International Benchmarking of German and Swiss Urban Public - - PowerPoint PPT Presentation

International Benchmarking of German and Swiss Urban Public Transport Sectors using Panel Data

By Astrid Cullmann, Mehdi Farsi, Massimo Filippini DIW Berlin and ETH Zürich (CEPE) INFRADAY 2008, TU-Berlin

• 2 -

Agenda

• 1. Issues and Motivation
• 2. Methods
• 3. Empirical Application
• 4. Results
• 5. Conclusions

Literature

• 3 -

Issues and Motivation

• European countries changed the regulatory approach in their public

transport sectors 1) Competitive Tendering 2) Incentive regulation instruments In order to improve the efficiency and quality

• Such instruments are usually based on the results obtained from a

benchmarking analysis, using production, distance or cost frontier models

• Regulators sometimes interested in performing an international

benchmarking

• 4 -

Issues and Motivation

Implication Implication

• Reliability of efficiency

estimates is crucial for an effective implementation

• Empirical evidence: estimates

are sensitive to the adopted benchmarking approach.

• Reliability of efficiency

estimates is crucial for an effective implementation

• Empirical evidence: estimates

are sensitive to the adopted benchmarking approach.

Problems Problems

• High level of output heterogeneity

(multi-utilities)

• Vehicles, shape of networks,
• rganization, coordination,

density of stops, different environmental characteristics

• Information is not available for all
• utput characteristics
• Omitted from the model

specifications

• Unobserved firm-specific

heterogeneity becomes more serious in cross-country, comparative efficiency analyses.

• High level of output heterogeneity

(multi-utilities)

• Vehicles, shape of networks,
• rganization, coordination,

density of stops, different environmental characteristics

• Information is not available for all
• utput characteristics
• Omitted from the model

specifications

• Unobserved firm-specific

heterogeneity becomes more serious in cross-country, comparative efficiency analyses.

• 5 -

Panel Data Models and Unobserved Heterogeneity

Unobserved firm-specific heterogeneity can be taken into account with conventional fixed or random effects in a panel data model. Unobserved firm-specific heterogeneity can be taken into account with conventional fixed or random effects in a panel data model.

SFA Panel data models FE and RE (GLS) model ML model RE with heterogeneity True FE and true RE Cross section models

Schmidt and Sickles (1984) Cornvell, Schmidt, Sickles (1990) Kumbhakar (1993) Heshmati and Kumbhakar(1994) Greene (2005a, b) Farsi, Filippini, Greene (2005, 2006) Farsi, Filippini, Kuenzle (2006) Pitt and Lee (1981) Battese and Coelli (1992)

• 6 -

ln Di nonnegative variable which can be associated with technical inefficiency .

• Given the stochastic error this model can be formulated in the common SFA form with the

combined error term

( )

I t m M m K k km K k K l K l K k kl K k K k K k k M n n m mn M m M m m m K

D T y x x x x x x x x y y y x ln ln ln ln ln 2 1 ln ln ln 2 1 ln ln

1 1 1 1 1 1 1 1 1 1 1 1

− + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + + = −

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

= − = − = − = − = = = =

γ δ β β α α α

Translog Input Distance Function

• 7 -

True Random Effects Model

Random-constant frontier model (conventional random-effects model with a skewed stochastic term)

ai normal i.i.d. in random-effects framework uit , vit half-normal variable representing inefficiency and a normal random variable that captures the statistical noise.

Unobserved firm-specific heterogeneity is accounted for by individual effects might be correlated with the explanatory variables, in which case the estimations might be affected by ‘heterogeneity bias.’ Random-constant frontier model (conventional random-effects model with a skewed stochastic term)

ai normal i.i.d. in random-effects framework uit , vit half-normal variable representing inefficiency and a normal random variable that captures the statistical noise.

Unobserved firm-specific heterogeneity is accounted for by individual effects might be correlated with the explanatory variables, in which case the estimations might be affected by ‘heterogeneity bias.’

( )

it it t mit M m Kit kit km K k K l Kit lit Kit kit kl K k K k Kit kit k M n nit mit mn M m M m mit m Kit

u v T y x x x x x x x x y y y x

i

− + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + + = −

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

= − = − = − = − = = = =

γ δ β β α α α ln ln ln ln 2 1 ln ln ln 2 1 ln ln

1 1 1 1 1 1 1 1 1 1 1 1

• 8 -

Random coefficients for some of the explanatory variables: Variation capture part of the correlation of the random intercept with the corresponding variables.

Intercept Two output coefficients Linear time trend

Random coefficients for some of the explanatory variables: Variation capture part of the correlation of the random intercept with the corresponding variables.

Intercept Two output coefficients Linear time trend

Random Coefficient Frontier Model

Random variables with a normal distribution. Different underlying production technologies Different scale economies Company specific technological progress Different underlying production technologies Different scale economies Company specific technological progress

( )

it it it mit M m Kit kit km K k K l Kit lit Kit kit kl K k K k Kit kit k M n nit mit mn M m M m mit mi K

u v T y x x x x x x x x y y y x

i it

− + + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + + = −

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

= − = − = − = − = = = =

γ δ β β α α α ln ln ln ln 2 1 ln ln ln 2 1 ln ln

1 1 1 1 1 1 1 1 1 1 1 1

• 9 -

Model Specification

Number of buses (X3) Structural Variable Size of the operating area (z1) Seat-kilometers in buses (y2) Seat-kilometers in streetcars (y1) Outputs Number of streetcars (x2) Number of employees (X1) Inputs Variables

Unbalanced panel with 56 multi-output local public transport companies

• 49 from Germany

(1994-2006), source: VDV statistics

• 7 from Switzerland

(1991-2003), source: Swiss Federal Statistical Office, annual reports

Supply oriented model

• 10 -

Estimation Results (TRE and RCM)

0.00

• 0.49

0.00

• 0.53

ln(y2) 0.00

• 0.07

0.00

• 0.09

ln(z1) 0.00 0.03 0.00 0.02 Trend 0.00

• 0.25

0.00

• 0.29

ln(y1) 0.00 0.31 0.00 0.34 ln(x3/x1) 0.00 0.19 0.00 0.19 ln(x2/x1) 0.00

• 0.13

0.21

• 0.10

Constant p-value Model 2 RCM p-value Model 1 TRE 0.00 0.01 Trend 0.00 0.07 ln(y2) 0.00 0.11 ln(y1) 0.00 0.62 Constant p-value Model 2 RCM Standard Deviation for random parameters (a)

Variation across companies different economies of scale and density different technological changes RC model can improve the estimates

• 11 -

Efficiency Analysis

0.585 0.469 Min 0.942 0.921 Median 707 707 Number of Observation 0.926 0.905 Mean 0.987 0.061 Model 1 True Random Effects Model 0.994 0.052 Model 2 Random Coefficient Model Max Std Dev

For Comparison Pitt and Lee 1981 For Comparison Pitt and Lee 1981 Pitt and Lee (1981): mean (0.78) median (0.76)) Battese and Coelli (1992): mean (0.80) Any unobserved, time-invariant, firm-specific heterogeneity is considered as inefficiency. Pitt and Lee (1981): mean (0.78) median (0.76)) Battese and Coelli (1992): mean (0.80) Any unobserved, time-invariant, firm-specific heterogeneity is considered as inefficiency. Summary Statistics of Efficiency Estimates

• 12 -

Correlation and Rank Correlation

0.004

Model I

1.101

Model II German (616) vs Swiss (91) Companies

• Kruskal-Wallis test no significant difference between Swiss and German

transit companies.

• Kruskal-Wallis test for Pitt and Lee Model and Battese and Coelli Model

significant difference between Swiss and German transit companies.

• Kruskal-Wallis test no significant difference between Swiss and German

transit companies.

• Kruskal-Wallis test for Pitt and Lee Model and Battese and Coelli Model

significant difference between Swiss and German transit companies. Kruskall Wallis Test Statistics

• 13 -

Conclusions

• Issue of unobserved heterogeneity, a concern especially for international

benchmarking, can be handled using panel data models that can account for stochastic variation in the model’s parameters.

• The input distance function is a legitimate modeling concept that can be

used to estimate the technical efficiency and its variations over time.

• When used in the random-coefficient framework, the model allows a better

control for the latent variations across companies regarding technological characteristics as well as temporal changes and technical progress.

• 14 -

Back up

• 15 -

Summary Statistics for Germany

405 21 77 171 616 Area in km2 2303000 4000 463609 584293 616 Seat km bus in 1000 Km 6187000 5000 1200087 964943 616 Seat km tram in 1000 Km 28519 86 5709 7211 616 Bus km in 1000 Km 34363 61 6412 5664 616 Tram km in 1000 Mm 470 2 100 135 616 Number busses 755 2 124 118 616 Number trams 2653 5 364 465 616 Network length bus in Km 155 3 41 49 616 Network length tram in Km 3996 30 893 978 616 Number of employees 1642000 40800 295151 366709 616 Inhabitants Germany Max Min

• Std. Dev.

Mean Obs Variable

• 16 -

Summary Statistics for Switzerland

275 90 63 169 91 Area in km2 2283553 121443 722588 974580 91 Seat km bus in 1000 Km 2926006 37387 923549 847835 91 Seat km tram in 1000 Km 18438 1525 5729 8121 91 Bus km in 1000 Km 20518 398 6916 6111 91 Tram km in 1000 Mm 314 30 105 167 91 Number busses 432 12 136 128 91 Number trams 362 42 94 139 91 Network length bus in Km 110 8 30 32 91 Network length tram in Km 2798 76 711 953 91 Number of employees 421802 76381 117492 285215 91 Inhabitants Switzerland Max Min

• Std. Dev.

Mean Obs Variable

• 17 -

Distance Function

• Capture multi-output context without specification of a behavioral assumption
• Definition on the output set with input minimization:
• Restrictions for homogeneity of degree +1 in inputs and symmetry:
• → Imposing homogeneity by dividing the specification of the translog function by an

arbitrarily chosen input

{ }

( , ) max :( / ) ( )

i

d x y x L y ρ ρ = ∈ and , 1

1 1 1

= = =

∑ ∑ ∑

= = = K k km K l kl K k k

δ β β

K i K i

X y x d y X x d / ) , ( ) , / ( =

• 18 -

Econometric Specification

Random Error Firm-specific component Model 2 Random Coefficient Model Model 1 True RE Greene 2004,2005

i

α

it

ε

it it it

u v − = ε

) , ( ~

2 u it

N u σ

+

) , ( ~

2 v it

N v σ

Capturing unobserved Heterogeneity

) , ( ~

2 α

σ α N

i

2

~ ( , )

i

N

β β

β μ σ ) , ( ~

2 α

σ α N

i

it it it

u v − = ε

) , ( ~

2 u it

N u σ

+

) , ( ~

2 v it

N v σ