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BIJ
18,5 State road transport undertakings
in India: technical efficiency
and its determinants
616
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 the
Benchmarking: An International passenger mobility in diverse terrains throughout the country, and thus lay a
Journal considerable impact on the life of masses. There is no doubt that an analysis of the
Vol. 18 No. 5, 2011
pp. 616-643 sources and determinants of operational efficiency would be a valuable aid to the policy
q Emerald Group Publishing Limited formulators in designing appropriate policies aiming to improve the overall health
1463-5771
DOI 10.1108/14635771111166794 and competitiveness of these undertakings. However, in Indian context, the analysis

2. of efficiency of SRTUs has not received considerable attention from the scholars, and SRTUs: technical
there are only a handful of studies on the subject matter in the academic journals (see
Section 3 for details). Our study intends to enrich the scant literature, and in particular,
efficiency
endeavours to gauge the extent of overall technical, pure technical and scale efficiencies
in SRTUs using a non-parametric, data driven, deterministic and non-statistical
technique known as data envelopment analysis (DEA). The choice of DEA over its
archrival stochastic frontier analysis (SFA) in the present context is directed by its 617
intrinsic 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 efficiency
of 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 and
Alkadi, 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 a
relative efficiency measurement technique in other major areas of transport sector like
airports (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 and
Pacheco, 2002; Pels et al., 2003; Bazargan and Vasigh, 2003; Pacheco and Fernades,
2003; Yu, 2004; Sarkis and Talluri, 2004; Scheraga, 2004; Bowlin, 2004; Capobianco and
Fernandes, 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.) and
railways (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 in
transport sector are voluminous. Nevertheless, the research on the efficiency of Indian
SRTUs using DEA and other frontier efficiency measurement techniques is still in the
stage of infancy. The available literature reviewed by us does not provide even a single
study which detected the presence of outliers in efficiency measurement, and examined
the 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

3. BIJ .
explain the significant factors affecting OTE, PTE and SE of SRTUs by using
18,5 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 issues
618 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).

4. In the Indian context, the SRTUs, over a period of time, have occupied a pivtol role by SRTUs: technical
virtue of certain inherent advantages like its affordability, flexibility, door-to-door efficiency
operations, 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 to
loss-incurring zones due to trade-off between the commercial objectives and social
responsibility, 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 619
of the state governments, both as a source of employment generation and as a source of
patronage by fare discounts to wider and wider segments of the population (The World
Bank, 2005). These concessions have cost the SRTUs hundreds of billions that have
never been compensated by the respective state governments. Currently, a stage has
been reached where these public undertakings are forced to meet large number of social
obligations without any budgetary support from their respective state governments.
As a result, most of these undertakings have to keep running their operations with huge
losses. To a large extent, this hinders the ability of these undertakings to supply
the 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 these
undertakings for reinventing the ways the SRTUs would emerge as an ideal
benchmarks in the passenger transport sector of the country.
3. Relevant literature review on Indian SRTUs’ efficiency
As mentioned in the introductory section, there exists a voluminous literature on the
efficiency of public transport system in developed countries. However, the research
on efficiency of SRTUs operating in India has been undertaken by a few researchers.
Using SFA, Kumbhakar and Bhattacharyya (1996) found a negative total factor
productivity (TFP) growth in 11 SRTUs out of the total of 31 for the period from
1983 to 1987. They observed the contribution of scale economies as an important
factor which varies widely across SRTUs. Ramanathan (1999) applied DEA to assess
the efficiency of 29 SRTUs operating in the year 1993-1994, and found that most of
the operators are using their fuel efficiently while large inefficiencies are observed
in the usage of fleet and staff. Furthermore, with the application of regression
analysis, 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. City
operations with a higher passenger density per bus tend to increase efficiency scores.
Using multilateral productivity index, Singh (2000a, b, c) provided a comparison of
TFP growth for 21 SRTUs during the period 1983-1984 to 1996-1997. It has been
noted 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.

5. BIJ Singh (2000d) and Jha and Singh (2000) confirmed the existence of U-shaped average
18,5 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 SRTUs
620 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.

6. Regarding determinants of TFP growth, the results reveal that change in employee-bus SRTUs: technical
ratio, change in depreciation cost, change in total earnings and change in total cost, efficiency
turn out to be the most significant variables in having impact on the change in
productivity. Using DEA, Bhagavath (2009) examined the technical efficiency of
44 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 for
the years 2004-2005 to 2007-2008. The efficiency scores are calculated by applying a
new slack DEA model with categorical DMUs. The results of DEA models confirm that
performance of the SRTUs has not improved over the earlier three years and has
improvement in the last year but still very far from the optimal level. Using DEA,
Nagadevara and Ramanayya (2010) analyzed inter-temporal variations in efficiency
of 25 depots of Karnatka SRTC over the period 2004-2005 to 2008-2009. They found
that 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 efficiency
frontier, have lost their edge and became relatively inefficient. The largest drop in
efficiency is seen in the Kolar depot.
In sum, the careful screening of the available literature on bus transport sector in
India reveals that a scant literature appears in Indian context relating to the efficiency
of SRTUs that applied DEA to evaluate technical efficiency of this sector. Thus, the
present study is intended to enrich the literature concerning the operational efficiency
of SRTUs and the factors explaining it using a two-stage DEA procedure. At first
stage, DEA has been used to obtain the diverse measures of efficiency, whereas the
second stage utilized Tobit analysis to know the significant factors influencing these
measures of efficiency.
4. Methodological framework
4.1 Measurement of overall, technical, pure technical and scale efficiencies: CCR and
BCC DEA models
The methodology used in this study is an extension upon the Farrell’s (1957) work by
Charnes et al. (1978), which they coined it as DEA. DEA floats a piecewise linear surface
to the rest on top of the observations (Seiford and Thrall, 1990). The DMUs that lie on the
frontier are the best practice institutions and retain a value of one. Those DMUs
enveloped by the extremal surface are scaled against a convex combination of the
DMUs 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 the
literature (see Charnes et al. (1994) for details). In the present study, we have used the
input-oriented CCR model named after Charnes et al. (1978), to get a scalar measure of
OTE. 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

7. BIJ input-oriented[1] 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

8. 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 o
measures are bounded between one and zero. The measure of SE does not indicate
whether the DMU in question is operating in the area of increasing or decreasing
returns-to-scale (DRS). P nature of returns-to-scale can be determined from the
The
magnitude of optimal n l* in the CCR model (Banker et al., 1984). Seiford and
j¼1 j
Zhu (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 j
4.2 Ranking of DMUs: Andersen and Petersen’s super-efficiency DEA model
It is significant to note that all efficient DMUs have the same efficiency scores equal to 1
in the CCR model. Therefore, it is impossible to rank or differentiate the efficient DMUs
with the CCR model. However, the ability to rank or differentiate the efficient DMUs is of
both theoretical and practical importance. Theoretically, the inability to differentiate the
efficient DMUs creates a spiked distribution at efficiency scores of 1. This poses analytic
difficulties to any post-DEA statistical inference analysis. In practice, further
discrimination 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 model
is to exclude the DMU under evaluation from the reference set. This allows a DMU to be
located on the efficient frontier, i.e. to be super-efficient. Therefore, the super-efficiency
score 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 the
super-efficiency score implies higher rank). However, the inefficient units which are not
on the efficient frontier, and with an initial DEA score of less than 1, would find their
relative 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 for
estimating the efficiency score of DMU o, the DMU o cannot form part of its reference
frontier, 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 these
LPs, the reference set involves n 2 1 DMUs. In particular, Andersen and Petersen’s
model for estimating super-efficiency score for DMU o (denoted by TE super ) can be
o
outlined as below:

9. !9
BIJ 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.

10. 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 consumed
10 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 bus
11 Agarwal et al. (2009) DEA and 1. Fleet size Revenue passenger-
MPI 2. Total staff kilometers
3. Fuel consumed
12 Agrawal (2009) DEA 1. Fleet size Passenger-kilometers
2. Total staff
3. Fuel consumed
13 Bhagavath (2009) DEA 1. Fleet size Revenue per bus per day
2. Average kilometer
traveled per bus
per day
3. Cost per bus
per day
Notes: (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 output
refers to Malmquist productivity index variables in the selected
Source: Author’s elaboration efficiency studies

11. BIJ
SRTUs Stage 1 Stage 2 Stage 3 Stage 4
18,5
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 0.820
626 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 0.807
Table II. Number of efficient SRTUs 2 4 5 5
Identification of
outliers 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

12. RTC from the analysis in stage 4. The analysis of super-efficiency scores pertaining to SRTUs: technical
stage 4 reveals that none of the 31 SRTUs are extreme (i.e. outlier) since all the efficient efficiency
SRTUs have super-efficiency scores less than 2. Therefore, we terminate our process of
identification of outliers at stage 4. Thus, our final sample after excluding outliers
includes 31 SRTUs.
6. Results and discussion 627
This section provides the empirical results obtained from input-oriented CCR and
BCC and super-efficiency DEA models. The results of Tobit regression analysis to
explore the root cause of inefficiency in the operations of SRTUs, have also been
presented. It is significant to note that input-oriented efficiency measures give the
extent 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 the
OTE scores for 31 SRTUs. We note that there exists wide variations in the level of OTE
across SRTUs, which varies between 46.4 and 100 percent. The average of OTE scores
turned 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 of
various efficiency measures). This suggests that by adopting best practices, SRTUs
can, on an average, reduce their inputs of fleet size, total number of staff, and fuel and
lubricants by at least 22.8 percent, and still produce the same level of outputs.
However, the potential reduction in inputs from adopting best-practice technology
varies among different SRTUs.
Recall that the SRTU with OTE score equal to 1 is deemed to be efficient and
represent a point on the efficient frontier. Of the 31 SRTUs, five SRTUs are found to be
technically efficient since they have OTE score of 1. These SRTUs together define the
best-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 the
production process of these SRTUs is not characterizing any waste of inputs. In DEA
terminology, these SRTUs are called peers and set an example of good operating
practices for inefficient SRTUs to emulate in their derive to reduce the inefficiency in
production 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 relatively
inefficient with OTE score less than 1. The results indicate a presence of marked
deviations of the SRTUs from the best-practice frontier. These inefficient SRTUs can
improve their efficiency by reducing inputs. OTE scores among the inefficient SRTUs
range from 0.464 for Maharashtra SRTC to 0.981 for TN STC (Madurai) Ltd This
finding implies that Maharashtra SRTC and TN STC (Madurai) Ltd can potentially
reduced their inputs 53.6 percent and 1.9 percent, respectively, while leaving their
output levels unchanged. This interpretation of OTE score can be extended for other
inefficient SRTUs in the sample. On the whole, we observed that OTIE levels range
from 1.9 to 53.6 percent among inefficient SRTUs.
6.1 Discrimination of efficient SRTUs
Table III also provides the super efficiency scores and ranks of 31 SRTUs on
the basis of super-efficiency scores (see columns 4 and 6). It is important to note

13. BIJ
OTE PTE SE Super efficiency
18,5 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 27
628 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 8
Table III. Notes: OTE refers to overall technical efficiency; PTE refers to pure technical efficiency; SE refers to
OTE, PTE, SE, scale efficiency; RTS refers to returns-to-scale; super efficiency scores calculated using CCR
super efficiency scores technology
and 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.

14. 6.2 Discrimination of inefficient SRTUs SRTUs: technical
Besides, discriminating the efficient SRTUs, we also made an attempt to separate out efficiency
the 26 inefficient SRTUs. For this, we utilized the quartile values of OTE scores
obtained from CCR model as three cut-off points to segregate the inefficient SRTUs into
four distinct categories: category I (highly inefficient), category II (below average),
category III (above average), and category IV (marginally inefficient) (see Table IV for
these quartile values). Among these categories, the SRTUs belonging to “most 629
inefficient” and “marginally inefficient” category require special attention. In the “most
inefficient” category, those SRTUs have been included which attained OTE score
below the first quartile value. The candidates of this group are worst performers in the
sample. It is significant to note that these SRTUs lack vitality in terms of the efficiency
of resource utilization. The Bihar STC, Calcutta STC, Gujarat STC, Himachal RTC,
Maharashtra SRTC, North Bengal STC, Ahmadabad MTS and BEST undertaking fall
in this category (Table V).
The SRTUs that have attained OTE score above the third quartile value but less
than 1 are included in “marginally inefficient” category. TN STC (Kumbakonam) and
TN STC (Madurai) Ltd, lie in this category. It is worth mentioning here that these
SRTUs are operating at a high level of operating efficiency even though they are not
fully efficient. In fact, these SRTUs are marginally inefficient and operating very close
to the efficient frontier. Further, these SRTUs can attain the status of efficient SRTUs
by bringing little improvements in the resource utilization process. In fact, these
SRTUs can be considered as “would be champions”. Therefore, the regulators must
pay a special attention to enhance their efficiency.
6.3 Decomposition of OTE: PTE and SE
It should be noted that OTE measure helps to measure combined inefficiency that is
due to both pure technical inefficiency (PTIE) and inefficiency due to inappropriate
scale size, i.e. scale inefficiency (SIE). However, in contrast to OTE measure, the PTE
measure derived from BCC model under assumption of variable returns to scale devoid
of the scale effects. Thus, the PTE scores provide that all the inefficiencies directly
result from managerial underperformance (i.e. managerial inefficiency) in organizing
the inputs. It is significant to note that PTE scores are greater than or equal to OTE
scores because BCC model forms a convex hull of intersecting planes which envelops
the data points more tightly than CRS conical hull. In DEA literature, the DMUs
attaining OTE scores equal to 1 are known as “globally efficient”. However, the DMUs
with PTE ¼ 1 and OTE – 1 are called “locally efficient”.
Descriptive statistics n OTE PTE SE
Mean 31 0.772 0.802 0.958
SD 31 0.181 0.163 0.070
Quartile 1 31 0.666 0.677 0.949
Quartile 2 (median) 31 0.752 0.783 0.990
Quartile 3 31 0.958 0.969 0.998
Maximum 31 1.000 1.000 1.000 Table IV.
Minimum 31 0.464 0.518 0.732 Descriptive statistics
of efficiency scores
Source: Author’s calculations for SRTUs

15. BIJ
Marginally
18,5 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, respectively
inefficient 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

16. scale of operations in these undertakings. Further, lower mean and high standard SRTUs: technical
deviation of the PTE scores compared to the SE scores indicate that a greater portion of efficiency
OTIE is due to PTIE.
6.4 Returns-to-scale
It is well acknowledge fact in theory of the firms that one of the basic objectives of
the firms is to operate at MPSS, i.e. with CRS in order to minimize costs and maximize 631
revenue. In the short run, firms may operate in the zone of IRS or DRS. However, in
the long run, they will move towards CRS by becoming larger or smaller to survive in
the competitive market. The process may involve the changes of a firms’ operating
strategy in terms of scaling up or scaling down of its size. The regulators may use this
information to determine whether the size of the representative firm in a particular
industry is appropriate or not. Recall that the existence of IRS or DRS can be identified
P
by the sum of intensity variables in the CCR model. If n lj , 1, then the SIE
i¼1
appears due to IRS. The implication of this is that the particular SRTU has sub-optimal
Pn
scale 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 also
provides the nature of returns-to-scale for individual SRTUs. The results indicate that
five 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, and
thus experiencing IRS. The policy implication of this finding is that these SRTUs can
enhance OTE by increasing their size. The remaining nine (i.e. 29 percent) SRTUs have
been observed to be operating in the zone of DRS, and thus downsizing seems to be an
appropriate 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 the
total number of SRTUs in the sample, we can say that there is a further room to
introduce modern technology so as to improve the technical efficiency of these SRTUs.
6.5 Areas for efficiency improvement: targets setting analysis
The optimum solution of linear program (1) provides non-zero input and output slacks
corresponding to input and output constraints. It is important to note that slacks exist
only for those SRTUs that are identified as inefficient in a particular DEA run. These
slacks provide the vital information concerning to the areas which an inefficient SRTU
needs 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 operational
efficiency and any non-zero input and output slacks should be reported to provide an
accurate indication of technical efficiency of a firm in a DEA analysis. Thus, the slacks
should be interpreted along with the efficiency scores. However, slacks represent only
the 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 to
push the DMU to the frontier (target) (Ozcan, 2008). The presence of non-zero slacks for
a DMU implies that the DMU under scrutiny can improve beyond the level implied by
the estimate of technical efficiency ( Jacobs et al., 2006). In the input-oriented DEA
model, the input-slack represents the excess input and output slack indicates the
output which is under produced (Avkiran, 1999; Ozcan, 2008).
For getting the more focused diagnostic information about the sources of inefficiency
for each SRTU with respect to the input and output variables, we computed target values

17. 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

18. Percentage
Target values of addition in Percentage saving in
output variables Target values of input variables outputs inputs
Inefficient SRTUs Y1 Y2 X1 X2 X3 Y1 Y2 X1 X2 X3
Andhra Pradesh SRTC 23,989.2 820,459.0 9,291.7 64,832.3 95,906.3 402.7 0 52.3 44.1 24.8
Bihar STC 2,690.8 12,847.1 222.9 1,258.3 1,722.2 0.0 0 65.0 71.2 45.3
Calcutta STC 1,722.5 18,208.5 246.0 1,563.8 2,241.8 0.0 0 78.5 79.4 53.5
Delhi S TC 3,670.3 120,137.5 1,365.8 9,509.8 14,058.3 0.0 0 60.6 66.6 18.0
Gujarat SRTC 7,764.1 265,540.0 3,007.2 20,982.9 31,039.9 100.3 0 62.8 58.0 44.3
Himachal RTC 3,911.0 64,824.0 801.5 5,334.1 7,769.5 0.0 0 53.9 38.9 33.4
Karnataka SRTC 7,154.4 244,690.0 2,771.1 19,335.3 28,602.7 27.2 0 46.1 22.2 27.9
Kerala SRTC 6,180.5 211,381.0 2,393.9 16,703.2 24,709.1 28.5 0 49.3 50.4 31.1
Maharashtra SRTC 14,339.4 490,423.5 5,554.0 38,753.1 57,327.3 151.9 0 64.8 62.1 53.6
North Bengal STC 1,456.2 12,177.7 174.7 1,077.8 1,528.3 0.0 0 79.6 79.8 52.0
Orissa SRTC 4,014.4 8,421.5 258.0 1,247.0 2,007.9 0.0 0 0.0 0.0 0.0
Rajasthan SRTC 6,080.8 207,971.3 2,355.3 16,433.8 24,310.5 14.4 0 47.9 26.5 27.0
Uttar Pradesh SRTC 7,135.4 244,038.0 2,763.7 19,283.8 28,526.5 79.4 0 60.1 46.9 27.3
North Best Karnataka RTC 4,524.1 154,729.6 1,752.3 12,226.7 18,086.9 2.0 0 56.0 39.4 28.2
Banglore Metropolitan TC 4,734.5 149,119.3 1,701.3 11,822.7 17,466.7 0.0 0 57.2 37.8 13.9
North Eastern Karnataka RTC 4,353.8 88,555.9 1,061.9 7,183.0 10,519.7 0.0 0 56.4 34.0 9.5
Metro TC. (Chennai) Ltd 4,666.3 125,765.0 1,457.4 10,041.8 14,795.3 0.0 0 47.4 43.4 18.0
TN STC (Coimbtore Dvn) Ltd 6,260.7 175,815.6 2,028.6 14,010.5 20,658.4 0.0 0 19.0 8.5 14.1
TN STC (Kumbakonam) Ltd 6,430.6 216,596.8 2,456.2 17,125.6 25,328.1 0.0 0 13.2 4.1 8.9
TN STC (Salem) Ltd 6,640.4 121,642.9 1,480.7 9,936.0 14,513.0 0.0 0 8.8 5.5 11.4
Kadanba TCL 3,395.1 9,948.0 286.4 1,484.7 1,766.3 0.0 0 32.9 27.6 27.6
Haryana ST 5,787.2 144,752.0 1,691.3 11,601.5 17,068.7 0.0 0 47.5 35.6 30.7
Punjab roadways 3,282.7 25,483.7 373.5 2,280.2 3,220.6 0.0 0 71.5 74.5 32.2
Ahmedbad MTS 3,059.0 15,430.2 262.0 1,493.2 2,052.1 0.0 0 61.8 61.9 39.6
BEST undertaking 6,866.9 101,238.0 1,277.2 8,410.1 12,206.2 0.0 0 62.3 75.5 51.5
Pimpri Chinchwad MT 2,669.2 4,672.0 276.0 1,375.4 1,269.8 0.0 0 4.2 29.1 4.2
Average 5,876.1 155,956.5 1,819.6 12,511.8 18,411.6 31.0 0 48.4 43.2 28.0
Notes: Y1 – revenue bus day; Y2 – passenger-kilometers performed; X1 – fleet size; X2 – staff; X3 – fuel and lubricants
Source: Author’s calculations
SRTUs: technical
addition in outputs and
and input variables and
Target values of output
efficiency
savings in inputs
633
Table VI.

19. BIJ additional DEA analyses. From Table VII, we observed that none of the efficient
18,5 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 MT
Table VII.
Jack-knifing analysis Source: Author’s calculations

20. .
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.
635
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 is
not drastically different from what has been observed in the case of model
I. Thus, we reject models II and III in favour of model I. In sum, we infer that our choice
of input and output variables is appropriate, and our aforementioned results are
quite robust.
6.8 Explaining technical efficiency: Tobit analysis
It is apparent from above analysis that the efficiency estimates differ substantially
across different SRTUs. The inter-undertakings differences can sometimes be
attributed 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 analysts
are often interested in determining whether these differences are significant in a
statistical sense. This can be done by using the regression analysis. Unfortunately, the
simple linear regression model encountered in most text-books is not appropriate here
because the range of efficiency scores obtained from DEA model is censored, and
therefore a simple application of ordinary least squares estimation procedure may
produce biased estimates if there is a significant position of the observations equal to
one (Resende, 2000). In such cases, the appropriate regression model is known as a
Tobit 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 scores
Model I 1
Model II 0.911 * 1
Model III 0.999 * 0.908 * 1
No. of efficient banks 5 3 5
Correlation coefficients of PTE scores
Model I 1
Model II 0.951 * 1
Model III 1* 0.950 * 1
No. of efficient banks 7 7 7
Note: *Significant values at the level of significance a ¼ 0.050 (two-tailed test) Table VIII.
Source: Author’s calculations Sensitivity analysis

21. 9
BIJ 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.

22. It has been observed that in the all the regression equations, the signs of the estimated SRTUs: technical
coefficients are in consonance of a priori expectations. Visualization of Table IX efficiency
discloses the facts that variable OR has significantly negatively affected the overall
and pure technical inefficiencies of sample SRTUs. Moreover, the coefficients of the
remaining four independent variables although satisfy a priori expectations,
but observed to be statistically insignificant. On the other hand, the variables SP and
OR found to be bearing a positive and statistically significant impact on SE. Further, 637
the coefficients of remaining three variables causing SIE have been observed to be
statistically insignificant. The direct connotation of these results is that OR has a
significant impact on OTE, PTE and SE, implying that higher the OR leads to higher
operational efficiency of SRTUs. In addition, higher levels of SP are needed to augment
the SE levels of SRTUs in India.
7. Conclusions
This paper endeavours to evaluate the extent of technical, pure technical, and scale
efficiencies in Indian public transport industry using cross-sectional data for 31 SRTUs
operating in the year 2006-2007. The empirical results indicate that the level of OTIE in
sample SRTUs is to the tune of 22.8 percent. The results suggest that by adopting the best
practices, SRTUs, on an average, can reduce their inputs by at least 22.8 percent. Thus, the
sample SRTUs are wasting about one-fourth of their resources in the production
operations. Out of the 31 SRTUs, five SRTUs have been identified as relatively efficient
with OTE score equal to one. On the basis of super-efficiency scores, we note that Orissa
SRTC is the industry leader. The analysis of decomposing OTIE reveals that managerial
inefficiency (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 thus
any expansion plan would enhance the efficiency of these undertakings.
From the target setting exercise, we observe that on an average, approximately
48.4 percent of fleet held, 43.1 percent of 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 efficient SRTUs. Further, it has been observed that on an average, SRTUs
can generate more revenue bus per day by approximately 31.01 percent. The
jack-knifing exercise ensures that our DEA results are quite robust. Sensitivity analysis
Measure of technical inefficiency
Regressor (parameter) OTIE p-values PTIE p-values SIE p-values
Constant (b1) 1.056684 0.0524 1.213662 0.0308 0.178851 0.4212
FU (b2) 2 0.000246 0.9450 2 0.001440 0.6941 0.000107 0.9412
SP (b3) 2 0.004122 0.3355 2 0.000198 0.9641 20.003638 * 0.0359
VP (b4) 2 4.95 £ 102 5 0.9400 2 0.000356 0.6036 0.000294 0.2659
FE (b5) 0.015157 0.8483 2 0.040904 0.6159 0.039672 0.2151
OR (b6) 2 0.010 * 0.006 2 0.009083 * 0.0130 20.003465 * 0.0199
Log likelihood 7.898289 5.178825 32.67461
Pseudo R 2 0.422586 0.346116 0.359957
Notes: (i) Figures in the parentheses are p values; (ii) *indicates that the coefficient is significant at Table IX.
5% level of significance Results of Tobit
Source: Authors’ calculations regression analysis