The current issue and full text archive of this journal is available at www.emeraldinsight.com/1463-5771.htmBIJ18,5 State road transport undertakings in India: technical efﬁciency and its determinants616 Sunil 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 state road transport undertakings (SRTUs) operating in India but also to explore the most inﬂuential factors explaining 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 compute various efﬁciency scores for individual SRTUs. A censored Tobit analysis is conducted to see which factors 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 different magnitude; the extent of average overall technical inefﬁciency (OTIE) in these SRTUs is to the tune of 22.8 percent, indicating that the sample SRTUs are wasting about one-fourth of their resources in the production operations; managerial inefﬁciency (as captured by the pure technical inefﬁciency) is a relatively more dominant source of OTIE; and operation in the zone of increasing returns-to-scale is a common feature for most of the undertakings. The multivariate regression analysis using Tobit analysis highlights that the occupancy ratio is the most signiﬁcant determinant for all the efﬁciency measures, and bears a positive relationship with overall technical, pure technical and scale efﬁciencies. 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 corrective measures to improve efﬁciency by altering input-output mix. Originality/value – This paper provides more robust estimates of relative efﬁciency of the SRTUs 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. Introduction The 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 theBenchmarking: An International passenger mobility in diverse terrains throughout the country, and thus lay aJournal considerable impact on the life of masses. There is no doubt that an analysis of theVol. 18 No. 5, 2011pp. 616-643 sources and determinants of operational efﬁciency would be a valuable aid to the policyq Emerald Group Publishing Limited formulators in designing appropriate policies aiming to improve the overall health1463-5771DOI 10.1108/14635771111166794 and competitiveness of these undertakings. However, in Indian context, the analysis
of efﬁciency of SRTUs has not received considerable attention from the scholars, and SRTUs: technicalthere 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, efﬁciencyendeavours 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 its 617intrinsic 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 production technology with multiple inputs and outputs; . DEA is competent to investigate the changes in efﬁciency resulting from inputs saving, and can also assess whether the reasons for such changes are improvements 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 public sector 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 Andersen and 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 by adjusting their inputs and outputs; and
BIJ . explain the signiﬁcant factors affecting OTE, PTE and SE of SRTUs by using18,5 Tobit regression analysis. The remainder of the paper is structured as follows. Section 2 provides an overview of SRTUs in India. Section 3 reviews the relevant literature on the subject matter. Section 4 presents the DEA models used for efﬁciency measurement. The data used and issues618 of measurement of inputs and outputs are discussed in Section 5. The empirical results are presented in Section 6, and conclusions are drawn in the ﬁnal section. 2. SRTUs in India: an overview Prior to independence in 1947, the passenger road transport sector in India was dominated by the private players, and there was unhealthy competition amongst operators who concentrated on the more remunerative routes. A consensus, however, has emerged that controlled monopoly is the only answer to the evils of unhindered and selﬁsh competition. Following the recommendations of some high-powered committees set up in the 1930s, the Motor Vehicle Act of 1939 has been enacted with the purpose to regulate road transport on the basis of healthy competition in the industry itself. In the post-independence era, the idea of nationalization of passenger road transport gained momentum so as to provide as an affordable, safe and reliable passenger services to people. Eventually, the Road Transport Corporation Act of 1950 has been enacted with a clear objective to meet the social obligations. This paved the way of nationalization of state carriages in ﬁve states, namely Andhra Pradesh, Gujarat, Haryana, Maharashtra and Punjab. However, in the rest of the country such services have been provided both by the public and private sectors, but in varying degree. The government, therefore, became not only the regulator of the road transport but also an operator in some states exclusively and in others alongside several other small operators. Currently, bus transport services are 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 its operational 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 trafﬁc movement in India has grown by leaps and bounds. A signiﬁcant change in the share of bus 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 passenger movements and 60 percent of freight movements as compared to its estimated share of 20 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 are corporations formed under the Road Transport Act of 1950, eight are government companies which have been formed under the Companies Act of 1956, eight are government departments controlled by the state governments, and eight are municipal undertakings operating owned and controlled by municipal corporations. These SRTUs are operating with more than a hundred thousand of vehicles and eight hundred thousand of 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 operation have crossed 450 billion passenger-kms mark. These undertakings operate 1,200 million passenger kilometers and carrying 245 million passengers daily. These undertakings provide direct employment to 0.73 million people (Government of India, 2007).
In the Indian context, the SRTUs, over a period of time, have occupied a pivtol role by SRTUs: technicalvirtue of certain inherent advantages like its affordability, ﬂexibility, door-to-door efﬁciencyoperations, 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 objectives 619of 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 efﬁciency levels and growth; . on an average, small-sized SRTUs experienced higher level of productive efﬁciency than their larger counterparts; . by and large, Tamil Nadu SRTUs seem to be more productive than their counterparts operating in other states of the country; and . the distribution of ranks of SRTUs with respect to their productive efﬁciency levels has remained broadly unchanged over the years.
BIJ Singh (2000d) and Jha and Singh (2000) conﬁrmed the existence of U-shaped average18,5 cost curve in the nine SRTUs from the period for 1984-1985 to 1996-1997 with the aid of SFA. Again in this study, smaller SRTUs appear to be more efﬁcient than their larger counterparts. These studies suggested that a policy that aims to change the size distribution of the SRTUs will help in increasing the efﬁciency of the Indian bus transport industry. Singh and Venkatesh (2003) also applied SFA on the 23 SRTUs620 using the dataset for the year 2000-2001. It has been noted that average efﬁciency is to the tune of 84.22 percent, and the extent of inefﬁciency ranges between 1.01 and 43.85 percent. Karne and Venkatesh (2003) analyzed the TFP growth and technical efﬁciency in Maharashtra State Road Transport Corporation (MSRTC) using DEA-based Malmquist productivity index (MPI). They note that during the study period (1996-1997 to 2001-2002), there has been a marginal improvement in TFP by 1.1 percent. Also, there have been negligible improvements in technical efﬁciency as well 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 consistently inefﬁcient, and efﬁciency of 11 SRTUs found to be varying from year to year. Using cross-sectional data for the year 2002-2003, Agrawal et al. (2006) utilized DEA to examine technical efﬁciency of State Road Transport Corporation (SRTC) of Uttar Pradesh, the largest state of India. They observed the regional average OTE to the tune of 87.8 percent before sensitivity analysis, and 92.7 percent after sensitivity analysis. Furhter, the average PTE reported to the tune of 95.16 percent. Ray and Venkatesh (2007) have also applied DEA to analyze the effects of decentralization of the efﬁciency of SRTUs in India for the period 1990-2005, and reported mild increase in efﬁciency of the studied corporations after the decentralization. Bishnoi and Sujata (2007) utilized DEA to measure the extent of technical efﬁciency of 20 depots of Haryana SRTC in the year 2006-2007. The study reported average overall technical and pure technical scores to the tune of 90.2 and 94.3 percent, respectively. Also 18 depots found to be operating in the zone of increasing returns-to-scale (IRS). They recommended the reduction of total staff by 25.58 percent, fuel consumption by 9.25 percent and ﬂeet strength by 13.72 percent for the inefﬁcient depots. Nagadevara and Ramanayya (2008) used DEA to identify the inefﬁcient depots at the district level in Andhra Pradesh Road Transport Corporation. Their sample consists of considered 23 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 with respect to all the four categories of services. Rangareddy depot with an efﬁciency score of 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 to 2000-2007 using DEA-based MPI. They found that on average, the TFP change is 1.9 percent per annum over the sample time period. Also no signiﬁcant change in technical efﬁciency but a remarkable technical progress has been noticed.
Regarding determinants of TFP growth, the results reveal that change in employee-bus SRTUs: technicalratio, change in depreciation cost, change in total earnings and change in total cost, efﬁciencyturn 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, 621 respectively; . average SE is 93.4 percent; and . SRTUs working as companies are found to be relatively more efﬁcient than others.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
BIJ input-oriented CCR and BCC DEA models for measuring efﬁciency scores for DMU o, under the different scale assumptions are as follows:18,5 ! 9 Xm Xs > ðiÞ min 2 þ o ¼ uo 2 1 TE 2 si þ þ sr > > > > uo ;l1 ;l2 ; ... ;ln ;si ;sr > > i¼1 r¼1 > > > > subject to > >622 > > X n > > > > ðiiÞ 2 lj xij þ si ¼ uo xio > > > > j¼1 > > > = X n ð1Þ þ ðiiiÞ lj yrj 2 sr ¼ yro > > > > j¼1 > > > > 2 þ ðivÞ si ; sr $ 0 ði ¼ 1; . . . ; m; r ¼ 1; . . . ; sÞ > > > > > > ðvÞ lj $ 0; if constant returns 2 to 2 scale > > > > > > X n > > ðviÞ lj ¼ 1; if variable returns 2 to 2 scale > > > > ; j¼1 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 that can 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 (s2 ) and output slack (sþ ) variables to be non-negative. i r 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-oriented TE measure under the assumption of constant returns-to-scale (CRS). The measure of efﬁciency provided by CCR model is known as OTE and denoted as uCCR . The last o restriction 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-oriented TE measure under the assumption of variable returns-to-scale. The measure of BCC efﬁciency provided by BCC model is known as PTE and denoted as uo . 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 ; s2 ; sþ (i.e. u* ; l* ; l* ; . . . ; l* ; s2 ; sþ ). * * i r o 1 2 n i r The interpretation of the results of above models can be summarized as: . If u* ¼ 1, then DMU under evaluation is a frontier point, i.e. there is no other o DMUs that are operating more efﬁciently than this DMU. Otherwise, if u* , 1, o
then the DMU under evaluation is inefﬁcient, i.e. this DMU can either increase SRTUs: technical its output levels or decrease its input levels. efﬁciency . The left-hand side of the constraints (ii) and (iii) is called the “reference set”, and the right-hand side represents a speciﬁc DMU under evaluation. The non-zero optimal l* represents the benchmarks for a speciﬁc DMU under evaluation. j The reference set provides coefﬁcients (l* ) to deﬁne hypothetical efﬁcient DMU. j * 623 . The efﬁcient targets for inputs and outputs can be obtained as xio ¼ u* xio 2 s2 ^ o i þ* and yro ¼ yro þ sr , respectively. These efﬁciency targets show how inputs can ^ be decreased and outputs increased to make the DMU under evaluation efﬁcient.The ratio (uCCR /uBCC ) provides a measure of SE. Note that all aforementioned efﬁciency o omeasures 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). P nature of returns-to-scale can be determined from the Themagnitude of optimal n l* in the CCR model (Banker et al., 1984). Seiford and j¼1 jZhu (1999) listed the following three cases: P (1) If n l* ¼ 1 in any alternate optima, then CRS prevail on DMU o. Pj¼1 j (2) If n l* , 1 in any alternate optima, then IRS prevail on DMU o. Pj¼1 j (3) If n l* . 1 in any alternate optima, then DRS prevail on DMU o. j¼1 j4.2 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 TE super ) can be ooutlined as below:
!9BIJ super X m X s > > > min TE o ¼ uosuper 21 s2 þ sþ > >18,5 super uo ;l;s2 ;sþ i r i¼1 i r¼1 r > > > > > > > subject to > > > > X n > > > þ lj yrj 2 sr ¼ yrk r ¼ 1; 2; . . . ; s > > >624 > > j¼1 > > > > > = j–o ð2Þ > > X n > > lj xij þ si ¼ uk xik i ¼ 1; 2; . . . ; m > 2 super > > > > > j¼1 > > > > > > j–o > > > > > > 2 þ s i ; sr $ 0 > > > > > > lj ð j – oÞ $ 0 j ¼ 1; 2; . . . ; n > ; Besides, providing the ranks to efﬁcient DMUs, the results of super-efﬁciency DEA model can be used in sensitivity testing and identiﬁcation of outliers (Coelli et al., 2005; Avkiran, 2006). 5. Database, selection of variables and identiﬁcation of outliers To realize the underlined objectives of the study, we utilize the database provided by the Research Wing of Ministry of Shipping, Road Transport and Highways, Government of India, New Delhi (March 2007). The study is conﬁned to the cross-sectional data on input and output variables for the year 2006-2007. In the bus transport sector there is considerable disagreement among the researchers about what constitute in the input and output vectors. Table I provides different set of input and output variables used in the academic studies pertaining to efﬁciency measurement in the Indian bus transport sector. In present study, we consider ﬂeet size, total number of staff, and fuel and lubricants as input variables, and revenue bus per day and passenger kilometers performed in a year are taken as output variables. The key limitation of DEA is that the efﬁciency results are very sensitive to the presence of outliers. To overcome this limitation of DEA methodology, we ﬁrst identiﬁed outliers among the initial sample of 34 SRTUs based on the super-efﬁciency score obtained from Andersen-Petersen’s DEA model, and then applied CCR and BCC models to obtain OTE and PTE scores. According to Avkiran (2006), any DMU having super-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. Our analysis 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 that there were only two SRTUs, namely Meghalaya STC and TN STC (Villupuram) Ltd, having super-efﬁciency score greater than unity. The presence of only two SRTUs represents very poor discriminatory power of the model.
S. no. Author (year) Approach Inputs Outputs SRTUs: technical efﬁciency 1 Ramanathan (1999) DEA 1. Fleet size Passenger-kilometers 2. Total staff 3. Fuel consumed in kiloliters 2 Singh (2000a, b, c) MIP 1. Number of buses held Passenger-kilometers 625 2. Total fuel (diesel) consumed 3. Number of employees 3 Singh (2000d) TCF Number of employees Passenger-kilometers 4 Jha and Singh (2000) SFA Number of employees Passenger-kilometers 5 Singh and Venkatesh (2003) SFA 1. Labour Effective-bus kilometers 2. Number of buses held 6 Karne and Venkatesh (2003) DEA and 1. Staff Passenger-kilometers MPI 2. Diesel 3. Other material 7 Agrawal et al. (2006) DEA 1. Fleet size Revenue passenger- 2. Total staff kilometers 3. Fuel consumed 8 Anjaneyulu et al. (2006) DEA 1. Fleet size 1. Annual vehicle 2. Number of employees kilometers 3. Annual material cost 2. Annual passenger 4. Fuel consumed kilometers 3. Vehicle kilometers per accident 9 Bishnoi and Sujata (2007) DEA 1. Fleet size Passenger-kilometers 2. Total staff 3. Fuel consumed10 Nagadevara and Ramanayya DEA 1. Cost of personnel 1. Vehicles utilization (2008, 2010) 2. Cost of fuel 2. Operating ratio 3. Number of buses 3. Operating proﬁts 4. Total earning 5. Earning per bus11 Agarwal et al. (2009) DEA and 1. Fleet size Revenue passenger- MPI 2. Total staff kilometers 3. Fuel consumed12 Agrawal (2009) DEA 1. Fleet size Passenger-kilometers 2. Total staff 3. Fuel consumed13 Bhagavath (2009) DEA 1. Fleet size Revenue per bus per day 2. Average kilometer traveled per bus per day 3. Cost per bus per dayNotes: (1) SFA refers to stochastic frontier analysis; (2) DEA refers to data envelopment analysis; Table I.(3) MIP refers to multilateral index procedure; (4) TCF refers to translog cost frontier; and (5) MPI Input and outputrefers to Malmquist productivity index variables in the selectedSource: Author’s elaboration efﬁciency studies
BIJ SRTUs Stage 1 Stage 2 Stage 3 Stage 418,5 Andhra Pradesh SRTC 0.752 0.752 0.752 0.752 Bihar STC 0.500 0.534 0.534 0.547 Calcutta STC 0.449 0.461 0.461 0.465 Delhi TC 0.820 0.820 0.820 0.820626 Gujarat SRTC 0.557 0.557 0.557 0.557 Himachal RTC 0.655 0.664 0.664 0.666 Karnataka SRTC 0.778 0.778 0.778 0.778 Kerala SRTC 0.689 0.689 0.689 0.689 Maharashtra SRTC 0.464 0.464 0.464 0.464 Meghalaya STC 4.347 Dropped Dropped Dropped North Bengal STC 0.458 0.475 0.475 0.480 Orissa SRTC 0.840 0.851 1.334 1.334 Rajasthan SRTC 0.735 0.735 0.735 0.735 Tripura RTC 0.733 1.442 2.424 Dropped Uttar Pradesh SRTC 0.727 0.727 0.727 0.727 North West Karnataka RTC 0.718 0.718 0.718 0.718 Banglore Metropolitan TC 0.860 0.861 0.861 0.861 North Eastern Karnataka RTC 0.895 0.902 0.902 0.905 Metro TC (Chennai) Ltd 0.816 0.819 0.819 0.820 State Exp.TC (TN Dvn) Ltd 0.930 0.970 1.047 1.047 TN STC (Coimbtore Dvn) Ltd 0.915 0.915 0.915 0.915 TN STC (Kumbakonam) Ltd 0.959 0.959 0.959 0.959 TN STC (Madurai) Ltd 0.981 0.981 0.981 0.981 TN STC (Salem) Ltd 0.944 0.945 0.945 0.945 TN STC (Villupuram) Ltd 1.154 1.154 1.154 1.154 Kadamba TCL 0.537 0.615 0.674 0.724 Chandigarh TU 0.992 1.079 1.232 1.277 Haryana ST 0.688 0.691 0.691 0.693 Punjab roadways 0.643 0.669 0.669 0.678 Nagaland ST 0.117 0.494 0.552 1.289 Ahmedabad MTS 0.555 0.595 0.595 0.604 BEST undertaking 0.475 0.482 0.482 0.485 Kolhapur MTU 0.979 2.054 Dropped Dropped Pimpri Chinchwad MT 0.471 0.611 0.695 0.958 Average efﬁciency 0.827 0.802 0.822 0.807Table II. Number of efﬁcient SRTUs 2 4 5 5Identiﬁcation ofoutliers SRTUs Source: Author’s calculations Further, Meghalaya STC with super-efﬁciency score of 4.347 appears to be clear outlier in accordance of the Avkiran’s criterion. Thus, we dropped Meghalaya STC from the sample with the objective to get reliable results and again calculated super-efﬁciency scores for the remaining 33 SRTUs. With the deletion of Meghalaya STC, the discriminatory power of the model improved, as indicated by the fact that number of efﬁcient SRTUs increased from 2 in stage 1 to 4 in stage 2. In stage 2, the Kolhapur MTU appeared as an outlier with the super-efﬁciency score of 2.054, and therefore, we excluded this SRTU in the next stage. In stage 3, we calculated the super-efﬁciency scores for 32 SRTUs. We note that the power of discrimination further improved with 5 SRTUs as efﬁciency against 4 SRTUs in stage 2. However, Tripura RTC with super-efﬁciency score equal to 2.424 emerged as an outlier. Hence, we excluded Tripura
RTC from the analysis in stage 4. The analysis of super-efﬁciency scores pertaining to SRTUs: technicalstage 4 reveals that none of the 31 SRTUs are extreme (i.e. outlier) since all the efﬁcient efﬁciencySRTUs 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 discussion 627This 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
BIJ OTE PTE SE Super efﬁciency18,5 SRTUs (u CCR) (u BCC) ( ¼ (u CCR)/(uBCC)) scores RTS Ranks 1 2 3 4 5 6 7 Andhra Pradesh SRTC 0.752 1.000 0.752 0.752 Decreasing 16 Bihar STC 0.547 0.606 0.903 0.547 Increasing 27628 Calcutta STC 0.465 0.518 0.899 0.465 Increasing 30 Delhi S TC 0.820 0.830 0.988 0.820 Increasing 14 Gujarat SRTC 0.557 0.586 0.949 0.557 Decreasing 26 Himachal RTC 0.666 0.677 0.984 0.666 Increasing 24 Karnataka SRTC 0.778 0.783 0.994 0.778 Decreasing 15 Kerela SRTC 0.689 0.690 0.998 0.689 Increasing 22 Maharashtra SRTC 0.464 0.634 0.732 0.464 Decreasing 31 North Bengal STC 0.480 0.565 0.851 0.480 Increasing 29 Orissa SRTC 1.000 1.000 1.000 1.334 Constant 1 Rajasthan SRTC 0.735 0.738 0.996 0.735 Increasing 17 Uttar Pradesh SRTC 0.727 0.740 0.983 0.727 Decreasing 18 North Best Karnataka RTC 0.718 0.723 0.993 0.718 Increasing 20 Banglore Metropolitan TC 0.861 0.867 0.994 0.861 Increasing 12 North Eastern Karnataka RTC 0.905 0.914 0.990 0.905 Increasing 11 Metro TC. (Chennai) Ltd 0.820 0.826 0.993 0.820 Increasing 13 State Exp. TC (TN Dvn) Ltd 1.000 1.000 1.000 1.047 Constant 5 TN STC (Coimbtore Dvn) Ltd 0.915 0.917 0.998 0.915 Increasing 10 TN STC (Kumbakonam) Ltd 0.959 0.961 0.998 0.959 Increasing 7 TN STC (Madurai) Ltd 0.981 1.000 0.981 0.981 Decreasing 6 TN STC (Salem) Ltd 0.945 0.969 0.975 0.945 Decreasing 9 TN STC (Villupuram) Ltd 1.000 1.000 1.000 1.154 Constant 4 Kadamba TCL 0.724 0.735 0.986 0.724 Increasing 19 Chandigarh TU 1.000 1.000 1.000 1.277 Constant 3 Haryana ST 0.693 0.694 0.998 0.693 Increasing 21 Punjab roadways 0.678 0.710 0.955 0.678 Increasing 23 Nagland ST 1.000 1.000 1.000 1.289 Constant 2 Ahmedbad MTS 0.604 0.652 0.927 0.604 Increasing 25 BEST undertaking 0.485 0.545 0.889 0.485 Decreasing 28 Pimpri Chinchwad MT 0.958 0.969 0.990 0.958 Decreasing 8Table III. Notes: OTE refers to overall technical efﬁciency; PTE refers to pure technical efﬁciency; SE refers toOTE, PTE, SE, scale efﬁciency; RTS refers to returns-to-scale; super efﬁciency scores calculated using CCRsuper efﬁciency scores technologyand RTS in SRTUs Source: Author’s calculations that for inefﬁcient SRTUs, the OTE and super-efﬁciency scores are identical. It has been observed that among ﬁve efﬁcient SRTUs, Orissa SRTC scored the highest super-efﬁciency score (1.334), and thus attained ﬁrst rank. On the basis of such a high rank, we can regard Orissa SRTU as a global leader of public passenger transport industry in India. The second and third ranks were attained by Nagaland ST and Chandigarh TU with super-efﬁciency scores of 1.289 and 1.277, respectively. With the super-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.
6.2 Discrimination of inefﬁcient SRTUs SRTUs: technicalBesides, discriminating the efﬁcient SRTUs, we also made an attempt to separate out efﬁciencythe 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 “most 629inefﬁcient” 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 SEMean 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 1.000 Table IV.Minimum 31 0.464 0.518 0.732 Descriptive statistics of efﬁciency scoresSource: Author’s calculations for SRTUs
BIJ Marginally18,5 Highly inefﬁcient Below average Above average inefﬁcient (OTE # Q1) (Q1 , OTE # Q2) (Q2 , TE # Q3) (OTE . Q3) (I) Bihar STC (27) (I) Andhra Pradesh (I) Karnataka SRTC (15) (I) TN STC SRTC (16) (Kumbakonam)630 (7) (II) Calcutta STC (30) (II) Kerela SRTC (22) (II) Benglore (II) TN STC Metropolitan (Madurai) Ltd (6) TC (12) (III) Gujarat STC (26) (III) Rajasthan (III) North Eastren SRTC (17) Karnataka RTC (11) (IV) Himachal RTC (24) (IV) Uttar Pradesh (IV) Metro TC. SRTC (18) (Chennai) Ltd (13) (V) Maharashtra SRTC (31) (V) North West (V) TN STC (Coimbtore Karnataka SRTC (20) Dvn.) Ltd (10) (VI) North Bengal STC (29) (VI) Kadamba (VI) TN STC (Salem) TCL (19) Ltd (9) (VII) Ahmedabad MTS (25) (VII) Haryana ST (21) (VII) Pimpri Chinchwad MT (8) (VIII) BEST undertaking (28) (VIII) Punjab roadways (VIII) Delhi STC (14) (23)Table V.Categorization of Note: Q1, Q2 and Q3 refer to ﬁrst quartile, second quartile and third quartile, respectivelyinefﬁcient SRTUs Source: Author’s calculations Table III also provides the PTE and SE scores for individual SRTUs. It has been observed that 7 SRTUs acquired the status of “locally efﬁcient” because they attained the PTE score equal to 1. Among these seven SRTUs, the 5 are “globally efﬁcient” with OTE score equal to 1. Further, for two SRTUs, namely Andhra Pradesh SRTC and TN STC (Madurai) Ltd that are locally efﬁcient but globally inefﬁcient under CRS assumption, we can infer that OTIE in these SRTUs is not caused by poor input utilization (i.e. managerial inefﬁciency), but rather is due to operation of these undertakings at inappropriate scale size. It has been further noticed that in the remaining 24 SRTUs (having PTE , 1) managerial inefﬁciency exists, albeit of different magnitude. In these SRTUs, OTIE stems from both PTIE and SIE as indicated by the fact that these SRTUs have both PTE and SE scores less than 1. Out of these 24 SRTUs, 12 SRTUs have PTE score less than SE score. This indicates that the inefﬁciency in resource utilization (i.e. OTIE) in these 12 SRTUs is primarily attributed 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 poor input 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 that 19.8 percentage points of the about 22.8 percent of OTIE is due to the managers of these undertakings who are not following appropriate management practices and selecting incorrect input combinations. The rest of OTIE appears due to inappropriate
scale of operations in these undertakings. Further, lower mean and high standard SRTUs: technicaldeviation of the PTE scores compared to the SE scores indicate that a greater portion of efﬁciencyOTIE 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 maximize 631revenue. 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 identiﬁed Pby the sum of intensity variables in the CCR model. If n lj , 1, then the SIE i¼1appears due to IRS. The implication of this is that the particular SRTU has sub-optimal Pnscale size. On the other hand, if i¼1 lj . 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
BIJ of these variables at SRTU level using OTE scores, optimum values of slacks and actual values of the variables. The target point ðx * ; y * Þ is deﬁned by the following formulae:18,5 9 x* ¼ u* xio 2 s2 i ¼ 1; 2; . . . ; m = * io k i * ð3Þ y* ¼ yro þ sþ ro r r ¼ 12; . . . ; s: ;632 where x* ¼ the target input i for oth SRTU, y* ¼ target output r for oth SRTU; io ro xio ¼ actual input i for oth SRTU; yro ¼ actual output r for oth SRTU; u* ¼ efﬁciency o * * score of the oth SRTU o; s2 ¼ optimal input slacks; and sþ ¼ optimal output slacks. i r Input slack(s) indicates the need for further reductions in corresponding input(s). Output slack(s) signals any additional output(s) which could be produced by the efﬁcient levels of inputs. The difference between the observed value and target value of inputs (xio 2 x* ) represents the quantity of inputs to be reduced, while the difference between io the target values and observed values of outputs ðy* 2 yro Þ represents the amount of ro outputs to be increased, to move the inefﬁcient SRTU on the efﬁciency frontier. Table VI provides the input and output slacks derived from CCR model for 26 inefﬁcient SRTUs. For interpreting the contents of the table, consider the case of a single SRTU, say, the worst inefﬁcient Maharashtra SRTC. The OTE score of Maharashtra SRTC is 0.464, implying that the Maharashtra SRTC could become technically efﬁcient (under the Farrell’s deﬁnition) provided if all of its inputs are proportionally reduced by 53.6 percent (i.e. (1-OTE score) £ 100). However, even with this required proportional reduction in all inputs, this SRTU would not be Pareto-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 slack adjustments are necessary because non-zero input and output slacks appear for this SRTU. Ultimately, Maharashtra SRTC has to make three adjustments in order to operate 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, and fuel and lubricants by 53.6 percent. Third, it has to augment revenue bus per day by 151.9 percent. The ﬁrst type of adjustment is known as radial adjustment, while second and third types of adjustments are known as the slack adjustments. The similar explanation can be extended for other inefﬁcient SRTUs. We have also observed that on average, approximately 48.4 percent of average ﬂeet held, 43.2 staff strength and 28 percent of fuel and lubricants could be theoretically reduced if all the inefﬁcient SRTUs operate at the same level as the best practice SRTUs (i.e. efﬁcient SRTUs). It is observed that on an average, the SRTUs can generate more revenue bus per day by approximately 31.01 percent and there is no possibility of improvement in the addition of passenger kilometers performed. However, there are considerable variations in saving in inputs and addition in outputs among inefﬁcient SRTUs. 6.6 Robustness of DEA results: Jack-kniﬁng analysis To investigate the robustness of DEA results in terms of stability of reference set, we followed Myrtveit and Stensurd (1999), Mostafa (2007a, b) and performed a procedure known as Jack-kniﬁng. For this, we dropped all the efﬁcient SRTUs one by one and studied 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
BIJ additional DEA analyses. From Table VII, we observed that none of the efﬁcient18,5 undertaking observed in the post-DEA analysis extreme because its removal did not bring any signiﬁcant change in average OTE of SRTUs in India. Further, the composition 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.634 6.7 Appropriateness of selected input and output variables: a sensitivity analysis It is well known fact that in DEA, the distribution of efﬁciency scores is very sensitive to the choice of input and output vectors. Thus, the selection of input and output variables for the DEA study requires a careful thought as the distribution of efﬁciency scores and rank order of DMUs are likely to be affected by the selection of variables and their number. Therefore, we checked whether our choice of inputs and outputs in the above used baseline model (so called model I) is appropriate and yields robust inferences. For this purpose, we carried out a sensitivity analysis by considering two additional 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 the model 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 variables that 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 the present sensitivity analysis, we have adopted Chen and Yeh’s (1999) criteria to reject a particular 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, Pimpri Chinchwad MT State Exp. TC (TN Dvn) Ltd 0.764 Orissa SRTC, TN STC (Villupuram) Ltd, Chandigarh TU, 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 Pimpri Chinchwad MTTable VII.Jack-kniﬁng analysis Source: Author’s calculations
. correlation coefﬁcient of efﬁciency scores of baseline model I with a speciﬁc case SRTUs: technical is high because a high correlation indicates almost identical results provided by efﬁciency the two cases; and/or . there are larger number of efﬁcient SRTUs in a speciﬁc case than model I since too many efﬁcient undertakings reduce the discrimination capability of the performance evaluation results. 635Table 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 andstatistically 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 IIICorrelation 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 7Note: *Signiﬁcant values at the level of signiﬁcance a ¼ 0.050 (two-tailed test) Table VIII.Source: Author’s calculations Sensitivity analysis
9BIJ y* ¼ b T xi þ 1i i > > > =18,5 yi ¼ y* if y* . 0; and ð4Þ i i > > > yi ¼ 0; otherwise; ;636 where 1i , N ð0; s 2 Þ, xi and b are vectors of explanatory variables and unknown parameters, respectively. “T” denotes the matrix transpose operator. The y* is a latent i variable and yi is the dependent variable. Following Loikkanen and Susiluoto (2002), the dependent variable yi is deﬁned as 1–DEA efﬁciency score. The following likelihood function (L) needs to be maximized to solve b and s based on 31 observations of yi and xi is: 9 Y Y 1 2 T 2 = L¼ ð1 2 F i Þ e 2ð1=2s Þð yi 2b xi Þ ð5Þ yi ¼0 2 1=2 yi .0 ð2ps Þ ; where: Z b T xi =s 1 2 Fi ¼ 1=2 e 2ðt =2Þ dt 21 ð2pÞ The ﬁrst product is over the observations for which the SRTU’s are 100 percent efﬁcient ( y ¼ 0) and the second product is over the observations for which SRTUs are inefﬁcient ( y . 0). Fi is the distribution function of the standard normal evaluated at b T xi =s. It is possible to estimate the unknown parameter vector b in the Tobit model in several ways. In this paper, we use the econometric software package EViews Version 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 held by an undertaking. The variable “SP” is measured by the average revenue earnings kilometer performed per worker per day. Further, “VP” is the average number of revenue earnings per kilometer performed by a bus per day. The variable “FE” reﬂects the average kilometer per liter of fuel. The explanatory variable “OR” is computed as the passenger kilometers performed to passenger kilometer offered. We estimated the following left-censored Tobit regressions for OTE, PTE and SE scores separately: 1 2 OTE i ðor 1 2 PTE i or 1 2 SE i Þ ¼ b0 þ b1 FU i þ b2 SP i þ b3 VP i þ b4 FE i þ b5 ORi þ 1i ð6Þ Thus, three censored regressions with OTIE, PTIE, SIE as dependant variables have been estimated using the aforementioned independent variables.