A Parametric and non parametri approach for permance aprisal of indian power generating companies by ISERP ISERP

Shafali Jain et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 1, Issue No. 2, 064 - 078

A Parametric and Non-Parametric Approach for Performance Appraisal of Indian Power Generating Companies

Tripta Thakur, Associate Professor, Electrical Department, MANIT-Bhopal, India-462003 tripta_thakur@yahoo.co.in,

Abstractâ&#x20AC;&#x201D; This work aims at evaluating the productivity and

and to bridge the demand-supply gap through the introduction of competition and improvement of efficiency, but did not proceed as it planned. At this stage it is essential to have documentation of the effects of such reforms. Such documentation has been done in developed countries, however from a few case studies: the experience of developing countries remains much less researched. This documentation can be made by performance evaluation for the structural change in electric power industry. We will be able to find out the direction of the structural change in electric power industry in India by analyzing the efficiency level of power generation companies in India. Such a review of performance of existing utilities is a need for the success of any reform program. Based on efficiency analysis, benchmarks can be set, and targets for improvement may be identified. The efficiency evaluation is also necessary for generating competition and for sector regulation. Efficiency measurement can form the core for introduction of the incentive based regulatory regimes and in promoting yardstick competition amongst a number of utilities. Since the country has not reached a mature stage in the development of electricity infrastructure unlike the case of developed countries, there is a very good opportunity to learn from mistakes and adopt a suitable model for the country. Internal efficiency improvements are always win-win options for the existing utilities as benchmarking the operational and financial aspects can free up resources, which can bring down the overall resource requirement for utilities [4]. All of this would however, require application of formal benchmarking techniques to evaluate performance at regular intervals. Benchmarking is the practice of comparing indicators of performance. Benchmarking has proven to be powerful way in pressurizing utilities to provide better services to customers.

efficiency analysis of Indian electricity generation companies (GENCOs) for the time period 2002-03 to 2007-08.The performance analysis or benchmarking of generation companies is evaluated using two methodologies- a non-parametric approach to frontier analysis commonly known as Data Envelopment Analysis (DEA) and a parametric approach known as Stochastic Frontier Analysis (SFA) using panel data of six years. Both methodology evaluates and uses total factor productivity (TFP) change as a benchmarking gauge. The total TFP change is decomposed into technical change and efficiency change and the efficiency analysis is investigated taking scale effect into account so as to separate pure technical efficiency and scale efficiency. In addition, the SFA allows analyzing the effect of restructuring in Indian electric power sector. This work in the field of generation sector of power will identify whether the companies/utilities are efficient or not, create benchmark for inefficient utilities by identifying their shortcomings and set the targets. This benchmarking will pressurize the generation companies to provide better services to customers. Such an analysis would offer valuable lessons to ensure that the new structure being adopted is better than the regulatory and legislative framework designed a few decades back. Efficiency measurement can form the core for introduction of the incentive based regulatory regimes and in promoting yardstick competition amongst a number of utilities.

Arun Shandilya, Professor, Electrical Department, MANIT-Bhopal India-462003 arunshandilya@yahoo.com

Shafali Jain, Research scholar, Electrical Department, MANIT-Bhopal, India-462003 shafalijain9@yahoo.co.in,

Index

Termsâ&#x20AC;&#x201D; Benchmarking, Generation companies, Restructuring, Return to scale, Scale efficiency, Technical efficiency, Total factor productivity change. I. INTRODUCTION

The electric power industry which had been maintained as a vertically integrated system in the past, the restructuring of electric power industry in many countries in the world has been performed in the way so as to raise efficiency by introducing competition [1]. The restructuring of electric power industry in India kept pace with the worldwide trend and started with the purpose of decreasing the electricity price

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The performance evaluation can be through by a number of approaches. Among many possible efficiency measurement methods, Data Envelopment Analysis (DEA) and Stochastic Frontier analysis (SFA) are most widely used for benchmarking. DEA has been used especially for the complicated systems with lots of inputs and outputs since its introduction by Charnes, Cooper and Rhodes in 1978 based on previous work by Farrell on production efficiency. This

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II. METHODOLOGY 1) DEA

Where yit is the output of the i-th firm in the t-th year; xit denotes a (1×K) vector of inputs;

f . is a functional form; t is a time trend representing technical change;  is a vector of unknown parameters to be estimated; the vit s are random errors, to be independent and identically distributed (i.i.d) with mean zero and variance  v2 , independent of the uits; the uit s are the technical inefficiency effects which are assumed to be defined by uit  exp  t  T ui , i =1,2,……N; t=1,2,……T and η is scalar parameter which accounts for time-varying effects. The technical efficiency measure are obtained as  uit  TEit  E  exp eit   (3)

In DEA, the data are enveloped by a piecewise linear frontier in such a way that radial distances to the frontier are minimized. The basic model of DEA, the CCR model, was proposed by Charnes, Cooper and Rhodes (1978). The CCR model was formulated as a linear programming (LP) problem concerned with, say, n decision making units (DMUs), electric utilities in the present analysis, which use varying quantities and combination of inputs Xi (i=1,…s) to produce varying quantities and combinations of outputs Yj (j=1,…m).The most common form of measurement of efficiency in case of a single output and single input framework is the ratio output/input [8]. In case of multiple outputs and inputs, it is a weighted combination of outputs to weighted combination of inputs, known as virtual outputs and virtual inputs, where the weights are derived from data instead of being fixed in advance. Efficiency of each DMU is measured and hence n optimization exercises are carried out. The following problem is solved to obtain the values of input weights (vi) and output weights (ur) as variables: max    r ur yro  o  i vi xio  u1 y1 j  ................us ysj s.t. 1 v1 x1 j  ................vm xmj (1)

A stochastic production function defined by Battese and Coelli (1995) In yit   f xit ,t ,    vit  uit (2)

paper presents a case study which provides productivity and efficiency analysis of generation utilities for the period 2003 to 2008, so that they can rank themselves, identify their shortcomings, set targets and tries to achieve those targets.

where j=1,…,n v1, v2,…. vm ≥0, u1, u2,…. us ≥0, The constraints imply that the ratio of ―virtualoutput‖ to ―virtualinput‖ should not exceed 1 for every DMU. The objective is to obtain weights vi and ur that maximize the ratio for DMUo. The optimal objective value θ* is at most 1. However, multiple solutions might exist for the above problem. Hence it is transformed into a linear programming problem using transformation developed by Charnes and Cooper. To allow for variable returns to scale Banker, Charnes and Cooper (1984) added the convexity constraint to the optimization problem and proposed variable return model (BCC).

where eit = vit - uit is the total error term which can be used to calculate the efficiency change component.

3) Malmquist Productivity Index (MPI)

The DEA and SFA techniques can be used to calculate Malmquist Index of productivity change over time, assuming the underlying technology is constant returns to scale (CRS) (Coelli et al., 1998). The Malmquist total factor productivity (TFP) index measures the TFP change between two data points by calculating the ratio of the distances of each point relative to a common technology. The distance function in terms of the above analysis can be defined as {Dt(xt,yt)}-1 = θt 2.1 SFA Model Specification The translogarithmic and the cobb-douglas production functions are the two most common functional forms, which have been used, in empirical studies on production, including frontier analysis [13] The cobb-douglas and translog production function models are defined in equations (4) and (5)

ln(Yit )  0  1 ln( X1it )   2 ln( X 2it )  t t vit uit (4)

2) SFA

ln(Yit )   0  1 ln( X 1it )   2 ln( X 2it )  11[ln( X 1it )]2 

The stochastic Frontier approach (SFA) specifies a functional form of the cost, profit or production relationship among inputs, outputs, and environmental factors and allow for random error. Hence it is also called parametric approach. It gives composite error model decomposed into two terms, a symmetric component representing statistical noise and an asymmetric one representing inefficiency.

 22[ln( X 2it )]2  12[ln( X 1it ) ln( X 2it )]  1t ln( X 1it )t 

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 2it ln( X 2it )t   t t   tt t 2 v it uit

(5)

The above model does not include the environmental variables. As pointed out by Coelli, Perelman and Romano (1999), measuring net efficiency is an important matter as it allows one to predict how companies would be ranked if they were able to work in equaling environments. Therefore, the

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most general function to be estimated including six additional environmental variables. After including environmental variables, the model becomes

ln(Yit )   0  1 ln( X 1it )   2 ln( X 2it )   t t  1 ln( Z1it ) 

 2 ln( Z 2it )   3 ln( Z 3it )   4 ( REGULATION)   5 ( FUELTYPE )  vit  uit

(7)

ln(Yit )   0  1 ln( X 1it )   2 ln( X 2it )  11[ln( X 1it )]2 

 22[ln( X 2it )]2  12[ln( X 1it ) ln( X 2it )]  1t ln( X 1it )t   2it ln( X 2it )t   t t   tt t 2  1 ln( Z1it )   2 ln( Z 2it )   3 ln( Z 3it )   4 ( REGULATION )   5 ( FUELTYPE ) v it uit

χ2=-2[L(H0)–L(Ha)] (9) The χ2 has a mixed chi-square distribution with the degree of freedom equal to the number of parameters excluded in the restricted model; L (H0) is the log – likelihood value of the restricted model. While L (Ha) is the Log- likelihood value of the un-restricted model. Maximum likelihood estimation procedure is used to estimate the parameters of the stochastic frontier equation 1. The parameters to be estimated include β and variance parameters such as σ2 = σu2 + σv2 and γ = σu2 /σ2. Where σ2 is the sum of the error variance, while γ measures the total variation of output from the frontier attributed to the existence of random noise or inefficiency as γ is bounded between zero and one, where if γ = 0, inefficiency is not present, hence deviation from the frontier is entirely due to random noise and if γ = 1, indicates that the deviation is due entirely to inefficiency (Battese & Coelli, 1995). The FRONTIER 4.1 version (Coelli, 1996) was used to obtain the maximum likelihood estimates (MLE) for the study.

(8)

constant return to scale and fixed elasticity of output with respect to production inputs. The generalized likelihood ratio test, which is defined by the test statistic, chi-square (χ2) is defined as:

Where ln = logarithm Yit = units generated by the power station (GWh)

X 1it = installed capacity (MW) X 2it = coal consumption (MT) Z1it = plant load factor (%) Z 2it = Energy losses (GWh) Z 3it = Per capita consumption (GWh) T = time trend  i and  i are unknown parameters to be estimated.

The two dummies are included in the namely, REGULATION and FUELTYPE .

2.3 Input-output selection and data source

model

otherwise 0; 2.2 Hypothesis testing

REGULATION  1, if utility is unbundled, otherwise 0; FUELTYPE  1, if GENCO uses coal as primary fuel,

As suggested by Coelli (1996), the alternative models would be estimated and the preferred model would be selected using Likelihood Ratio (LR) test. The generalized likelihood ratio test was conducted on certain hypotheses relating to the estimated parameters such as: (1) The production function is specified by a Cobb-Douglas functional form (that is, H0: βjk =0); (2) There is absence of inefficiency effects that is there is stochastic effects in the production (H0: γ = 0); (3) The half normal model is adequate representation of the data (H0: µ = 0); (4) Technically inefficiency effects are absent from the production function model i.e. model is equivalent to the average response function (Full Frontier Model), which can be efficiently estimated by ordinary least square (OLS) regression (H0: γ = δ0=δ1= δ2= δ3= δ4= δ5= δ6= 0); (5) Panel data is not applicable to the model (H0: η = 0). The final hypothesis although not tested with generalized likelihood ratio test but based on the assumption, that the selected Cobb-Douglas functional form is characterized by

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There can be a number of input/output variables for evaluating the efficiency of electric utilities. The most important job in this efficiency analysis is the right selection of inputs and outputs. No universally applicable rational template is available for selection of variables. In the context of efficiency measurement, the inputs must reflect the resources used and the outputs chosen must represent the activity levels of the utilities. A study of standard literature reveals significant insights into the choice of variables. The most widely used variables based on international experience have been outlined in the literature. Input variables chosen has been shown in table I. DEA and SFA were used to derive the benchmarks based on the comparison of the 30 generation companies (GENCOs) in which 8 entities were the SEBs, 7 entities comprised various electricity departments (EDs), and 15 entities comprised the unbundled state-owned electric utilities (SOEUs). The physical data for various states were obtained for the different years from ―Gen eral Review‖ published by Central Electricity Authority (CEA) [10].

3.1 DEA based MPI Following Fare et al. (1994), the Malmquist input oriented TFP change index between period s and period t is given by: 1/ 2

mi ( ys , xs , yt , xt ) 

dit  yt , xt   dis  yt , xt  dis  ys , xs     dis  yt , xt   dit  yt , xt  dit  ys , xs  

where the first ratio on the right hand side measured change in efficiency between periods s and t. The remaining part of the index in the equation measures technical change, so that tfpch = effch × techch

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effch 

d it  yt , xt  d is  yt , xt 

 d s  y , x  d s  y , x  techch   it t t  it s s   d i  yt , xt  d i  ys , xs  

1/ 2

TABLE I PERFORMANCE PARAMETERS DEA model Inputs

SFA model Output

Installed capacity (MW)

Inputs

Units generated (GWh)

Coal consumption (MT)

Output

Installed capacity (MW)

Units generated (GWh)

Coal consumption (MT)

Environmental variables Plant load factor (%) System losses (GWh)

exhibited decreasing returns to scale suggesting that the utilities exceeded their most productive scale size. This outcome supports the unbundling policy of the GoI, as envisaged in the Electricity Act. The management of the utilities, in general, does not have control over their scale of operation. Therefore, it is quite appropriate to assess efficiency relative to the VRS frontier. So, the technical efficiency of utilities is measured against the VRS frontier. To explore the scale effects, the BCC formulation that assumes a VRS by taking into consideration the sizes of utilities was employed. This formulation ensures that similar sized utilities are benchmarked and compared with each other. The average technical efficiency is 0.772. The results indicate the possibility of restructuring of several utilities that display low scale efficiencies (Table III). The low value of scale efficiencies and the fact that these utilities exhibit decreasing returns to scale indicate that these have considerable scope for improvements in their efficiencies by resizing (downsizing) their scales of operations to the optimal scale defined by more productive utilities in the sample. 2) SFA Results

where, tfpch signifies change in total productivity, which is caused by the joint influence of effch, i.e. the change in efficiency from period s to t and techch, the geometric mean of the shift in technology between the two periods, evaluated at xt and also at xs. The value of the indices greater than one signifies increase in productivity.

Per capita consumption (GWh) Dummy Regulation Dummy Fuel type

2.3.2 SFA based MPI Efficiency change between two adjacent period s and t for the ith firm /utility can be obtained as effch= TEit/TEis and technical change index between period s and t for the ith firm can be calculated directly from the estimated parameters.  f xis , s,    f xit ,t ,    techch  1   1   s t    

1/ 2

III. ANALYSIS OF THE RESULTS

1) DEA results CCR model measures the overall efficiency which is the efficiency measured against the CRS frontier. The results are presented in Table III. It is evident from Table II that Indian GENCOs display significant variations in efficiency levels. The total efficiency had a mean score of 0.6 for all the utilities and almost half of the utilities lie below this average value. Only two utilities turned out to be the best practices and the remaining 28 utilities exhibited varying degree of inefficiencies. It is also observed that all the companies, with the exception of the best practices and one utility (Nagaland),

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2.1 Hypotheses test results The results of the likelihood ratio tests are presented in Table III The first hypothesis is conducted to find whether the Cobb Douglas is the right functional form. The first hypothesis that the Cobb-Douglas functional form was the best-fit functional form for the data was accepted. The second hypothesis that there was absence of inefficiency effects in the production

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TABLE II RESULTS OF DEA MODEL

Technical Efficiency (VRS)

Utility

Total Efficiency (CRS)

Haryana

0.569

0.802

0.709

DRS

16 9 8

Himachal Pradesh

0.97

16 18

Jammu & Kashmir

0.588

18 16

Punjab

0.668

0.978

0.683

Rajasthan

0.701

0.981

0.714

Uttar Pradesh

0.552

0.773

0.714

Uttrakhand

0.787

Delhi

0.703

Gujarat

0.713

Madhya Pradesh

0.532

Chhattisgarh

0.51

Maharashtra

0.616

Goa

0.971

Andhra Pradesh

0.566

Karnataka

0.53

Kerala

Scale Efficiency (SE)

Returns to Scale (RTS)

Benchmarks

16 9 8

DRS

9 18

DRS

9 18

16 18

DRS

0.713

DRS

0.745

0.714

DRS

9 18

0.713

0.715

DRS

9 18

0.616

DRS

0.971

16 18

0.97

0.584

DRS

9 15 12

0.53

DRS

T DRS

S.No

Tamil Nadu

0.503

0.962

0.523

DRS

15 12

Puducherry

Bihar

0.067

0.124

0.543

DRS

16 8 18

Jharkhand

0.361

0.516

0.698

DRS

16 9 8

Orissa

0.548

0.929

0.59

DRS

8 16 9

West Bengal

0.517

0.724

0.714

DRS

9 18

Sikkim

0.449

16 18

Assam

0.86

18 16

Manipur

0.063

16 18

Meghalaya

0.741

16 18

Nagaland

0.409

IRS

Tripura

0.934

16 18

Arunachal Pradesh

0.438

16 18

Mizoram

0.158

18 16

Mean

0.6

0.772

0.795

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TABLE III HYPOTHESES TEST RESULTS χ2-critical value

χ2-calculated value

H0: βjk =0

12.59

11.58

H0: Accepted

H0: γ = 0

5.138

204.4

H0: Rejected

H0: µ = 0

7.045

213.64

H0: Rejected

H0: γ = δ0=δ1= δ2= δ3= 0

1.37

-366.16

H0: Rejected

H0: η = 0

3.84

547.8

H0: Rejected

companies. Nagaland is having the highest SFA based TFP change and Manipur is having the highest DEA based TFP change, though these companies are technically as well as scale inefficient companies. The comparative analysis of average efficiencies is shown in fig 1 and the comparative productivity results are shown in fig 2. There are differences between the SFA and DEA results. In case of DEA results of productivity, 21utilities are having TFP change value greater than 1 that means showing technical progress. While in SFACD form, 22 (almost same) utilities have TFP change greater than 1. SFA translog form shows that almost all the generation companies are having TFP change of value greater than 1.

process was rejected, while the third hypothesis that the half normal representation is correct distributional form for the data is also rejected. The fourth hypothesis that the inefficiency effects are absent from the production function model i.e. model is equivalent to the average response function (Full frontier model), which can be efficiently estimated by ordinary least square (OLS) regression is also rejected for the model. The last hypotheses that the panel data is not applicable for the model is also rejected that means the panel data can be applied to the model.

Decision

Null Hypotheses

3.2 Parameter estimation and interpretation

The estimates of the stochastic frontier production function for cobb-douglas (CD) and translog (TR) form are presented in Table IV. The estimated coefficients of the explanatory variables showed that installed capacity and coal consumption had positive effect on the change in output. This means an increase in the installed capacity and coal consumption increases plant output and vice-versa. Both coefficients are significant at 1% level and 5% of significance respectively for the accepted cobb-douglas form. The negative variables of the inefficient function mean positive impact on technical efficiency, and vice-versa. All environmental factors are significant except dummy regulation. The energy losses has unexpected negative sign, so here we can conclude that in this particular analysis the inefficiency cannot be reduced by reducing the energy losses. The output elasticities are shown in Table VII. It is clear that the production elasticity is dominated by the capital or installed capacity elasticity.

3.3 Comparative efficiency and productivity analysis The yearly DEA efficiencies for CRS and VRS, and SFA efficiencies for both CD and TR models are shown in table V. The average efficiencies are also shown for the GENCOs in table. It is quite clear that DEA VRS > SFA TR > SFA CD > DEA CRS. Gujarat generating company is having the highest average efficiency over the period of six years with CRS, VRS, SFA CD and SFA TR of 0.667, 1, 0.953 and 0.956 respectively. The mean CRS, VRS, SFA CD and SFA TR efficiencies are 0.541, 0.730, 0.627 and 0.647 as seen from Table VI. Table VIII shows TFP changes for the generating ISSN: 2230-7818

IV CONCLUSIONS

From the comparison of SFA and DEA model, the average CRS TE, VRS TE and SFA TE efficiency scores are 0.541, 0.73 and 0.627 respectively. We can conclude that VRS TE > SFA TE> CRS TE. Himachal Pradesh is having the highest average CRS efficiency score of 0.862 and Gujarat is having the highest SFA efficiency score of 0.953 and Mizoram is having least CRS and SFA efficiency score. For the SFA model, the production elasticities are dominated by installed capacity elasticity which is equal to 0.817 while the fuel elasticity is 0.1144. The RTS value is 0.9314 indicating that the utilities are exhibiting decreasing returns to scale (DRS). This supports unbundling policy of government of India. The γ parameter is 0.998 that means 99.8 % deviations are due to inefficiency effects and 0.2 % is noise effects. REFERENCES [1] [2]

[3] [4]

Tripta Thakur, S.G. Deshmukh, and S.C. Kaushik, .― Efficiency Evaluation of The State Owned Electric Utilities In India‖, Energy Policy, 34(17), 1187-1198, 2007. D.K. Jha & R. Shrestha, ―Measuring Efficiency of Hydropower plants in Nepal using Data Envelopment Analysis‖ , IEEE Transactions on Power Systems, Vol. 21 , No 4 ,pp 1502-1511, November 2006. M.Saleem, ― Technical Efficiency in Electricity Sector of PakistanThe impact of Private and Public Ownership.‖, PhD. Tripta Thakur, S.G.Deshmukh, S.C.Kaushik, and Mukul Kulshrestha, ― Impact assessment of the Electricity Act 2003 on the Indian power sector.‖, Energy Policy, vol. 33, no. 9, pp. 1187-1198, 2005.

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MoP , 2009. Ministry of Power website, http://powermin.nic.in/ K.P.Kannan, N.V.Pillai, 2000. Plight of the Power Sector in India: SEBs and Their saga of inefficiency. Working Paper No. 308, November 2000. Centre For Development Studies, thiruvananthapuram.

[7]

P.Chitkara, ― A Data Envelopment analysis Approach to Evaluation of Opeartional Inefficiencies in Power Generating Units: A Case Study of Indian Power Plants.‖ IEEE Transactions on Power Systems, Vol. 14, no. 2, May 1999. B. Golany, Y. Roll, and D. Rybak,‖Measuring Efiiciency of Power Plants in Israel by Data Envelopment Analysis.‖ IEEE Transactions on Engineering Managrment, vol. 41, no. 3, pp. 291-301, Aug. 1994. A. Vaninsky, ― Efficiency of electric power generation in the United States: Analysis and forecast based on data envelopment analysis.‖, Energy Economics, vol. 28, pp. 326-338, 2006. All India Electricity Statistics , General Review , Central Electricity Authority, New Delhi, 2004-2009. K. sarica and I. Or, ― Efficiency assessment of Turkish power plants using data envelopment analysis.‖ ,Energy, vol. 32, pp. 1484-1499, 2007. R. F. Lovado, ― Benchmarking the efficiency of Philippines Electric Cooperatives Using Stochastic Frontier Analysis and Data Envelopment Analysis‖,Third East West Center International Graduate Student Conference, Hawaii, Feb. 2004. T. Coelli, D.S. Prasado Rao, and George E. Battese, ― An Introduction to Efficiency and Productivity Analysis.‖ W.W. Cooper and K. Tone, ― Measures of inefficiency in data envelopment analysis and stochastic frontier estimation.‖, European Journal of Operational Research, 99(72-88), 1997. A. Charnes, W.W. Cooper and E. Rhodes, ― Mesauring the efficiency of decision making units‖, European Journal of Operational Research, vol. 2, no. 6, pp 429-444. R. Meenakumari and N. Kamraj, ― Measurement of Relative Efficiency of State Owned Electric Utilities in India Using Data Envelopment analysis.‖, Modern Applied Science, vol. 2, no. 5 , pp 6171, Sep 2008. V.K.Yadav, N.P. Padhy, and H.O.Gupta, ― Assessing the performance of electric utilities of developing countries: An intercountry comparison using DEA‖, IEEE Transaction. Tripta Thakur, ― Benchmarking study for the Indian Electric Electric utilities Data Envelopment Analysis‖, IEEE Transactions on Power Systems, pp 545-549, 2005.

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TABLE IV SFA PARAMETER ESTIMATIONS

Variables

Parameters

Cobb Douglas (CD)

Translog (TR)

Coefficient

t-ratio

Coefficient

t-ratio

Production factors β0

0.7578*

4.83

0.8429**

2.98

In(Installed capacity)

β1

0.8170*

52.426

0.8399*

14.545

In(Coal consumption)

β2

0.1144*

In(Installed capacity)*ln(installed capacity)

β11

In(coal consumption)*ln(coal consumption)

β22

In(Installed capacity)*ln(coal consumption)

β12

In(Installed capacity)*time

β1t

time time*time

5.398

β2t βt

0.0048

0.648

βtt

Inefficiency factors Intercept In(Plant load factor) In(Energy losses) In(Per capita consumption)

2.183

0.0703**

2.971

0.0009

-0.561

0.0377**

-2.36

0.0051

-0.048

-0.0022

0.43

0.0383

1.13

-0.0051

1.055

δ0

-4.8666*

-4.621

-5.1128*

-5.64

δ1

-0.9471**

-3.215

-0.8651*

-5.392

δ2

-1.1250*

-6.203

-1.1422*

-6.256

δ3

3.0131*

-6.059

-3.0584*

-10.103

δ4

0.0576**

2.214

0.0353

1.335

δ5

-0.5815*

-3.445

-7.09**

-2.483

σ2

2.1342*

5.548

2.1275*

5.748

0.9983*

993.63

0.9987*

1418.78

LLF

-63.34

Dummy (Regulation)

0.0873**

In(coal consumption)*time

Intercept

Dummy (Fuel type) Variance factors Sigma squared Gamma

-57.55*

Loglikelihood function

Note: This value is obtained from table 1 of Kodde and Palm (1986) which gives critical values for the tests of null hypotheses. *,**,*** Estimate is significant at 1%, 5%, 10% level of significance respectively

ISSN: 2230-7818

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TABLE V SFA AND DEA EFFICIENCIES

2002-03

1 2 3

Utility

Haryana

DEA CRS 0.605

Himachal Pradesh Jammu & Kashmir

0.755

DEA VRS

SFA CD

SFA TR

DEA CRS

DEA VRS

SFA CD

SFA TR

0.917

0.888

0.91

0.644

0.915

0.928

0.857

0.866

0.927

0.755

0.212

2003-04

0.212

0.608 0.158

0.67 0.18

Punjab

0.607

0.995

0.954

0.96

Rajasthan

0.687

0.961

0.97

Uttar Pradesh

0.596

0.915

0.879

0.91

Uttrakhand

0.808

0.83

Delhi

0.442

Gujarat

0.624

Madhya Pradesh

0.615

Chhattisgarh

0.692

Maharashtra

0.593

Goa

0.864

Andhra Pradesh

0.541

Karnataka

0.498

Kerala

0.964

0.965

0.597

0.947

0.892

0.905

0.583

0.933

0.854

0.875

0.955

0.971

0.621

0.721

0.64

0.907

0.901

0.95

0.96

0.605

0.997

0.936

0.932

0.896

0.922

0.94

0.576

0.909

0.871

0.876

0.943

0.95

0.667

0.918

0.907

0.941

0.92

0.594

0.944

0.914

0.84

0.586

0.565

0.574

0.864

0.806

0.871

0.858

0.86

0.499

0.893

0.81

0.784

0.859

0.785

0.79

0.506

0.836

0.812

0.737

0.59

0.677

0.549

0.889

0.87

0.818

0.793

0.752

0.957

0.96

0.952

0.934

0.122

0.229

0.193

0.19

0.088

0.15

0.143

0.139

0.295

0.498

0.47

0.321

0.511

0.496

0.489

Bihar

Jharkhand

West Bengal

0.42

0.531

Puducherry

Orissa

0.361

0.866

Tamil Nadu

0.396

0.626

0.462

0.396

0.857

S.No

0.314

0.473

0.466

0.48

0.468

0.856

0.745

0.746

0.566

0.872

0.853

0.88

0.58

0.93

0.854

0.873 0.119

0.144

0.14

0.122

0.124

Assam

0.399

0.321

0.35

0.293

0.291

0.32

Manipur

0.003

Meghalaya

0.734

0.548

0.66

0.619

0.543

0.647

Sikkim

0.144

Nagaland

0.096

0.1

0.09

0.1

0.102

0.09

Tripura

0.582

0.443

0.53

0.72

0.625

0.732

Arunachal Pradesh

0.088

0.082

0.08

0.102

0.105

0.099

Mizoram

0.036

0.04

0.038

0.04

0.037

Mean

0.508

0.697

0.838

0.62

0.509

0.722

0.636

0.641

ISSN: 2230-7818

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2004-05

S.No

Utility

2005-06

DEA CRS

DEA VRS

SFA CD

SFA TR

DEA CRS

DEA VRS

SFA CD

SFA TR

0.456

0.667

0.665

0.6695

0.659

0.857

0.87

0.881

Haryana

Himachal Pradesh

0.836

0.9107

0.805

0.894

Jammu & Kashmir

0.362

0.275

0.3225

0.421

0.307

0.369

Punjab

0.553

0.856

0.898

0.8763

0.682

0.932

0.962

0.961

Rajasthan

0.649

0.951

0.933

0.9439

0.77

0.962

0.973

Uttar Pradesh

0.524

0.769

0.76

0.7723

0.538

0.724

0.737

Uttrakhand

0.681

0.7174

0.977

0.754

0.814

Delhi

0.693

0.951

0.9491

0.726

0.969

0.931

0.92

Gujarat

0.68

0.97

0.9714

0.706

0.959

0.961

Madhya Pradesh

0.567

0.829

0.847

0.8446

0.558

0.725

0.74

0.754

Chhattisgarh

0.695

0.934

0.9203

0.83

0.968

Maharashtra

0.592

0.935

0.8977

0.623

0.919

0.879

Goa

0.914

0.9271

0.936

0.949

Andhra Pradesh

0.545

0.974

0.878

0.8443

0.528

0.863

0.799

0.763

Karnataka

0.468

0.78

0.7448

0.488

0.779

0.767

0.729

Kerala

0.858

0.77

0.639

0.884

0.759

Tamil Nadu

0.457

0.84

0.786

0.7347

0.465

0.814

0.757

0.7

Puducherry

0.946

0.918

0.9

0.854

Bihar

0.041

0.077

0.068

0.0669

0.04

0.063

0.066

0.067

Jharkhand

0.302

0.439

0.456

0.4456

0.351

0.464

0.49

0.481

Orissa

0.524

0.981

0.823

0.8197

0.457

0.63

0.66

0.661

West Bengal

0.613

0.934

0.9332

0.696

0.983

Sikkim

0.201

0.199

0.1899

0.1

0.095

0.096

Assam

0.171

0.36

0.347

0.3645

0.194

0.351

0.333

0.357

Manipur

0.004

0.0037

0.006

0.005

0.006

Meghalaya

0.753

0.571

0.6844

0.616

0.46

0.559

Nagaland

0.015

0.0132

0.015

0.014

0.013

Tripura

0.881

0.676

0.7944

0.709

0.532

0.64

Arunachal Pradesh

0.007

0.072

0.07

0.132

0.117

0.125

Mizoram

0.016

0.014

0.0147

0.027

0.024

0.026

0.52

0.732

0.631

0.63

0.438

0.705

0.624

0.63

Mean

ISSN: 2230-7818

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2006-07 S.No

Utility

2007-08

DEA CRS

DEA VRS

SFA CD

SFA TR

DEA CRS

DEA VRS

SFA CD

SFA TR

Haryana

0.664

0.894

0.9139

0.569

0.802

0.774

0.809

Himachal Pradesh

0.93

0.728

0.8194

0.97

0.874

0.947

Jammu & Kashmir

0.579

0.411

0.5025

0.588

0.475

0.57

Punjab

0.63

0.99

0.945

0.9455

0.668

0.978

0.954

0.965

Rajasthan

0.643

0.976

0.9

0.9189

0.701

0.981

0.938

0.962

Uttar Pradesh

0.551

0.825

0.765

0.7852

0.552

0.773

0.745

0.782

Uttrakhand

0.869

0.682

0.7121

0.787

0.741

0.727

Delhi

0.646

0.877

0.8721

0.703

0.898

0.908

Gujarat

0.651

0.942

0.9434

0.713

0.962

0.973

Madhya Pradesh

0.573

0.867

0.799

0.8185

0.532

0.745

0.733

0.765

Chhattisgarh

0.684

0.906

0.8995

Maharashtra

0.589

0.906

0.8662

Goa

0.929

0.9624

Andhra Pradesh

0.51

0.919

0.798

0.7681

Karnataka

0.551

0.882

0.8529

Kerala

Tamil Nadu

Puducherry

Bihar

0.021

Jharkhand

0.429

Orissa

0.552

West Bengal

0.673

Sikkim

0.105

Assam

0.375

Manipur

0.016

Meghalaya

0.476

Nagaland

Tripura

29 30

0.485

0.713

0.716

0.733

0.912

0.898

0.971

0.772

0.865

0.566

0.97

0.798

0.848

0.53

0.882

0.826

0.889

0.7952

0.889

0.918

0.948

0.817

0.7581

0.503

0.962

0.817

0.785 0.851

0.924

0.9186

0.924

0.041

0.0453

0.067

0.124

0.041

0.12

0.653

0.608

0.6043

0.361

0.516

0.608

0.511

0.982

0.825

0.8374

0.548

0.929

0.825

0.838

0.905

0.9322

0.517

0.724

0.905

0.747

0.105

0.1

0.1044

0.449

0.1

0.423

0.375

0.269

0.323

0.86

0.269

0.888

0.016

0.015

0.0163

0.063

0.015

0.059

0.476

0.342

0.4351

0.741

0.342

0.754

0.131

0.128

0.1215

0.409

0.128

0.376

0.807

0.584

0.7363

0.934

0.584

0.921

Arunachal Pradesh

0.169

0.142

0.1623

0.438

0.142

0.415

Mizoram

0.028

0.024

0.0277

0.158

0.024

0.15

0.544

0.752

0.632

0.65

0.6

0.772

0.632

0.71

0.046

Mean

0.51

0.616

ISSN: 2230-7818

TABLE VII SFA ELASTICITIES

With respect to

Estimated elasticity

Installed capacity (E1)

0.817

Fuel (E2) Time Returns to scale

0.114 1.0048 0.931

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TABLE VI SFA AND DEA AVERAGE EFFICIENCIES S.No

Utility

DEA CRS

DEA VRS

SFA CD

SFA TR

Haryana

0.588

0.874

0.834

0.852

Himachal Pradesh

0.862

0.919

0.786

0.862

Jammu & Kashmir

0.523

0.426

0.331

0.395

Punjab

0.584

0.959

0.946

0.945

Rajasthan

0.66

0.976

0.931

0.946

Uttar Pradesh

0.596

0.823

Uttrakhand

0.866

0.939

Delhi

0.68

0.948

Gujarat

0.667

Madhya Pradesh

0.595

0.829

Chhattisgarh

0.634

Maharashtra

Goa

0.81

0.77

0.796

0.867

0.865

0.953

0.956

0.819

0.833

0.952

0.898

0.896

0.636

0.926

0.897

0.841

0.904

0.82

0.853

Andhra Pradesh

0.61

0.915

0.824

0.811

Karnataka

0.514

0.94

0.822

0.793

Kerala

0.891

0.808

0.709

Tamil Nadu

0.573

0.875

0.81

0.767

0.788

Puducherry

0.911

0.934

0.905

Bihar

0.223

0.115

0.092

0.105

Jharkhand

0.291

0.514

0.521

0.5

Orissa

0.46

0.809

0.724

0.73

West Bengal

0.568

0.921

0.906

0.891

Sikkim

0.286

0.187

0.127

0.179

Assam

0.366

0.44

0.305

0.434

Manipur

0.047

0.016

0.008

0.015

Meghalaya

0.555

0.657

0.468

0.624

Nagaland

0.228

0.081

0.118

Tripura

0.657

0.772

0.574

0.725

Arunachal Pradesh

0.252

0.156

0.11

0.159

Mizoram Mean

0.068 0.541

0.051 0.730

0.027 0.627

0.048 0.647

IJ ISSN: 2230-7818

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Fig 1 S FA and DEA Efficiencies DEA-TFPCH

S FA (CD)-TFPCH

S FA (TR)-TFPCH

2 .5 2 .1 1.7 1.3

Efficiency Score

2 .9

0 .9

0 .5

Utility

Fig 2 SFA and DEA TFP changes

DEA CRS

SFA CD

SFA TR

TFP changes

0 .8

DEA VRS

0 .6

0 .4

0 .2

Utility

ISSN: 2230-7818

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TABLE VIII SFA AND DEA TFP CHANGES

DEA S.No

Efficienc y Change

Utility

SFA CD

SFA TR

Technical Change

TFP Change

Efficiency Change

Technical Change

TFP Change

Efficienc y Change

Technica l Change

TFP Chang e 1.024

Haryana

0.988

0.987

0.992

1.0048

0.997

0.996

1.028

Himachal Pradesh

1.051

1.038

1.092

1.0048

1.097

1.065

1.053

1.121

Jammu & Kashmir

1.226

1.034

1.268

1.332

1.0048

1.338

1.195

1.055

1.2617

Punjab

1.019

1.001

1.0048

1.006

1.024

1.030

Rajasthan

1.004

0.997

1.0048

1.001

1.025

1.026

Uttar Pradesh

0.985

0.984

0.969

1.0048

0.973

0.986

1.022

1.008

Uttrakhand

0.953

1.039

0.991

0.999

1.0048

1.003

1.007

1.051

1.059

Delhi

1.097

1.082

1.0048

1.087

1.054

1.036

1.092

Gujarat

1.027

1.003

1.0048

1.008

1.009

1.020

1.028

Madhya Pradesh

0.971

0.957

1.0048

0.962

0.979

1.025

1.003

Chhattisgarh

0.941

0.951

1.0048

0.955

0.97

1.030

1.000

Maharashtra

1.008

1.007

0.994

1.0048

0.999

1.001

1.015

1.016

Goa

1.023

1.013

1.036

1.033

1.0048

1.038

1.025

1.067

1.094

Andhra Pradesh

1.009

1.002

1.0048

1.007

1.005

1.020

1.024

Karnataka

1.012

1.017

1.0048

1.022

1.011

1.023

1.034

Kerala

1.096

1.059

1.0048

1.064

1.048

1.115

Tamil Nadu

0.989

0.987

1.0048

0.992

0.995

1.019

1.014

Puducherry

0.988

1.0048

0.993

0.997

1.069

1.066

Bihar

0.888

0.887

1.109

1.0048

1.114

1.023

1.043

1.067

Jharkhand

1.041

1.024

1.0048

1.029

1.02

1.031

1.052

Orissa

1.117

1.146

1.0048

1.152

1.084

1.030

1.116

West Bengal

0.982

0.973

1.0048

0.978

0.988

1.024

1.011

Sikkim

1.256

0.999

1.254

1.586

1.0048

1.594

1.288

1.068

1.375

Assam

Manipur

Meghalaya

Nagaland

Tripura

29 30

1.051

1.225

1.266

1.0048

1.272

1.164

1.051

1.223

1.818

1.007

1.83

2.009

1.0048

2.019

1.574

1.067

1.680

1.002

1.025

1.028

1.05

1.0048

1.055

1.033

1.060

1.095

1.337

2.864

1.0048

2.877

1.816

1.070

1.944

1.099

1.023

1.124

1.118

1.0048

1.123

1.079

1.062

1.145

Arunachal Pradesh

1.379

1.001

1.381

1.469

1.0048

1.476

1.266

1.067

1.352

Mizoram Mean

1.347

1.006

1.354

1.898

1.0048

1.907

1.434

1.067

1.530

1.354

1.2

1.0048

1.205

1.1

1.04

1.154

1.166

ISSN: 2230-7818

1.347

1.006

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