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The main aim of this paper is to measure the technical efficiency of publicly owned urban bus companies (UBCs) in India for the period 2000-01 to 2012-13. To examine the efficiency as well as determinants of the same, we estimated a stochastic production frontier based on a translog production function using the maximum likelihood methods. The empirical results reveal that profit and fleet utilization have a significant influence on technical efficiency of UBCs. We find that substantial inefficiencies, averaging between 12 to 41 percent, exist; in general, small and large size UBCs are more efficient than their medium size counterparts. Therefore, there exist s no linear relationship between technical effi ciency and firm size. We also examined the temporal relationship of the cross-sectional rankings of individual UBCs’ technical efficiency estimates. To address this issue, we calculated Kendall’s index of rank concordance and coefficient of variation of technical efficiency for sample period. It is found that, by and large, there has been stability in ranks across UBCs in regard to their technical efficiency.

Public transport system in urban India heavily relies on its bus transport system. Bus transport services are now available in most of the metropolitan cities, thanks to the Government of India’s Jawaharlal Nehru National Urban Renewal Mission (JNNURM) [

UBCs in India operate with around 24,000 buses and employ close to 156,000 people. During the year 2012-13, latest year for which data are available, the total bus-kilometers operated by them were more than 1.6 billion and the volume of operations had crossed the mark of 80 billion passenger-kilometers. However, from the very beginning, UBCs in India faced huge financial losses from their operation. UBCs’ total revenue during the year 2012-13 was just Rs. 66,025 million in comparison to total cost of Rs. 109,345 million. Due to this, they faced a net loss of more than Rs. 43 billion during the year 2012-13. On an average, every bus-km operated by these companies resulted in a loss of more than Rs. 25 during the same year.

Nevertheless, since UBCs in India offer their services with a social aim, financial losses faced by them are not bad per se. For government owned public transport companies, efficiency is more important than profitability. Efficiency has long been a critical consideration in both policy and operational decisions of public transport operators, and public transport efficiency has recently become even more vital [

There are several approaches to measure transport operators’ efficiency; parametric and non-parametric frontiers are the two main approaches to measure efficiency (for comparison, see, [

The main of aim of this paper is to examine the efficiency of UBCs in India in a manner that allows the efficiency to vary both over time as well as across firms. The analysis is conducted using the stochastic frontier analysis (SFA) of the production function model specified by Battese and Coelli [

The remainder of this paper is organized as follows: Section 2 discusses the approach used to estimate the technical efficiency and choice of functional form. Section 3 describes the sample UBCs and the data. Section 4 presents the results. Section 5 concludes the study.

In line with the work of Battese and Coelli [

Y i t = exp ( X i t β + V i t − U i t ) (1)

where, Y i t _{ }is output of i^{th} firm ( i = 1 , 2 , ⋯ , N ) in the t^{th} period ( t = 1 , 2 , ⋯ , T ); X i t is a (1 × K) vector of input quantities of the i^{th} firm in the t^{th} period; β is a (K × 1) vector of unknown parameters to be estimated; V i t is a random variable which is assumed to be independent and identically distributed and have N ( 0 , σ V 2 ) distribution and independent of U i t ; the U i t is non-negative random variable, associated with technical inefficiency of production, which is assumed to be independently distributed as truncations at zero of the N ( μ , σ U 2 ) distribution, where μ = Z i t δ ; and Z i t is a (1 × P) vector of explanatory variables associated with technical inefficiency of the i^{th} firm in the t^{th} period and δ is a (P × 1) vector of unknown parameters to be estimated.

A number of empirical studies (e.g., [

U i t = Z i t δ + W i t (2)

where, W i t is an unobservable random variable assumed to be independently distributed, obtained by truncation of the normal distribution with mean zero and variance, σ 2 , such that the U i t is non-negative. The condition that U i t is non-negative ensures that all observations lie on or below the production frontier.

Given the specification of the model, the hypothesis that the technical efficiency effects are non-random is expressed by H_{0}: γ = 0 , where γ = σ U 2 / ( σ U 2 + σ V 2 ) . Battese and Corra [^{th} firm during t^{th} period is obtained as:

T E i t = exp ( − U i t ) = exp ( − Z i t δ − W i t ) (3)

Since stochastic production function estimation requires a specific functional form of the production function, we specified (1) by the translog production function:

ln Y = β 0 + ∑ k = 1 K β k ln X k + 1 2 ∑ k = 1 K ∑ l = 1 K β k l ln X k ln X l + V − U (4)

where all the variables have their previous meaning. It can be noted that when β k l = 0 , the translog production function reduces to a Cobb-Douglas one.

De Borger et al. [

Therefore, a single variable as a measure of output and two variables as inputs is used for this study. The total number of employees and the total operating expenses are used as inputs and traffic revenue is used to measure the output. Total operating expenses include expenses on fuel (diesel and CNG if any), lubricants, springs, auto spare parts, tyres and tubes, batteries, general items, reconditioned items, etc. These expenses are related to the operation of buses; therefore, total operating expenses could be viewed as a proxy for physical inputs. Many studies (e.g., [

ln Y i t = β 0 + β 1 ln X 1 i t + β 2 ln X 2 i t + 1 2 β 11 ( ln X 1 i t ) 2 + 1 2 β 22 ( ln X 2 i t ) 2 + β 12 ln X 1 i t ln X 2 i t + V i t − U i t (5)

where Y is traffic revenue (Rs. in million), X 1 is total number of employees, and X 2 is total operating expenses (Rs. in million).

Another objective of this study is to identify determinants of technical efficiency. Various studies have examined the inefficiency determinants, but they have tendency to focus on the variables such as market organization, regulatory system, network characteristics, etc. which are outside the firm’s control [

U i t = δ 0 + δ 1 Z 1 i t + δ 2 Z 2 i t + δ 3 Z 3 i t + W i t (6)

where Z 1 is fleet utilization (in % age), Z 2 is profit (Rs. in million), and Z 3 is firm size (Bus-Km in million).

The estimation is carried out using the maximum likelihood methods from the statistical program Frontier Version 4.1 where the stochastic frontier i.e., Equation (5), as well as the determinants of inefficiency i.e., Equation (6), are estimated in a single stage. We sought simpler models nested in base model on the basis of the likelihood ratio (LR) test. The LR test statistic is written as:

λ = 2 [ l ( h u ) − l ( h r ) ] (7)

where l ( h u ) represents the value of the log of the likelihood function with unrestricted values of parameters and l ( h r ) represents the log of the likelihood function with maximum likelihood estimation of the parameter vector h with r restrictions. The statistic λ is distributed as a χ 2 with r degrees of freedom under the null hypothesis that the restrictions hold.

Annual data for a sample of eight UBCs from 2000-01 to 2012-13 are used for the purpose of estimation. Sample is based on availability of consistent data. Sample UBCs include Bangalore Metropolitan Transport Corporation (BMTC), Calcutta State Transport Corporation (CSTC), Delhi Transport Corporation (DTC), Ahmedabad Municipal Transport Service (AMTS), Brihanmumbai Electricity Supply and Transport Undertaking (BEST), Kolhapur Municipal Transport Undertaking (KMTU), Thane Municipal Transport Undertaking (TMTU), and Metropolitan Transport Corporation Limited (Chennai) (MTCL).

Sample UBCs are publicly owned, operate throughout their respective jurisdiction (often throughout the city), mainly provide intra-urban bus transport services, and do business in the field of passenger transportation only, but differ in size and the level of output produced. The size of the UBCs, as measured by bus-kilometers (BKm) in 2012-13, ranges from 11 million BKm for KMTU to 464 million BKm for BMTC. Fleet strength of UBCs varies drastically, from 139 buses for KMTU to 6330 buses for BMTC. Number of workers employed by UBCs also varies from 1058 for KMTU to 36,796 for BEST. In almost all respect, KMTU is the smallest UBC whereas BMTC is the largest one.

In Model 1, the estimated value of γ is greater than zero and statistically significant which implies the presence of random component of the technical

UBCs | Pass.-Km (million) | Bus-Km (million) | Pass. carried (million) | No. of employees | No. of buses held | Traffic revenue/bus-km (Rs.) | Profit/bus-km (Rs.) |
---|---|---|---|---|---|---|---|

BMTC | 21,056 | 464 | 1769 | 34,273 | 6330 | 33 | −3 |

DTC | 18,797 | 354 | 1075 | 34,376 | 5603 | 32 | −82 |

MTCL | 18,796 | 344 | 1754 | 23,519 | 3585 | 32 | −3 |

BEST | 11,446 | 265 | 1410 | 36,796 | 4259 | 49 | −24 |

AMTS | 1902 | 54 | 240 | 5428 | 1120 | 25 | −35 |

CSTC | 1218 | 26 | 108 | 5485 | 779 | 24 | −57 |

TMTU | 670 | 15 | 88 | 2313 | 313 | 44 | −25 |

KMTU | 390 | 11 | 27 | 1058 | 139 | 31 | −1 |

Variables | Parameters | Estimated MLE coefficients | |||
---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 4 | ||

Constant | β 0 | 2.011 (1.97) | 7.024 (7.14) | 3.875 (3.32) | 5.902 (3.09) |

ln(total number of employees) | β 1 | −1.711 (3.53) | −1.817 (2.87) | −2.252 (4.29) | −1.205 (1.30) |

ln(total operating expenses) | β 2 | 2.936 (5.79) | 1.494 (1.74) | 3.058 (5.49) | 1.583 (2.11) |

1/2 * [ln(total number of employees)]^{2} | β 11 | 0.566 (3.83) | 0.289 (0.64) | 0.652 (4.13) | 0.242 (0.83) |

1/2 * [ln(total operating expenses)]^{2} | β 22 | 0.323 (2.51) | 0.006 (0.007) | 0.336 (2.35) | 0.050 (0.19) |

[ln(total number of employees)]* [ln(total operating expenses)] | β 12 | −0.476 (3.38) | −0.081 (0.15) | −0.502 (3.28) | −0.139 (0.53) |

Constant | δ 0 | 2.583 (5.75) | 0.064 (0.07) | −2.881 (0.51) | 1.262 (8.27) |

Fleet utilization | δ 1 | −0.0336 (4.34) | −0.0079 (0.44) | ||

Profit | δ 2 | −0.0000234 (2.27) | −0.0000797 (0.67) | ||

Firm size | δ 3 | 0.0001 (0.14) | −0.0045 (6.72) | ||

Sigma-squared | σ 2 = σ U 2 + σ V 2 | 0.093 (3.27) | 0.254 (0.92) | 0.939 (0.61) | 0.060 (4.18) |

Gamma | γ = σ U 2 σ U 2 + σ V 2 | 0.951 (33.62) | 0.932 (1.05) | 0.996 (143.99) | 0.885 (5.58) |

Log likelihood function | 37.687 | 1.753 | 6.595 | 19.272 |

Restrictions imposed on coefficients | Value of λ | Critical χ 0.95 2 -value | Decision on H_{0} |
---|---|---|---|

δ 2 = δ 3 = 0 | 71.87 | 5.99 | Rejected |

δ 1 = δ 3 = 0 | 62.18 | 5.99 | Rejected |

δ 1 = δ 2 = 0 | 36.83 | 5.99 | Rejected |

γ = δ 0 = δ 1 = δ 2 = δ 3 = 0 | 87.14 | 11.07 | Rejected |

β 11 = β 22 = β 12 = 0 | 17.85 | 7.81 | Rejected |

inefficiency effects. Therefore, the term U i t cannot be excluded from the regression and parameter estimation by the method of ordinary least squares is inappropriate. In the MLE estimation, γ is positive and statistically significant, implying that public bus transport industry specific technical efficiency is important in explaining the total variability of yield produced. However, it may be noted that 95 percent of the variation in production is due to technical inefficiency and only 5 percent is due to the stochastic random error.

The signs of the coefficients of Model 1 reveal that total operating expenses is a key factor for production and therefore, its increase will yield positive returns. The signs of the inefficiency determinants estimated coefficients show that fleet utilization and profit negatively affect the transport operators’ technical inefficiency. That is, fleet utilization and firms’ profit assist the transport operators to be more efficient. Since fleet utilization largely depends on average age of buses and their maintenance, it is directly related to the investment made by the firms. Consequently, investment in terms of new buses and materials affect the technical efficiency of transport operators. Therefore, the greater the capital invested, the more the company is technically efficient. The negative sign of δ 2 reveals that technical efficiency can be affected by the availability of financial resources.

Most of the transport operators in our sample have faced financial losses during almost every year of the sample period; however, firms which face lesser losses are more efficient than those that have accumulated huge losses. For example, in 2012-13, losses faced by BMTC, MTCL, and KMTU was less than 10% of their traffic revenue while their average efficiency score was 0.937 whereas losses faced by DTC, AMTS, and CSTC was more than 100% of their traffic revenue and their average efficiency score was only 0.647. Model 1 result shows that technical efficiency does not vary with firm size; the hypothesis that δ 3 is equal to zero could not be rejected even at ten percent level of significance. However, the estimated coefficient of firm size in Model 4 is negative and statistically significant. This indicates that larger bus transport operators are likely to be more technically efficient than their smaller counterparts since larger firms are able to invest more in new technology and assets than the smaller ones.

Large size UBCs | Medium size UBCs | Small size UBCs | All the UBCs | |
---|---|---|---|---|

Mean | 0.829 | 0.589 | 0.881 | 0.782 |

Median | 0.895 | 0.521 | 0.906 | 0.870 |

Minimum | 0.542 | 0.352 | 0.661 | 0.352 |

Maximum | 0.981 | 0.954 | 0.951 | 0.981 |

Coefficient of variation (CoV) | 0.159 | 0.342 | 0.094 | 0.233 |

N | 52 | 26 | 26 | 104 |

efficiency are lower for medium size UBCs than their other counterparts. This suggests that, on an average, small and large size UBCs deviate less from their respective production frontier than medium size UBCs. Moreover, coefficient of variation of technical efficiency is the lowest for small size UBCs and the highest for medium size ones. The relationship of technical efficiency and coefficient of variation of the same with firm size is quite similar; neither technical efficiency nor coefficient of variation of technical efficiency has positive or negative relationship with the firm size.

BMTC | DTC | MTCL | BEST | AMTS | CSTC | TMTU | KMTU | Weighted average | |
---|---|---|---|---|---|---|---|---|---|

2000-01 | 0.869 | 0.669 | 0.699 | 0.894 | 0.700 | 0.352 | 0.912 | 0.661 | 0.743 |

2001-02 | 0.942 | 0.975 | 0.716 | 0.909 | 0.677 | 0.392 | 0.936 | 0.812 | 0.863 |

2002-03 | 0.963 | 0.608 | 0.821 | 0.932 | 0.593 | 0.408 | 0.894 | 0.899 | 0.805 |

2003-04 | 0.981 | 0.584 | 0.813 | 0.914 | 0.587 | 0.419 | 0.879 | 0.944 | 0.799 |

2004-05 | 0.967 | 0.600 | 0.767 | 0.896 | 0.575 | 0.401 | 0.883 | 0.941 | 0.791 |

2005-06 | 0.958 | 0.646 | 0.725 | 0.907 | 0.763 | 0.385 | 0.845 | 0.949 | 0.799 |

2006-07 | 0.927 | 0.570 | 0.734 | 0.902 | 0.804 | 0.426 | 0.854 | 0.907 | 0.790 |

2007-08 | 0.907 | 0.546 | 0.799 | 0.942 | 0.871 | 0.430 | 0.895 | 0.929 | 0.813 |

2008-09 | 0.867 | 0.542 | 0.844 | 0.926 | 0.909 | 0.466 | 0.904 | 0.951 | 0.815 |

2009-10 | 0.892 | 0.624 | 0.905 | 0.954 | 0.954 | 0.460 | 0.923 | 0.936 | 0.857 |

2010-11 | 0.895 | 0.741 | 0.863 | 0.954 | 0.885 | 0.417 | 0.878 | 0.940 | 0.856 |

2011-12 | 0.932 | 0.758 | 0.900 | 0.934 | 0.768 | 0.400 | 0.916 | 0.670 | 0.866 |

2012-13 | 0.915 | 0.679 | 0.945 | 0.961 | 0.850 | 0.412 | 0.698 | 0.951 | 0.863 |

Mean | 0.924 | 0.657 | 0.810 | 0.925 | 0.764 | 0.413 | 0.878 | 0.884 | 0.820 |

CoV | 0.040 | 0.178 | 0.098 | 0.025 | 0.169 | 0.073 | 0.068 | 0.117 | 0.046 |

All the UBCs except TMTU experienced improvement in their efficiency over the sample period. Two UBCs, KMTU (44%) and MTCL (35%), achieved tremendous improvement in their technical efficiency in a span of twelve years from 2000-01 to 2012-13. AMTS (21%) and CSTC (17%) also experienced significant improvement; improvement in their technical efficiency was higher than that in the industry (16%) during the sample period. Technical efficiency of BEST (7%) and BMTC (5%) improved only marginally. DTC (1%), which is the second least efficient firm in the sample, experienced negligible change in its technical efficiency from 2000-01 to 2012-13. Only one firm, TMTU (-23%), faced considerable decline in its technical efficiency. As far as fluctuation in technical efficiency is concerned, DTC was the most volatile and BEST was the least.

Finally, it is natural to ask whether the efficiency ranks of the UBCs differ significantly across the years. Specifically, we are interested in examining the temporal relationship of the cross-sectional rankings of individual UBCs’ efficiency estimates. To address this issue, we calculate Kendall’s index of rank concordance [

Year | Coefficient of variation of technical efficiency | Kendall’s index of rank concordance | χ 2 test statistic for Kendall’s index |
---|---|---|---|

2000-01 | 0.253 | 1.0000 | |

2001-02 | 0.247 | 0.7143* | 10.00 |

2002-03 | 0.265 | 0.6773* | 14.22 |

2003-04 | 0.271 | 0.6726 | 18.83 |

2004-05 | 0.274 | 0.7048 | 24.67 |

2005-06 | 0.248 | 0.7222 | 30.33 |

2006-07 | 0.236 | 0.7425 | 36.38 |

2007-08 | 0.245 | 0.7470 | 41.83 |

2008-09 | 0.234 | 0.7149 | 45.04 |

2009-10 | 0.223 | 0.6752 | 47.26 |

2010-11 | 0.214 | 0.6903 | 53.15 |

2011-12 | 0.234 | 0.6756 | 56.75 |

2012-13 | 0.241 | 0.6715 | 61.11 |

trend from 2001-02 to 2004-05 and 2010-11 till 2012-13. The second column of

K I t = Variance ( ∑ t = 0 T A R ( T E ) i t ) Variance ( τ ∗ A R ( T E ) i 0 ) (8)

where, A R ( T E ) i t is the actual rank of i^{th} UBC in technical efficiency level in year t; A R ( T E ) i 0 is the actual rank of i^{th} UBC in technical efficiency level in the initial year 0; and τ is the number of years for which data are used in constructing the index.

The value of the Kendall’s index of rank concordance ranges from zero to one. The denominator of the index is the maximum sum of ranks, which would be obtained if there is no change in rankings over time. The index is calculated for the first two sets of rankings (i.e., first two years), then for the first three sets of rankings and so on for all the sets of rankings (i.e., for all the years) [

χ 2 = τ ( N − 1 ) K I

where τ is the number of years of ranking, N is the number of UBCs, and K I is the calculated Kendall’s index of rank concordance. There are ( N − 1 ) degrees of freedom. Since critical value of chi-square at the 5% level of significance, χ 0.05 , 7 2 , is 14.07, the null hypothesis of no association between ranks of different years is rejected in all the cases except in two starred cases (see,

The efficiency of urban bus transport services has been exhaustively studied in developed countries (see, e.g., [

To examine the technical efficiency of UBCs and determinants of the same, we estimated a stochastic production frontier based on a translog production function using maximum likelihood methods. The main findings of the study can be stated as follows. First, total operating expenses is a key factor for production and therefore, any increase in related inputs (fuel, lubricants, springs, auto spare parts, tyres and tubes, batteries, etc.) will yield positive returns. Second, fleet utilization and profit negatively affect the transport operators’ inefficiency. That is, fleet utilization and firms’ profit assist the operators to be more efficient. Since fleet utilization is directly related to the investment made by the firms, investment in terms of new buses and materials would make the operators more efficient. Similarly, since profitability and efficiency is positively related and most of the transport operators in our sample face financial losses, financial discipline and minimizing the losses would lead to improvement in their technical efficiency. Estimation result shows that technical efficiency does not vary significantly with firm size. Therefore, results reveal that the technical efficiency of UBCs can be explained by their fleet utilization and profit. These two variables, in some ways, are indicators of UBCs’ managerial efficiency. Therefore, UBCs can improve their technical efficiency by improving their managerial efficiency. This finding may be of interest to policy makers and company managers. They should try to have better understanding of inefficiencies and give more consideration to efficiency determinants.

Third, we find that substantial inefficiencies, averaging between 12 to 41 percent, exist in UBCs. In general, small and large size UBCs are more efficient than their medium size counterparts. There exists no linear relationship between technical efficiency of UBCs and their size. Among the sample UBCs, BEST was the most efficient firm followed by BMTC whereas CSTC was the least efficient. In fact, CSTC was the least efficient firm during every year from 2000-01 to 2012-13 whereas BEST was the most efficient during the last four years. Moreover, all the UBCs except one experienced improvement in their technical efficiency over the sample period.

Fourth, we examined the temporal relationship of the cross-sectional rankings of individual UBCs’ technical efficiency estimates. To address this issue, we calculated Kendall’s index of rank concordance along with coefficient of variation of technical efficiency for sample period. By and large, there has been stability in ranks across UBCs in regard to their technical efficiency. This shows that the UBCs that were relatively inefficient earlier are still relatively inefficient; consequently, there is no evidence of efficiency convergence among UBCs in India.

This paper is part of a seed money project on Performance Analysis of Public Transport in Indian Cities sponsored by the Indian Institute of Management, Lucknow, India. I thank the Director and Dean (Research) of the institute for providing me with an initiation grant for this study.

Singh, S.K. (2017) Efficiency of Urban Bus Companies in India: A Stochastic Frontier Analysis. Theoretical Economics Letters, 7, 1925-1939. https://doi.org/10.4236/tel.2017.77130