source of employment generation and as a source ofpatronage by fare discounts to wider and wider segments of the population (The WorldBank, 2005). These concessions have cost the SRTUs hundreds of billions that havenever been compensated by the respective state governments. Currently, a stage hasbeen reached where these public undertakings are forced to meet large number of socialobligations without any budgetary support from their respective state governments.As a result, most of these undertakings have to keep running their operations with hugelosses. To a large extent, this hinders the ability of these undertakings to supplythe optimum level of services both in terms of quality as well as quantity. Furthermore,these undertakings have relatively few incentives to run their business efficiently.In the present study, an attempt has been made to assess the technical efficiency of theseundertakings for reinventing the ways the SRTUs would emerge as an idealbenchmarks in the passenger transport sector of the country.

3. Relevant literature review on Indian SRTUs’ efficiencyAs mentioned in the introductory section, there exists a voluminous literature on theefficiency of public transport system in developed countries. However, the researchon efficiency of SRTUs operating in India has been undertaken by a few researchers.Using SFA, Kumbhakar and Bhattacharyya (1996) found a negative total factorproductivity (TFP) growth in 11 SRTUs out of the total of 31 for the period from1983 to 1987. They observed the contribution of scale economies as an importantfactor which varies widely across SRTUs. Ramanathan (1999) applied DEA to assessthe efficiency of 29 SRTUs operating in the year 1993-1994, and found that most ofthe operators are using their fuel efficiently while large inefficiencies are observedin the usage of fleet and staff. Furthermore, with the application of regressionanalysis, he observed that the age of fleet has a negative influence on the efficiency,and efficiency tends to reduce if the area of operation happens to be hilly. Cityoperations with a higher passenger density per bus tend to increase efficiency scores.Using multilateral productivity index, Singh (2000a, b, c) provided a comparison ofTFP growth for 21 SRTUs during the period 1983-1984 to 1996-1997. It has beennoted that:

. there is wide disparity among SRTUs according to their productive efficiencylevels and growth;

. on an average, small-sized SRTUs experienced higher level of productiveefficiency than their larger counterparts;

. by and large, Tamil Nadu SRTUs seem to be more productive than theircounterparts operating in other states of the country; and

. the distribution of ranks of SRTUs with respect to their productive efficiencylevels has remained broadly unchanged over the years.

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Singh (2000d) and Jha and Singh (2000) confirmed the existence of U-shaped averagecost curve in the nine SRTUs from the period for 1984-1985 to 1996-1997 with the aid ofSFA. Again in this study, smaller SRTUs appear to be more efficient than their largercounterparts. These studies suggested that a policy that aims to change the sizedistribution of the SRTUs will help in increasing the efficiency of the Indian bustransport industry. Singh and Venkatesh (2003) also applied SFA on the 23 SRTUsusing the dataset for the year 2000-2001. It has been noted that average efficiency is tothe tune of 84.22 percent, and the extent of inefficiency ranges between 1.01 and43.85 percent. Karne and Venkatesh (2003) analyzed the TFP growth and technicalefficiency in Maharashtra State Road Transport Corporation (MSRTC) usingDEA-based Malmquist productivity index (MPI). They note that during the studyperiod (1996-1997 to 2001-2002), there has been a marginal improvement in TFP by1.1 percent. Also, there have been negligible improvements in technical efficiency aswell as technical change.

Anjaneyulu et al. (2006) studied the efficiency of 44 SRTUs with the help of DEA.They found that eight SRTUs were consistently efficient, 24 were consistentlyinefficient, and efficiency of 11 SRTUs found to be varying from year to year. Usingcross-sectional data for the year 2002-2003, Agrawal et al. (2006) utilized DEA toexamine technical efficiency of State Road Transport Corporation (SRTC) ofUttar Pradesh, the largest state of India. They observed the regional average OTEto the tune of 87.8 percent before sensitivity analysis, and 92.7 percent after sensitivityanalysis. Furhter, the average PTE reported to the tune of 95.16 percent. Ray andVenkatesh (2007) have also applied DEA to analyze the effects of decentralization ofthe efficiency of SRTUs in India for the period 1990-2005, and reported mild increase inefficiency of the studied corporations after the decentralization. Bishnoi and Sujata(2007) utilized DEA to measure the extent of technical efficiency of 20 depots ofHaryana SRTC in the year 2006-2007. The study reported average overall technical andpure technical scores to the tune of 90.2 and 94.3 percent, respectively. Also 18 depotsfound to be operating in the zone of increasing returns-to-scale (IRS). Theyrecommended the reduction of total staff by 25.58 percent, fuel consumption by9.25 percent and fleet strength by 13.72 percent for the inefficient depots. Nagadevaraand Ramanayya (2008) used DEA to identify the inefficient depots at the district levelin Andhra Pradesh Road Transport Corporation. Their sample consists of considered23 depots providing four categories of services:

(1) inter-district services;

(2) intra-district services;

(3) inter rural services; and

(4) inter-state services.

Empirical findings show that Adilabad and Srikakulam depots were inefficient withrespect to all the four categories of services. Rangareddy depot with an efficiency scoreof 0.8146 had the lowest efficiency score across all the four categories of services.

Agarwal et al. (2009) examined TFP growth of 34 SRTUs for the period 1989-1990 to2000-2007 using DEA-based MPI. They found that on average, the TFP changeis 1.9 percent per annum over the sample time period. Also no significant changein technical efficiency but a remarkable technical progress has been noticed.

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Regarding determinants of TFP growth, the results reveal that change in employee-busratio, change in depreciation cost, change in total earnings and change in total cost,turn out to be the most significant variables in having impact on the change inproductivity. Using DEA, Bhagavath (2009) examined the technical efficiency of44 SRTUs operating during the year 2000-2001. It has been found that:

. only eight out of 44 SRTUs are scale efficient;

. average overall and pure technical efficiencies are 89.4 and 83.4 percent,respectively;

. average SE is 93.4 percent; and

. SRTUs working as companies are found to be relatively more efficient thanothers.

Agrawal (2009) analysed the trends of technical and scale efficiencies of 29 SRTUs forthe years 2004-2005 to 2007-2008. The efficiency scores are calculated by applying anew slack DEA model with categorical DMUs. The results of DEA models confirm thatperformance of the SRTUs has not improved over the earlier three years and hasimprovement in the last year but still very far from the optimal level. Using DEA,Nagadevara and Ramanayya (2010) analyzed inter-temporal variations in efficiencyof 25 depots of Karnatka SRTC over the period 2004-2005 to 2008-2009. They foundthat 11 depots remained on the efficiency frontier for all the five year under study.The depots, namely Mangalore-1, Arasikere and Kolar started off on the efficiencyfrontier, have lost their edge and became relatively inefficient. The largest drop inefficiency is seen in the Kolar depot.

In sum, the careful screening of the available literature on bus transport sector inIndia reveals that a scant literature appears in Indian context relating to the efficiencyof SRTUs that applied DEA to evaluate technical efficiency of this sector. Thus, thepresent study is intended to enrich the literature concerning the operational efficiencyof SRTUs and the factors explaining it using a two-stage DEA procedure. At firststage, DEA has been used to obtain the diverse measures of efficiency, whereas thesecond stage utilized Tobit analysis to know the significant factors influencing thesemeasures of efficiency.

4. Methodological framework4.1 Measurement of overall, technical, pure technical and scale efficiencies: CCR andBCC DEA modelsThe methodology used in this study is an extension upon the Farrell’s (1957) work byCharnes et al. (1978), which they coined it as DEA. DEA floats a piecewise linear surfaceto the rest on top of the observations (Seiford and Thrall, 1990). The DMUs that lie on thefrontier are the best practice institutions and retain a value of one. Those DMUsenveloped by the extremal surface are scaled against a convex combination of theDMUs on the frontier facet closest to it and have values somewhere between 0 and 1.Several different mathematical programming DEA models have been proposed in theliterature (see Charnes et al. (1994) for details). In the present study, we have used theinput-oriented CCR model named after Charnes et al. (1978), to get a scalar measure ofOTE. We also applied the input-oriented BCC model named after Banker et al. (1984),to obtain the PTE (also known as managerial efficiency). Formal notations of used

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input-oriented[1] CCR and BCC DEA models for measuring efficiency scores for DMU o,under the different scale assumptions are as follows:

ðiÞuo;l1;l2; ... ;ln;s

2i;sþr

min TEo ¼ uo 2 1Xmi¼1

s2iþXsr¼1

sþr

!

subject to

ðiiÞXnj¼1

ljxij þ s2i¼ uoxio

ðiiiÞXnj¼1

ljyrj 2 sþr¼ yro

ðivÞ s2i; sþ

r$ 0 ði ¼ 1; . . . ;m; r ¼ 1; . . . ; sÞ

ðvÞ lj $ 0; if constant returns 2 to 2 scale

ðviÞXnj¼1

lj ¼ 1; if variable returns 2 to 2 scale

9>>>>>>>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>>>>>>>;

ð1Þ

where:

xio ¼ amount of input i used by DMU o.

yro ¼ amount of output r used by DMU o.

m ¼ the number of outputs.

s ¼ the number of inputs.

n ¼ the number of DMUs.

1 ¼ a small positive number.

The solution to problem (1) is interpreted as the largest contraction of DMU o’s input thatcan be carried out, given that DMU o will stay within the reference technology.The restrictions (ii) and (iii) form the convex reference technology. The restriction (iv)restricts the input slack (s2i ) and output slack (sþr ) variables to be non-negative.The restriction (v) limits the intensity variables to be non-negative. The model involving(i)-(v) is known as envelopment form of CCR model and provides Farrell’s input-orientedTE measure under the assumption of constant returns-to-scale (CRS). The measure ofefficiency provided by CCR model is known as OTE and denoted as uCCRo . The lastrestriction imposes variable returns-to-scale assumption on the reference technology.The model involving (i)-(vi) is known as BCC model and provides Farrell’s input-orientedTE measure under the assumption of variable returns-to-scale. The measure ofefficiency provided by BCC model is known as PTE and denoted as uBCC

o .The CCR and BCC models need to be solved n times, once for each DMU to obtain

the optimal values for uo; l1; l2; . . . ; ln; s2i ; s

þr (i.e. u*o ; l

*1 ; l

*2 ; . . . ; l

*n ; s

2*

i ; sþ*

r ).The interpretation of the results of above models can be summarized as:

. If u*o ¼ 1, then DMU under evaluation is a frontier point, i.e. there is no otherDMUs that are operating more efficiently than this DMU. Otherwise, if u*o , 1,

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then the DMU under evaluation is inefficient, i.e. this DMU can either increaseits output levels or decrease its input levels.

. The left-hand side of the constraints (ii) and (iii) is called the “reference set”, andthe right-hand side represents a specific DMU under evaluation. The non-zerooptimal l*j represents the benchmarks for a specific DMU under evaluation.The reference set provides coefficients (l*j ) to define hypothetical efficient DMU.

. The efficient targets for inputs and outputs can be obtained as xio ¼ u*o xio 2 s2*

iand yro ¼ yro þ sþ

*r , respectively. These efficiency targets show how inputs can

be decreased and outputs increased to make the DMU under evaluation efficient.

The ratio (uCCRo /uBCCo ) provides a measure of SE. Note that all aforementioned efficiencymeasures are bounded between one and zero. The measure of SE does not indicatewhether the DMU in question is operating in the area of increasing or decreasingreturns-to-scale (DRS). The nature of returns-to-scale can be determined from themagnitude of optimal

Pnj¼1l

*j in the CCR model (Banker et al., 1984). Seiford and

Zhu (1999) listed the following three cases:

(1) IfPn

j¼1l*j ¼ 1 in any alternate optima, then CRS prevail on DMU o.

(2) IfPn

j¼1l*j , 1 in any alternate optima, then IRS prevail on DMU o.

(3) IfPn

j¼1l*j . 1 in any alternate optima, then DRS prevail on DMU o.

4.2 Ranking of DMUs: Andersen and Petersen’s super-efficiency DEA modelIt is significant to note that all efficient DMUs have the same efficiency scores equal to 1in the CCR model. Therefore, it is impossible to rank or differentiate the efficient DMUswith the CCR model. However, the ability to rank or differentiate the efficient DMUs is ofboth theoretical and practical importance. Theoretically, the inability to differentiate theefficient DMUs creates a spiked distribution at efficiency scores of 1. This poses analyticdifficulties to any post-DEA statistical inference analysis. In practice, furtherdiscrimination across the efficient DMUs is also desirable to identify ace performers.For getting strict a ranking among efficient DMUs, Andersen and Petersen (1993)proposed the super-efficiency DEA model. The core idea of super-efficiency DEA modelis to exclude the DMU under evaluation from the reference set. This allows a DMU to belocated on the efficient frontier, i.e. to be super-efficient. Therefore, the super-efficiencyscore for efficient DMU can, in principle, take any value greater than or equal to 1.This procedure makes the ranking of efficient DMUs possible (i.e. the higher thesuper-efficiency score implies higher rank). However, the inefficient units which are noton the efficient frontier, and with an initial DEA score of less than 1, would find theirrelative efficiency score unaffected by their exclusion from the reference set of DMUs.

In the super-efficiency DEA model, when the linear programme (LP) is run forestimating the efficiency score of DMU o, the DMU o cannot form part of its referencefrontier, and hence if it was a fully efficient unit in the original standard DEA model(like CCR model in the present study) it may now have efficiency score greater than 1.This LP is required to be run for each of the n DMUs in the sample, and in each of theseLPs, the reference set involves n 2 1 DMUs. In particular, Andersen and Petersen’smodel for estimating super-efficiency score for DMU o (denoted by TEsuper

o ) can beoutlined as below:

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623

usupero ;l;s2

i;sþr

min TE supero ¼ u super

o 2 1Xmi¼1

s2i þXsr¼1

sþr

!

subject toXnj ¼ 1

j – o

ljyrj 2 sþr ¼ yrk r ¼ 1; 2; . . . ; s

Xnj ¼ 1

j – o

ljxij þ s2i ¼ usuperk xik i ¼ 1; 2; . . . ;m

s2i ; sþr $ 0

ljð j – oÞ $ 0 j ¼ 1; 2; . . . ; n

9>>>>>>>>>>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>>>>>>>>>>;

ð2Þ

Besides, providing the ranks to efficient DMUs, the results of super-efficiency DEAmodel can be used in sensitivity testing and identification of outliers (Coelli et al., 2005;Avkiran, 2006).

5. Database, selection of variables and identification of outliersTo realize the underlined objectives of the study, we utilize the database provided bythe Research Wing of Ministry of Shipping, Road Transport and Highways,Government of India, New Delhi (March 2007). The study is confined to thecross-sectional data on input and output variables for the year 2006-2007. In the bustransport sector there is considerable disagreement among the researchers about whatconstitute in the input and output vectors. Table I provides different set of input andoutput variables used in the academic studies pertaining to efficiency measurement inthe Indian bus transport sector. In present study, we consider fleet size, total number ofstaff, and fuel and lubricants as input variables, and revenue bus per day andpassenger kilometers performed in a year are taken as output variables.

The key limitation of DEA is that the efficiency results are very sensitive to thepresence of outliers. To overcome this limitation of DEA methodology, we firstidentified outliers among the initial sample of 34 SRTUs based on the super-efficiencyscore obtained from Andersen-Petersen’s DEA model, and then applied CCR and BCCmodels to obtain OTE and PTE scores. According to Avkiran (2006), any DMU havingsuper-efficiency score above value of 2 may be considered as outlier in the sample.Table II provides the super-efficiency scores for identifying outliers in the sample. Ouranalysis evolves four different stages to identify the presence of outliers in the sample.In the first stage, we applied the super-efficiency model on 34 SRTUs, and noted thatthere were only two SRTUs, namely Meghalaya STC and TN STC (Villupuram) Ltd,having super-efficiency score greater than unity. The presence of only two SRTUsrepresents very poor discriminatory power of the model.

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S. no. Author (year) Approach Inputs Outputs

1 Ramanathan (1999) DEA 1. Fleet size Passenger-kilometers2. Total staff3. Fuel consumed in

kiloliters2 Singh (2000a, b, c) MIP 1. Number of buses held Passenger-kilometers

2. Total fuel (diesel)consumed

3. Number of employees3 Singh (2000d) TCF Number of employees Passenger-kilometers4 Jha and Singh (2000) SFA Number of employees Passenger-kilometers5 Singh and Venkatesh (2003) SFA 1. Labour Effective-bus kilometers

2. Number of buses held6 Karne and Venkatesh (2003) DEA and

MPI1. Staff Passenger-kilometers

2. Diesel3. Other material

7 Agrawal et al. (2006) DEA 1. Fleet size Revenue passenger-kilometers2. Total staff

3. Fuel consumed8 Anjaneyulu et al. (2006) DEA 1. Fleet size

2. Number of employees3. Annual material cost4. Fuel consumed

1. Annual vehiclekilometers

2. Annual passengerkilometers

3. Vehicle kilometers peraccident

9 Bishnoi and Sujata (2007) DEA 1. Fleet size Passenger-kilometers2. Total staff3. Fuel consumed

10 Nagadevara and Ramanayya(2008, 2010)

DEA 1. Cost of personnel 1. Vehicles utilization

2. Cost of fuel 2. Operating ratio3. Number of buses 3. Operating profits

4. Total earning5. Earning

per bus11 Agarwal et al. (2009) DEA and

MPI1. Fleet size Revenue passenger-

kilometers2. Total staff3. Fuel consumed

12 Agrawal (2009) DEA 1. Fleet size Passenger-kilometers2. Total staff3. Fuel consumed

13 Bhagavath (2009) DEA 1. Fleet size Revenue per bus per day2. Average kilometer

traveled per busper day

3. Cost per busper day

Notes: (1) SFA refers to stochastic frontier analysis; (2) DEA refers to data envelopment analysis;(3) MIP refers to multilateral index procedure; (4) TCF refers to translog cost frontier; and (5) MPIrefers to Malmquist productivity indexSource: Author’s elaboration

Table I.Input and output

variables in the selectedefficiency studies

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Further, Meghalaya STC with super-efficiency score of 4.347 appears to be clear outlierin accordance of the Avkiran’s criterion. Thus, we dropped Meghalaya STC from thesample with the objective to get reliable results and again calculated super-efficiencyscores for the remaining 33 SRTUs. With the deletion of Meghalaya STC, thediscriminatory power of the model improved, as indicated by the fact that number ofefficient SRTUs increased from 2 in stage 1 to 4 in stage 2. In stage 2, the KolhapurMTU appeared as an outlier with the super-efficiency score of 2.054, and therefore, weexcluded this SRTU in the next stage. In stage 3, we calculated the super-efficiencyscores for 32 SRTUs. We note that the power of discrimination further improved with5 SRTUs as efficiency against 4 SRTUs in stage 2. However, Tripura RTC withsuper-efficiency score equal to 2.424 emerged as an outlier. Hence, we excluded Tripura

SRTUs Stage 1 Stage 2 Stage 3 Stage 4

Andhra Pradesh SRTC 0.752 0.752 0.752 0.752Bihar STC 0.500 0.534 0.534 0.547Calcutta STC 0.449 0.461 0.461 0.465Delhi TC 0.820 0.820 0.820 0.820Gujarat SRTC 0.557 0.557 0.557 0.557Himachal RTC 0.655 0.664 0.664 0.666Karnataka SRTC 0.778 0.778 0.778 0.778Kerala SRTC 0.689 0.689 0.689 0.689Maharashtra SRTC 0.464 0.464 0.464 0.464Meghalaya STC 4.347 Dropped Dropped DroppedNorth Bengal STC 0.458 0.475 0.475 0.480Orissa SRTC 0.840 0.851 1.334 1.334Rajasthan SRTC 0.735 0.735 0.735 0.735Tripura RTC 0.733 1.442 2.424 DroppedUttar Pradesh SRTC 0.727 0.727 0.727 0.727North West Karnataka RTC 0.718 0.718 0.718 0.718Banglore Metropolitan TC 0.860 0.861 0.861 0.861North Eastern Karnataka RTC 0.895 0.902 0.902 0.905Metro TC (Chennai) Ltd 0.816 0.819 0.819 0.820State Exp.TC (TN Dvn) Ltd 0.930 0.970 1.047 1.047TN STC (Coimbtore Dvn) Ltd 0.915 0.915 0.915 0.915TN STC (Kumbakonam) Ltd 0.959 0.959 0.959 0.959TN STC (Madurai) Ltd 0.981 0.981 0.981 0.981TN STC (Salem) Ltd 0.944 0.945 0.945 0.945TN STC (Villupuram) Ltd 1.154 1.154 1.154 1.154Kadamba TCL 0.537 0.615 0.674 0.724Chandigarh TU 0.992 1.079 1.232 1.277Haryana ST 0.688 0.691 0.691 0.693Punjab roadways 0.643 0.669 0.669 0.678Nagaland ST 0.117 0.494 0.552 1.289Ahmedabad MTS 0.555 0.595 0.595 0.604BEST undertaking 0.475 0.482 0.482 0.485Kolhapur MTU 0.979 2.054 Dropped DroppedPimpri Chinchwad MT 0.471 0.611 0.695 0.958Average efficiency 0.827 0.802 0.822 0.807Number of efficient SRTUs 2 4 5 5

Source: Author’s calculations

Table II.Identification ofoutliers SRTUs

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RTC from the analysis in stage 4. The analysis of super-efficiency scores pertaining tostage 4 reveals that none of the 31 SRTUs are extreme (i.e. outlier) since all the efficientSRTUs have super-efficiency scores less than 2. Therefore, we terminate our process ofidentification of outliers at stage 4. Thus, our final sample after excluding outliersincludes 31 SRTUs.

6. Results and discussionThis section provides the empirical results obtained from input-oriented CCR andBCC and super-efficiency DEA models. The results of Tobit regression analysis toexplore the root cause of inefficiency in the operations of SRTUs, have also beenpresented. It is significant to note that input-oriented efficiency measures give theextent of inputs which can be proportionately reduced by keeping output unchanged.Given efficiency scores, the amount of inefficiency can be obtained as:Inefficiency ð%Þ ¼ ð1 2 efficiency scoreÞ £ 100. Column 2 of Table III provides theOTE scores for 31 SRTUs. We note that there exists wide variations in the level of OTEacross SRTUs, which varies between 46.4 and 100 percent. The average of OTE scoresturned out to be 0.772, indicating that the magnitude of overall technical inefficiency(OTIE) is to the tune of 22.8 percent (see Table IV for the descriptive statistics ofvarious efficiency measures). This suggests that by adopting best practices, SRTUscan, on an average, reduce their inputs of fleet size, total number of staff, and fuel andlubricants by at least 22.8 percent, and still produce the same level of outputs.However, the potential reduction in inputs from adopting best-practice technologyvaries among different SRTUs.

Recall that the SRTU with OTE score equal to 1 is deemed to be efficient andrepresent a point on the efficient frontier. Of the 31 SRTUs, five SRTUs are found to betechnically efficient since they have OTE score of 1. These SRTUs together define thebest-practice or efficient frontier, and thus form the reference set for inefficient SRTUs.The resource utilization process in these SRTUs is functioning well. It means that theproduction process of these SRTUs is not characterizing any waste of inputs. In DEAterminology, these SRTUs are called peers and set an example of good operatingpractices for inefficient SRTUs to emulate in their derive to reduce the inefficiency inproduction operations. The efficient SRTUs are Orissa SRTC, State Exp. TC (TN Dvn.),TN STC (Villupram) Ltd, Chandigarh TU and Nagaland ST (Table III).

From the Table III, we further note that the remaining 26 SRTUs are relativelyinefficient with OTE score less than 1. The results indicate a presence of markeddeviations of the SRTUs from the best-practice frontier. These inefficient SRTUs canimprove their efficiency by reducing inputs. OTE scores among the inefficient SRTUsrange from 0.464 for Maharashtra SRTC to 0.981 for TN STC (Madurai) Ltd Thisfinding implies that Maharashtra SRTC and TN STC (Madurai) Ltd can potentiallyreduced their inputs 53.6 percent and 1.9 percent, respectively, while leaving theiroutput levels unchanged. This interpretation of OTE score can be extended for otherinefficient SRTUs in the sample. On the whole, we observed that OTIE levels rangefrom 1.9 to 53.6 percent among inefficient SRTUs.

6.1 Discrimination of efficient SRTUsTable III also provides the super efficiency scores and ranks of 31 SRTUs onthe basis of super-efficiency scores (see columns 4 and 6). It is important to note

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that for inefficient SRTUs, the OTE and super-efficiency scores are identical. It hasbeen observed that among five efficient SRTUs, Orissa SRTC scored the highestsuper-efficiency score (1.334), and thus attained first rank. On the basis of such a highrank, we can regard Orissa SRTU as a global leader of public passenger transportindustry in India. The second and third ranks were attained by Nagaland ST andChandigarh TU with super-efficiency scores of 1.289 and 1.277, respectively. With thesuper-efficiency scores of 1.154 and 1.047, the TN STC (Villupram) Ltd and State Exp.TC (TN Dvn.) Ltd placed at fourth and fifth positions, respectively.

SRTUsOTE

(u CCR)PTE

(u BCC)SE

( ¼ (u CCR)/(uBCC))Super efficiency

scores RTS Ranks1 2 3 4 5 6 7

Andhra Pradesh SRTC 0.752 1.000 0.752 0.752 Decreasing 16Bihar STC 0.547 0.606 0.903 0.547 Increasing 27Calcutta STC 0.465 0.518 0.899 0.465 Increasing 30Delhi S TC 0.820 0.830 0.988 0.820 Increasing 14Gujarat SRTC 0.557 0.586 0.949 0.557 Decreasing 26Himachal RTC 0.666 0.677 0.984 0.666 Increasing 24Karnataka SRTC 0.778 0.783 0.994 0.778 Decreasing 15Kerela SRTC 0.689 0.690 0.998 0.689 Increasing 22Maharashtra SRTC 0.464 0.634 0.732 0.464 Decreasing 31North Bengal STC 0.480 0.565 0.851 0.480 Increasing 29Orissa SRTC 1.000 1.000 1.000 1.334 Constant 1Rajasthan SRTC 0.735 0.738 0.996 0.735 Increasing 17Uttar Pradesh SRTC 0.727 0.740 0.983 0.727 Decreasing 18North Best Karnataka RTC 0.718 0.723 0.993 0.718 Increasing 20Banglore Metropolitan TC 0.861 0.867 0.994 0.861 Increasing 12North Eastern KarnatakaRTC 0.905 0.914 0.990 0.905 Increasing 11Metro TC. (Chennai) Ltd 0.820 0.826 0.993 0.820 Increasing 13State Exp. TC (TN Dvn) Ltd 1.000 1.000 1.000 1.047 Constant 5TN STC (Coimbtore Dvn)Ltd 0.915 0.917 0.998 0.915 Increasing 10TN STC (Kumbakonam) Ltd 0.959 0.961 0.998 0.959 Increasing 7TN STC (Madurai) Ltd 0.981 1.000 0.981 0.981 Decreasing 6TN STC (Salem) Ltd 0.945 0.969 0.975 0.945 Decreasing 9TN STC (Villupuram) Ltd 1.000 1.000 1.000 1.154 Constant 4Kadamba TCL 0.724 0.735 0.986 0.724 Increasing 19Chandigarh TU 1.000 1.000 1.000 1.277 Constant 3Haryana ST 0.693 0.694 0.998 0.693 Increasing 21Punjab roadways 0.678 0.710 0.955 0.678 Increasing 23Nagland ST 1.000 1.000 1.000 1.289 Constant 2Ahmedbad MTS 0.604 0.652 0.927 0.604 Increasing 25BEST undertaking 0.485 0.545 0.889 0.485 Decreasing 28Pimpri Chinchwad MT 0.958 0.969 0.990 0.958 Decreasing 8

Notes: OTE refers to overall technical efficiency; PTE refers to pure technical efficiency; SE refers toscale efficiency; RTS refers to returns-to-scale; super efficiency scores calculated using CCRtechnologySource: Author’s calculations

Table III.OTE, PTE, SE,super efficiency scoresand RTS in SRTUs

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6.2 Discrimination of inefficient SRTUsBesides, discriminating the efficient SRTUs, we also made an attempt to separate outthe 26 inefficient SRTUs. For this, we utilized the quartile values of OTE scoresobtained from CCR model as three cut-off points to segregate the inefficient SRTUs intofour distinct categories: category I (highly inefficient), category II (below average),category III (above average), and category IV (marginally inefficient) (see Table IV forthese quartile values). Among these categories, the SRTUs belonging to “mostinefficient” and “marginally inefficient” category require special attention. In the “mostinefficient” category, those SRTUs have been included which attained OTE scorebelow the first quartile value. The candidates of this group are worst performers in thesample. It is significant to note that these SRTUs lack vitality in terms of the efficiencyof resource utilization. The Bihar STC, Calcutta STC, Gujarat STC, Himachal RTC,Maharashtra SRTC, North Bengal STC, Ahmadabad MTS and BEST undertaking fallin this category (Table V).

The SRTUs that have attained OTE score above the third quartile value but lessthan 1 are included in “marginally inefficient” category. TN STC (Kumbakonam) andTN STC (Madurai) Ltd, lie in this category. It is worth mentioning here that theseSRTUs are operating at a high level of operating efficiency even though they are notfully efficient. In fact, these SRTUs are marginally inefficient and operating very closeto the efficient frontier. Further, these SRTUs can attain the status of efficient SRTUsby bringing little improvements in the resource utilization process. In fact, theseSRTUs can be considered as “would be champions”. Therefore, the regulators mustpay a special attention to enhance their efficiency.

6.3 Decomposition of OTE: PTE and SEIt should be noted that OTE measure helps to measure combined inefficiency that isdue to both pure technical inefficiency (PTIE) and inefficiency due to inappropriatescale size, i.e. scale inefficiency (SIE). However, in contrast to OTE measure, the PTEmeasure derived from BCC model under assumption of variable returns to scale devoidof the scale effects. Thus, the PTE scores provide that all the inefficiencies directlyresult from managerial underperformance (i.e. managerial inefficiency) in organizingthe inputs. It is significant to note that PTE scores are greater than or equal to OTEscores because BCC model forms a convex hull of intersecting planes which envelopsthe data points more tightly than CRS conical hull. In DEA literature, the DMUsattaining OTE scores equal to 1 are known as “globally efficient”. However, the DMUswith PTE ¼ 1 and OTE – 1 are called “locally efficient”.

Descriptive statistics n OTE PTE SE

Mean 31 0.772 0.802 0.958SD 31 0.181 0.163 0.070Quartile 1 31 0.666 0.677 0.949Quartile 2 (median) 31 0.752 0.783 0.990Quartile 3 31 0.958 0.969 0.998Maximum 31 1.000 1.000 1.000Minimum 31 0.464 0.518 0.732

Source: Author’s calculations

Table IV.Descriptive statistics

of efficiency scoresfor SRTUs

SRTUs: technicalefficiency

629

Table III also provides the PTE and SE scores for individual SRTUs. It has beenobserved that 7 SRTUs acquired the status of “locally efficient” because they attainedthe PTE score equal to 1. Among these seven SRTUs, the 5 are “globally efficient” withOTE score equal to 1. Further, for two SRTUs, namely Andhra Pradesh SRTC and TNSTC (Madurai) Ltd that are locally efficient but globally inefficient under CRSassumption, we can infer that OTIE in these SRTUs is not caused by poor inpututilization (i.e. managerial inefficiency), but rather is due to operation of theseundertakings at inappropriate scale size. It has been further noticed that in theremaining 24 SRTUs (having PTE , 1) managerial inefficiency exists, albeit ofdifferent magnitude. In these SRTUs, OTIE stems from both PTIE and SIE asindicated by the fact that these SRTUs have both PTE and SE scores less than 1. Out ofthese 24 SRTUs, 12 SRTUs have PTE score less than SE score. This indicates thatthe inefficiency in resource utilization (i.e. OTIE) in these 12 SRTUs is primarilyattributed to the managerial inefficiency rather than to the SIE.

Turning to the analysis of PTE and SE measures for the sample as a whole,we observed that OTIE in Indian state road transportation industry is due to both poorinput utilization (i.e. PTIE), and failure to operate at most productive scale size (MPSS)(i.e. SIE). The average PTE score for 31 SRTUs has been observed to be 0.802(see Table IV for descriptive statistics of OTE, PTE, and SE scores). This implies that19.8 percentage points of the about 22.8 percent of OTIE is due to the managers ofthese undertakings who are not following appropriate management practices andselecting incorrect input combinations. The rest of OTIE appears due to inappropriate

Highly inefficient(OTE # Q1)

Below average(Q1 , OTE # Q2)

Above average(Q2 , TE # Q3)

Marginallyinefficient(OTE . Q3)

(I) Bihar STC (27) (I) Andhra PradeshSRTC (16)

(I) Karnataka SRTC (15) (I) TN STC(Kumbakonam)(7)

(II) Calcutta STC (30) (II) Kerela SRTC (22) (II) BengloreMetropolitanTC (12)

(II) TN STC(Madurai) Ltd (6)

(III) Gujarat STC (26) (III) RajasthanSRTC (17)

(III) North EastrenKarnatakaRTC (11)

(IV) Himachal RTC (24) (IV) Uttar PradeshSRTC (18)

(IV) Metro TC.(Chennai) Ltd (13)

(V) Maharashtra SRTC (31) (V) North WestKarnataka SRTC (20)

(V) TN STC (CoimbtoreDvn.) Ltd (10)

(VI) North Bengal STC (29) (VI) KadambaTCL (19)

(VI) TN STC (Salem)Ltd (9)

(VII) Ahmedabad MTS (25) (VII) Haryana ST (21) (VII) Pimpri ChinchwadMT (8)

(VIII) BEST undertaking (28) (VIII) Punjab roadways(23)

(VIII) Delhi STC (14)

Note: Q1, Q2 and Q3 refer to first quartile, second quartile and third quartile, respectivelySource: Author’s calculations

Table V.Categorization ofinefficient SRTUs

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scale of operations in these undertakings. Further, lower mean and high standarddeviation of the PTE scores compared to the SE scores indicate that a greater portion ofOTIE is due to PTIE.

6.4 Returns-to-scaleIt is well acknowledge fact in theory of the firms that one of the basic objectives ofthe firms is to operate at MPSS, i.e. with CRS in order to minimize costs and maximizerevenue. In the short run, firms may operate in the zone of IRS or DRS. However, inthe long run, they will move towards CRS by becoming larger or smaller to survive inthe competitive market. The process may involve the changes of a firms’ operatingstrategy in terms of scaling up or scaling down of its size. The regulators may use thisinformation to determine whether the size of the representative firm in a particularindustry is appropriate or not. Recall that the existence of IRS or DRS can be identifiedby the sum of intensity variables in the CCR model. If

Pni¼1lj , 1, then the SIE

appears due to IRS. The implication of this is that the particular SRTU has sub-optimalscale size. On the other hand, if

Pni¼1lj . 1, then the SIE occurs due to DRS.

The connotation of this is that the SRTU has supra-optimal scale size. Table III alsoprovides the nature of returns-to-scale for individual SRTUs. The results indicate thatfive efficient SRTUs (i.e. 16 percent) are operating at MPSS and experiencing CRS.Further, 17 SRTUs (i.e. 55 percent) are operating below their optimal scale size, andthus experiencing IRS. The policy implication of this finding is that these SRTUs canenhance OTE by increasing their size. The remaining nine (i.e. 29 percent) SRTUs havebeen observed to be operating in the zone of DRS, and thus downsizing seems to be anappropriate strategic option for these SRTUs in their pursuit to reduce unit costs.On the whole, as the numbers of SRTUs which are operating at IRS are dominant in thetotal number of SRTUs in the sample, we can say that there is a further room tointroduce modern technology so as to improve the technical efficiency of these SRTUs.

6.5 Areas for efficiency improvement: targets setting analysisThe optimum solution of linear program (1) provides non-zero input and output slackscorresponding to input and output constraints. It is important to note that slacks existonly for those SRTUs that are identified as inefficient in a particular DEA run. Theseslacks provide the vital information concerning to the areas which an inefficient SRTUneeds to improve upon in its drive towards attaining the status of efficient one.Coelli et al. (2005) clearly pointed out that both the Farrell’s measure of operationalefficiency and any non-zero input and output slacks should be reported to provide anaccurate indication of technical efficiency of a firm in a DEA analysis. Thus, the slacksshould be interpreted along with the efficiency scores. However, slacks represent onlythe left-over portions of inefficiencies after proportional reductions in inputs or outputs.If a DMU cannot reach the efficient frontier (to its efficient target), slacks are needed topush the DMU to the frontier (target) (Ozcan, 2008). The presence of non-zero slacks fora DMU implies that the DMU under scrutiny can improve beyond the level implied bythe estimate of technical efficiency ( Jacobs et al., 2006). In the input-oriented DEAmodel, the input-slack represents the excess input and output slack indicates theoutput which is under produced (Avkiran, 1999; Ozcan, 2008).

For getting the more focused diagnostic information about the sources of inefficiencyfor each SRTU with respect to the input and output variables, we computed target values

SRTUs: technicalefficiency

631

of these variables at SRTU level using OTE scores, optimum values of slacks and actualvalues of the variables. The target point ðx *; y *Þ is defined by the following formulae:

x*io ¼ u*k xio 2 s2*

i i ¼ 1; 2; . . . ;m

y*ro ¼ yro þ sþ*

r r ¼ 12; . . . ; s:

9=; ð3Þ

where x*io ¼ the target input i for oth SRTU, y*ro ¼ target output r for oth SRTU;xio ¼ actual input i for oth SRTU; yro ¼ actual output r for oth SRTU; u*o ¼ efficiencyscore of the oth SRTU o; s2

*

i ¼ optimal input slacks; and sþ*

r ¼ optimal output slacks.Input slack(s) indicates the need for further reductions in corresponding input(s). Outputslack(s) signals any additional output(s) which could be produced by the efficient levelsof inputs. The difference between the observed value and target value of inputs(xio 2 x*io) represents the quantity of inputs to be reduced, while the difference betweenthe target values and observed values of outputs ðy*ro 2 yroÞ represents the amount ofoutputs to be increased, to move the inefficient SRTU on the efficiency frontier.

Table VI provides the input and output slacks derived from CCR model for26 inefficient SRTUs. For interpreting the contents of the table, consider the case of asingle SRTU, say, the worst inefficient Maharashtra SRTC. The OTE score ofMaharashtra SRTC is 0.464, implying that the Maharashtra SRTC could becometechnically efficient (under the Farrell’s definition) provided if all of its inputs areproportionally reduced by 53.6 percent (i.e. (1-OTE score) £ 100). However, even withthis required proportional reduction in all inputs, this SRTU would not bePareto-efficient, as it would be operating on the vertical section of the efficient frontier.In order to project this SRTU to a Pareto-efficient point, some further slackadjustments are necessary because non-zero input and output slacks appear for thisSRTU. Ultimately, Maharashtra SRTC has to make three adjustments in order tooperate at the efficient frontier. First, it has to reduce all inputs by 53.6 percent. Second,it has to reduce average fleet size by 64.8 percent, staff strength by 62.1 percent, andfuel and lubricants by 53.6 percent. Third, it has to augment revenue bus per day by151.9 percent. The first type of adjustment is known as radial adjustment, while secondand third types of adjustments are known as the slack adjustments. The similarexplanation can be extended for other inefficient SRTUs.

We have also observed that on average, approximately 48.4 percent of average fleetheld, 43.2 staff strength and 28 percent of fuel and lubricants could be theoreticallyreduced if all the inefficient SRTUs operate at the same level as the best practiceSRTUs (i.e. efficient SRTUs). It is observed that on an average, the SRTUs can generatemore revenue bus per day by approximately 31.01 percent and there is no possibility ofimprovement in the addition of passenger kilometers performed. However, there areconsiderable variations in saving in inputs and addition in outputs among inefficientSRTUs.

6.6 Robustness of DEA results: Jack-knifing analysisTo investigate the robustness of DEA results in terms of stability of reference set, wefollowed Myrtveit and Stensurd (1999), Mostafa (2007a, b) and performed a procedureknown as Jack-knifing. For this, we dropped all the efficient SRTUs one by one andstudied the impact of their removal on the average TE and composition of reference set.Since we have five efficient SRTUs, in our original DEA analysis, we ran five

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un

jab

road

way

s3,

282.

725

,483

.737

3.5

2,28

0.2

3,22

0.6

0.0

071

.574

.532

.2A

hm

edb

adM

TS

3,05

9.0

15,4

30.2

262.

01,

493.

22,

052.

10.

00

61.8

61.9

39.6

BE

ST

un

der

tak

ing

6,86

6.9

101,

238.

01,

277.

28,

410.

112

,206

.20.

00

62.3

75.5

51.5

Pim

pri

Ch

inch

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MT

2,66

9.2

4,67

2.0

276.

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41,

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00

4.2

29.1

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Av

erag

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876.

115

5,95

6.5

1,81

9.6

12,5

11.8

18,4

11.6

31.0

048

.443

.228

.0

Notes:

Y1

–re

ven

ue

bu

sd

ay;

Y2

–p

asse

ng

er-k

ilom

eter

sp

erfo

rmed

;X

1–

flee

tsi

ze;

X2

–st

aff;

X3

–fu

elan

dlu

bri

can

tsSource:

Au

thor

’sca

lcu

lati

ons

Table VI.Target values of outputand input variables andaddition in outputs and

savings in inputs

SRTUs: technicalefficiency

633

additional DEA analyses. From Table VII, we observed that none of the efficientundertaking observed in the post-DEA analysis extreme because its removal did notbring any significant change in average OTE of SRTUs in India. Further, thecomposition of reference sets in these DEA runs did not show any drastic change.On the whole, we note that our DEA results are quit robust.

6.7 Appropriateness of selected input and output variables: a sensitivity analysisIt is well known fact that in DEA, the distribution of efficiency scores is very sensitiveto the choice of input and output vectors. Thus, the selection of input and outputvariables for the DEA study requires a careful thought as the distribution of efficiencyscores and rank order of DMUs are likely to be affected by the selection of variablesand their number. Therefore, we checked whether our choice of inputs and outputs inthe above used baseline model (so called model I) is appropriate and yields robustinferences. For this purpose, we carried out a sensitivity analysis by considering twoadditional models, namely models II and III, with different input and output vectors.In case of model II, the output vector includes the same variables that included in themodel I, and the input vector contains two distinct input variables:

(1) operating expenses; and

(2) non-operating expenses.

On the other hand, in case of model III, the input vector contains the same input variablesthat are included in model I and the output vector includes the three variables:

(1) revenue bus per day;

(2) passenger kilometers; and

(3) vehicle kilometers.

In all cases, we applied CCR and BCC models for computing efficiency scores. In thepresent sensitivity analysis, we have adopted Chen and Yeh’s (1999) criteria to reject aparticular model in favour of model I. Accordingly, model I is preferable when:

Efficient SRTUs removed Mean OTE Reference set

Orissa SRTC 0.767 State Exp. TC (TN Dvn) Ltd, TN STC (Villupuram)Ltd, Chandigarh TU, Nagaland ST, PimpriChinchwad MT

State Exp. TC (TN Dvn) Ltd 0.764 Orissa SRTC, TN STC (Villupuram) Ltd, ChandigarhTU, Nagaland ST

TN STC (Villupuram) Ltd 0.792 Orissa SRTC, State Exp. TC (TN Dvn) Ltd, TN STC(Kumbakonam) Ltd, TN STC (Madurai) Ltd, TN STC(Salem) Ltd, Chandigarh TU and Nagaland ST

Chandigarh TU 0.788 Orissa SRTC, State Exp. TC (TN Dvn) Ltd, TN STC(Villupuram) Ltd, Nagaland ST

Nagaland ST 0.766 Orissa SRTC, State Exp. TC (TN Dvn) Ltd, TN STC(Villupuram) Ltd, Chandigarh TU and PimpriChinchwad MT

Source: Author’s calculationsTable VII.Jack-knifing analysis

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634

. correlation coefficient of efficiency scores of baseline model I with a specific caseis high because a high correlation indicates almost identical results provided bythe two cases; and/or

. there are larger number of efficient SRTUs in a specific case than model I sincetoo many efficient undertakings reduce the discrimination capability of theperformance evaluation results.

Table VIII reports the results of the sensitivity analysis.From Table VIII, we note that OTE and PTE scores of model I bear a very high and

statistically significant correlation with that obtained from models II and III. Further,the discrimination power of models II and III in terms of number of efficient SRTUs isnot drastically different from what has been observed in the case of modelI. Thus, we reject models II and III in favour of model I. In sum, we infer that our choiceof input and output variables is appropriate, and our aforementioned results arequite robust.

6.8 Explaining technical efficiency: Tobit analysisIt is apparent from above analysis that the efficiency estimates differ substantiallyacross different SRTUs. The inter-undertakings differences can sometimes beattributed to the differences in factors such as access to technology, structural rigidities(e.g. pattern of ownership), time lags to learn technology, differential incentive systems,level of profitability and organizational factors. Industrial economists and analystsare often interested in determining whether these differences are significant in astatistical sense. This can be done by using the regression analysis. Unfortunately, thesimple linear regression model encountered in most text-books is not appropriate herebecause the range of efficiency scores obtained from DEA model is censored, andtherefore a simple application of ordinary least squares estimation procedure mayproduce biased estimates if there is a significant position of the observations equal toone (Resende, 2000). In such cases, the appropriate regression model is known as aTobit or Censored regression model which handles data that is skewed and truncated(Avkiran, 1999). The standard Tobit model can be defined as follows for observation(SRTUs) i:

Model I Model II Model III

Correlation coefficients of OTE scoresModel I 1Model II 0.911 * 1Model III 0.999 * 0.908 * 1No. of efficient banks 5 3 5Correlation coefficients of PTE scoresModel I 1Model II 0.951 * 1Model III 1 * 0.950 * 1No. of efficient banks 7 7 7

Note: *Significant values at the level of significance a ¼ 0.050 (two-tailed test)Source: Author’s calculations

Table VIII.Sensitivity analysis

SRTUs: technicalefficiency

635

y*i ¼ bTxi þ 1i

yi ¼ y*i if y*i . 0; and

yi ¼ 0; otherwise;

9>>>=>>>;

ð4Þ

where 1i , N ð0;s 2Þ, xi and b are vectors of explanatory variables and unknownparameters, respectively. “T” denotes the matrix transpose operator. The y*i is a latentvariable and yi is the dependent variable. Following Loikkanen and Susiluoto (2002),the dependent variable yi is defined as 1–DEA efficiency score. The followinglikelihood function (L) needs to be maximized to solveb andsbased on 31 observations ofyi and xi is:

L ¼yi¼0

Yð1 2 FiÞ

yi.0

Y 1

ð2ps 2Þ1=2e2ð1=2s 2Þð yi2bTxiÞ

2

9=; ð5Þ

where:

Fi ¼

Z bTxi=s

21

1

ð2pÞ1=2e2ðt 2=2Þdt

The first product is over the observations for which the SRTU’s are 100 percentefficient ( y ¼ 0) and the second product is over the observations for which SRTUs areinefficient ( y . 0). Fi is the distribution function of the standard normal evaluated atbTxi=s. It is possible to estimate the unknown parameter vector b in the Tobit modelin several ways. In this paper, we use the econometric software package EViewsVersion 5.0 to estimate the parameters using the method of maximum likelihood.

The explanatory variables that have been used to explain technical inefficiency are:. fleet utilization (FU);. staff productivity (SP);. vehicle productivity (VP);. fuel efficiency (FE); and. occupancy ratio (OR).

However, FU can be defined as the ratio of the buses on the road to the average fleet heldby an undertaking. The variable “SP” is measured by the average revenue earningskilometer performed per worker per day. Further, “VP” is the average number of revenueearnings per kilometer performed by a bus per day. The variable “FE” reflects theaverage kilometer per liter of fuel. The explanatory variable “OR” is computed asthe passenger kilometers performed to passenger kilometer offered. We estimated thefollowing left-censored Tobit regressions for OTE, PTE and SE scores separately:

1 2 OTEi ðor 1 2 PTEi or 1 2 SEiÞ ¼ b0 þ b1FUi þ b2SPi þ b3VPi

þ b4FEi þ b5ORi þ 1i ð6Þ

Thus, three censored regressions with OTIE, PTIE, SIE as dependant variables havebeen estimated using the aforementioned independent variables.

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636

It has been observed that in the all the regression equations, the signs of the estimatedcoefficients are in consonance of a priori expectations. Visualization of Table IXdiscloses the facts that variable OR has significantly negatively affected the overalland pure technical inefficiencies of sample SRTUs. Moreover, the coefficients of theremaining four independent variables although satisfy a priori expectations,but observed to be statistically insignificant. On the other hand, the variables SP andOR found to be bearing a positive and statistically significant impact on SE. Further,the coefficients of remaining three variables causing SIE have been observed to bestatistically insignificant. The direct connotation of these results is that OR has asignificant impact on OTE, PTE and SE, implying that higher the OR leads to higheroperational efficiency of SRTUs. In addition, higher levels of SP are needed to augmentthe SE levels of SRTUs in India.

7. ConclusionsThis paper endeavours to evaluate the extent of technical, pure technical, and scaleefficiencies in Indian public transport industry using cross-sectional data for 31 SRTUsoperating in the year 2006-2007. The empirical results indicate that the level of OTIE insample SRTUs is to the tune of 22.8 percent. The results suggest that by adopting the bestpractices, SRTUs, on an average, can reduce their inputs by at least 22.8 percent. Thus, thesample SRTUs are wasting about one-fourth of their resources in the productionoperations. Out of the 31 SRTUs, five SRTUs have been identified as relatively efficientwith OTE score equal to one. On the basis of super-efficiency scores, we note that OrissaSRTC is the industry leader. The analysis of decomposing OTIE reveals that managerialinefficiency (as captured by the PTIE) is relatively more dominant source of OTIE.We further note that majority of SRTUs are operating in the zone of IRS, and thusany expansion plan would enhance the efficiency of these undertakings.

From the target setting exercise, we observe that on an average, approximately48.4 percent of fleet held, 43.1 percent of staff strength, and 28 percent of fuel andlubricants could be theoretically reduced if all the inefficient SRTUs operate at the samelevel as the efficient SRTUs. Further, it has been observed that on an average, SRTUscan generate more revenue bus per day by approximately 31.01 percent. Thejack-knifing exercise ensures that our DEA results are quite robust. Sensitivity analysis

Measure of technical inefficiencyRegressor (parameter) OTIE p-values PTIE p-values SIE p-values

Constant (b1) 1.056684 0.0524 1.213662 0.0308 0.178851 0.4212FU (b2) 20.000246 0.9450 20.001440 0.6941 0.000107 0.9412SP (b3) 20.004122 0.3355 20.000198 0.9641 20.003638 * 0.0359VP (b4) 24.95 £ 1025 0.9400 20.000356 0.6036 0.000294 0.2659FE (b5) 0.015157 0.8483 20.040904 0.6159 0.039672 0.2151OR (b6) 20.010 * 0.006 20.009083 * 0.0130 20.003465 * 0.0199Log likelihood 7.898289 5.178825 32.67461Pseudo R 2 0.422586 0.346116 0.359957

Notes: (i) Figures in the parentheses are p values; (ii) *indicates that the coefficient is significant at5% level of significanceSource: Authors’ calculations

Table IX.Results of Tobit

regression analysis

SRTUs: technicalefficiency

637

provides that the choice of input and output variables is appropriate. On the basis of theresults obtained from Tobit regression analysis, we infer that the OR bears a positiverelationship with overall technical, pure technical and scale efficiencies, and thus higheroccupancy is needed to augment the operational efficiency of these undertakings.In addition, higher levels of SP can enhance the SE levels of these undertakings.

In sum, the empirical results suggest that there exists a substantial room forimproving the resource use efficiency of SRTUs operating in India. The efforts shouldbe made in improving the managerial competence of these operators. The managementof these undertakings should make every effort to reduce the cost of operations byoptimizing manpower cost, fuel, and spares. Further, managers of these undertakingsneed more autonomy in revising fares in tune with the periodic cost escalations. Alongwith using cost cutting measures, the efforts should also be made to augment revenueby optimal scheduling of buses, dynamic pricing, and strong control on revenueleakages. The fleet utilisation has to be increased to become scale efficient for the scaleinefficient undertakings. Further, efforts are required to be made in the direction ofreplacement of old buses and induction of modern buses for raising the efficiency.Above all, regular training should be imparted to the drivers and supporting staff forimproving the quality of service with the objective to augment the level of customersatisfaction, and to create consciousness among them for fuel conservation.

The future work could extend our research in various directions not considered inthis study. First, using the data over a longer period, one may perhaps analyze theinter-temporal variations in technical efficiency of these undertakings. Second, usingthe panel data, one may use MPI approach to analyze the TFP growth in the state roadtransport industry in India.

Note

1. Concerning the model’s orientation, Coelli and Perelman (1999) show that the choice oforientation does not significantly alter efficiency estimation results. The choice of theappropriate orientation is not as crucial as it is in the econometric estimation case and,in many instances, the choice of orientation will have only minor influences upon the scoresobtained.

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Further reading

Matas, A. and Raymond, J. (1998), “Technical characteristics and efficiency of urban buscompanies: the case of Spain”, Transportation, Vol. 25 No. 3, pp. 243-63.

Ramanathan, R. (2000), “A holistic approach to compare energy efficiencies of different transportmodes”, Energy Policy, Vol. 28 No. 11, pp. 743-7.

About the authorSunil Kumar has been an Associate Professor in Economics at Punjab School of Economics,Guru Nanak Dev University, Amritsar, Punjab, India since 1994. He received a mark ofdistinction for his MSc (Hons.) in Economics degree. He has also completed his MPhil and PhDdegrees from Punjab School of Economics. He has had more than two dozen research paperspublished in various journals including American Journal of Accounting and Finance,International Journal of Productivity and Performance Management, International Review ofEconomics, Global Business Review, Artha Vijnana: Indian Journal of Development Economics,The Indian Journal of Economics. He also wrote a research book entitled, Productivity and FactorSubstitution: Theory and Analysis. At present, three research scholars are working forPhD degree under his guidance. His professional memberships include the Indian Society ofRegional Science and Indian Economic Association. Sunil Kumar can be contacted at:sunil12eco@yahoo.com

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