- 1 -

Benchmarking

With An Application to Electricity Distribution

GAP Workshop14 December 2005, Berlin

Astrid Cullmann , DIW Berlin

E E²

- 2 -

Agenda

1. Overview - Benchmarking Methodologies

2. Application in the Electricity Sector

3. Transfer to the Airports

Literature

- 3 -

Overview of Benchmarking Techniques

Benchmarking

PartialApproaches

(one-dimensional)

Multi-dimensional Approaches

Frontier Approaches Average Approaches

PerformanceIndicators

Parametric ParametricInduced

ApproachNon-Parametric

DataEnvelopment

Analysis(DEA)

StochasticFrontierAnalysis

(SFA)

OrdinarayLeast Squares

(OLS)

Total FactorProductivity

(TFP)

Stochastic DEA

(SDEA)

CorrectedOrdinary

Least Squares(COLS)

ModifiedOrdinary

Least Squares(MOLS)

- 4 -

Data Envelopment Analysis (DEA) – (I)

Ye.g. units sold

Xe.g. labour, network size

0

C B A

Efficiency FrontierDEA CRS

Efficiency FrontierDEA VRS

,max ( ´ / ´ ),

´ / ´ 1, 1,2,...

, 0

u v i i

i i

u y v x

u y v x j N

u v

,max ( ,́ ),

´ 1

´ ´ 0, 1,2...,

, 0,

i

i

i i

y

v x

y x j N

,min ,

0

0

0

i

i

y Y

x X

- 5 -

Data Envelopment Analysis (II)

Advantages:

- Identifies a set of peer firms (efficient firms with similar input and output mixes) for each inefficient firm.

- Can easily handle multiple output.

- Does not assume a functional form for the frontier or a distributional form for the inefficiency error term.

Drawbacks:

- May be influenced by noise.

- Traditional hypothesis tests are not possible.

- Requires large sample size for robust estimates, which may not be available early on in the life of a regulator.

→ Sensitivity Analysis by Bootstrapping

- 6 -

Stochastic Frontier Analysis (SFA) (I)

X

PSFA = f2(Y)

Efficiency of firm ESFA = EF/BF

0

POLS = α+f1(Y)

Y

B

F

E

SFA Assumption about the residuals

- vi are random variables

assumed to be iid, independent of the

- ui usually assumed to be half normal distributed (truncated)

accounting for technical inefficiency

ln( )exp( )

exp( ) ln

i i ii i

i i

y x u yu TE

x x y

[ | ]i i iE u v u

ln( )i i i iy x v u

- 7 -

Stochastic Frontier Analysis (SFA) (I)

Specify production (or cost) function:

1) Cobb Douglas

2) Translog Functional Form

Shortcoming;

Can handle only one output:

→ Aggregation

→ Distance Functions

- The decomposition of the error term into noise and efficiency component may be affected by the particular distributional forms specified.

0 1 2ln( ) ln( ) ln( ) ( )i i i i iQ K L V U

2 20 2 3 4

5

ln( ) ln( ) ln( ) ln( ) ln( )

ln( ) ln( ) ( )i i i i i

i i i i

Q K L K L

K L V U

- 8 -

Agenda

1. Overview - Benchmarking Methodologies

2. Application in the Electricity Sector

2. Transfer to the Airports

Literatur

- 9 -

Efficiency Analysis in the Electricity Distribution

1) Efficiency Analysis of German Local Distribution Utilities

2) Efficiency Analysis of East European Distribution Companies (Poland, Hungary, Czech Republic, Slovakia) in Comparison to Germany

The Issue:

- Increased use of efficiency analysis in the regulation of network industries

- Reform of the electricity sector: Incentive based regulation

- EU Directive 2003/54/EC and German Energy Law (July 2005)

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Choice of Variables

Inputs

LABOR: number of employees

NETWORK LENGTH: approximation for capital input (factored: high-, medium- and low-voltage lines; 5;1.6;1)

Outputs

UNITS SOLD (in MWh)

NUMBER OF CUSTOMERS (residential)

INVERSE DENSITY INDEX: (supplied area in square kilometres per inhabitants)

• Number of customers is determined by industry and households within the supply area can be considered as a given date

• Demand of the end users is quite inelastic and must be satisfied

Output is fix, input has to be minimized

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Our Empirical Application

I) We analyze technical efficiency (no cost data is available, VDEW data 2001)

DEA is applied as main productivity analysis technique:

- Constant Returns to Scale (Variable Returns to Scale for verification)

- Input-orientated approach

Input distance function approach with SFA for verification

II) Specify a translog functional form, general unrestricted form

Truncated normal distribution for the technical inefficiency random variables

Specification of Battese and Coelli, 1995

Maximum likelihood method to estimate the parameters (Frontier Version 2.1, Coelli)

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Selected Results

DEA, Model 2, CRS

0%

20%

40%

60%

80%

100%

1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307

utility number

Eff

icie

ncy

in %

DEA Model 4 - CRS all countriesPoland (1-33), Slovak Rep. (34-36), Czech Rep. (37-43), Hungary (44-47), Germany (48-84)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

Firm number

technic

al effic

iency s

core

s

Poland

S.R.

C. R.

Hungary

Germany

- German local distribution:

- East German Utilities more efficient

- East European regional Distribution

- Poland features by far the lowest efficiency scores

- Scale inefficient

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Measurement of Scale Efficiency

DEA Model 1 - Scale Efficiency East European countriesPoland (1-33), Slovak Rep. (34-36), Czech Rep. (37-43), Hungary (44-47)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Firm number

scale

effic

iency s

core

s

Difference Results DEA, Model 2, VRS-CRS

0%10%20%30%40%50%60%70%

1 16 31 46 61 76 91 106

121

136

151

166

181

196

211

226

241

256

271

286

301

utility number

Eff

icic

ien

cy C

han

ge

in

per

cen

t p

oin

ts

• Difference Model 2, DEA: VRS – CRS

• Economies of Scale seem to be limited, “big is not necessarily beautiful”

• Evidence for economies of scale in Poland (area of increasing returns to scale)

• Slovakia: scale inefficiency due to decreasing returns to scale

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Agenda

1. Overview - Benchmarking Methodologies

2. Application in the Electricity Sector

3. Transfer to the Airports

Literatur

- 15 -

Transfer to Airport Benchmarking

- Decide which methodologies to use:

Stochastic Frontier Analysis not widely used. Integrate SFA, at least for verification and validation method

- Focus on technical efficiency or allocative efficiency?

- Dynamic analysis with panel data?

Special Issue → technical change

Panel Data Models

- Choose appropriate input and output factors

Difficult task → many activities, heterogeneous

- 16 -

Literature

Aigner, Dennis J., Lovell Ashley C., Schmidt Peter, 1977. Formulation and Estimation of stochastic Frontier Production Function Models. Journal of Econometrics 6/1, 21-37.

Christensen, L.R., Jorgensen, D.W. and Lau, L.J. 1971. Conjugate Duality and the Transcendental Logarithmic Production Function. Econometrica 39, 225-256

Coelli, Tim, Prasada Rao, Dodla S., Battese, George E., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, Bostron/Dordrecht/London,

Coelli, Tim, 1996. A Guide to Frontier Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation. CEPA Working Paper 96/7, Department of Econometrics, University of New England, Armidale NSW Australia.

Estache, Antonio, Rossi Martin A., Ruzzier Christian A., 2004. The Case for International Coordination of Electricity Regulation: Evidence from the Measurement of Efficiency in South America. Journal of Regulatory Economics 25/3, 271-295.

EBRD, Transition Report 2004, London.

Filippini, Massimo, Hrovatin, Nevenka, Zoric, Jelena, 2004. Regulation of the Slovenian Electricity Distribution Companies. Energy Policy 32, 335-344.

Jamasb, Tooraj, Pollitt, Michael, 2003. International Benchmarking and Yardstick Regulation: An Application to European Electricity Distribution Utilities. Energy Policy 31, 1609-1622.

Kocenda, Evzen, Cabelka, Stepan, 1999. Liberalization in the Energy Sector in the CEE-Countries: Transition and Growth. Osteuropa-Wirtschaft 44/1, 196-225.

Shephard, Ronald W., 1970. Theory of Cost and Production Functions. Princeton University Press, Princeton.

Frontier Economics, and Consentec (2003) Netzpreisaufsicht in der Praxis, Abschlussbericht für VIK und BDI, London.

Riechmann, C. (2000) Kostensenkungsbedarf bei Deutschen Stromverteilern, Wirtschaftswelt Energie, 55, 6-8.

Schiffer, H-W. (2002) Energiemarkt Deutschland, 8. Auflage, Köln, TÜV-Verlag GmbH.