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
Agenda 1. Issues and Motivation 2. Methods 3. Empirical Application 4. Results 5. Conclusions Literature - 2 -
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 - 3 -
Issues and Motivation Implication Problems Implication Problems • Reliability of efficiency • High level of output heterogeneity • Reliability of efficiency • High level of output heterogeneity estimates is crucial for an (multi-utilities) estimates is crucial for an (multi-utilities) effective implementation effective implementation • Vehicles, shape of networks, • Vehicles, shape of networks, • Empirical evidence: estimates organization, coordination, • Empirical evidence: estimates organization, coordination, are sensitive to the adopted density of stops, different are sensitive to the adopted density of stops, different benchmarking approach. environmental characteristics benchmarking approach. environmental characteristics • Information is not available for all • Information is not available for all output characteristics output characteristics • Omitted from the model • Omitted from the model specifications specifications • Unobserved firm-specific • Unobserved firm-specific heterogeneity becomes more heterogeneity becomes more serious in cross-country, serious in cross-country, comparative efficiency analyses. comparative efficiency analyses. - 4 -
Panel Data Models and Unobserved Heterogeneity SFA Panel data models Cross section models Unobserved firm-specific Unobserved firm-specific heterogeneity can be heterogeneity can be taken into account with taken into account with conventional fixed or conventional fixed or FE and RE (GLS) RE with ML model True FE and random effects in a panel random effects in a panel model heterogeneity true RE data model. data model. Greene (2005a, b) Schmidt and Sickles Pitt and Lee Kumbhakar (1993) (1984) (1981) Farsi, Filippini, Greene (2005, Heshmati and 2006) Cornvell, Schmidt, Battese and Kumbhakar(1994) Sickles (1990) Coelli (1992) Farsi, Filippini, Kuenzle (2006) - 5 -
Translog Input Distance Function − ⎛ ⎞ M M M K 1 ( ) 1 x ∑ ∑ ∑ ∑ − = α + α + α + β k ⎜ ⎟ ln x ln y ln y ln y ln K 0 m m mn m n k ⎝ ⎠ 2 x = = = = K m 1 m 1 n 1 k 1 − − − ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ K 1 K 1 K 1 M 1 ∑ ∑ x x ∑ ∑ x k l k + β + δ + γ − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ln ln ln ln y T ln D kl km m I t ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 x x x = = K K = = K k 1 l 1 k 1 m 1 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 - 6 -
True Random Effects Model � Random-constant frontier model (conventional random-effects model with a � Random-constant frontier model (conventional random-effects model with a skewed stochastic term) skewed stochastic term) − ⎛ ⎞ M M M K 1 ( ) ∑ 1 ∑ ∑ ∑ x kit − = α + α + α + β ⎜ ⎟ ln x ln y ln y ln y ln Kit m mit mn mit nit k ⎝ ⎠ i 2 x = = = = Kit m 1 m 1 n 1 k 1 − − − ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ K 1 K 1 K 1 M 1 x x x ∑ ∑ ∑ ∑ + β kit lit + δ kit + γ + − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ln ln ln ln y T v u kl km mit t it it ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 x x x = = Kit Kit = = Kit k 1 l 1 k 1 m 1 ai normal i.i.d. in random-effects framework ai normal i.i.d. in random-effects framework uit , vit half-normal variable representing inefficiency and a normal random variable that uit , vit half-normal variable representing inefficiency and a normal random variable that captures the statistical noise. captures the statistical noise. Unobserved firm-specific heterogeneity is accounted for by individual effects � Unobserved firm-specific heterogeneity is accounted for by individual effects � might be correlated with the explanatory variables, in which case the estimations might be correlated with the explanatory variables, in which case the estimations might be affected by ‘heterogeneity bias.’ might be affected by ‘heterogeneity bias.’ - 7 -
Random Coefficient Frontier Model Random coefficients for some of the explanatory variables: Variation capture part of Random coefficients for some of the explanatory variables: Variation capture part of the correlation of the random intercept with the corresponding variables. the correlation of the random intercept with the corresponding variables. − ⎛ ⎞ M M M K 1 ( ) ∑ 1 ∑ ∑ ∑ x − = α + α + α + β kit ⎜ ⎟ ln x ln y ln y ln y ln K mi mit mn mit nit k ⎝ ⎠ it i 2 x = = = = Kit m 1 m 1 n 1 k 1 − − − ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ K 1 K 1 K 1 M 1 x x x ∑ ∑ ∑ ∑ kit lit kit + β + δ + γ + − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ln ln ln ln y T v u kl km mit it it it ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 x x x = = Kit Kit = = Kit k 1 l 1 k 1 m 1 Intercept Intercept Random variables with a normal distribution. Two output coefficients Two output coefficients Linear time trend Linear time trend Different underlying production technologies Different underlying production technologies Different scale economies Different scale economies Company specific technological progress Company specific technological progress - 8 -
Model Specification Variables Unbalanced panel with 56 multi-output local Inputs public transport Number of employees (X1) companies Number of streetcars (x2) Number of buses (X3) - 49 from Germany (1994-2006), source: Outputs VDV statistics Seat-kilometers in streetcars (y1) Seat-kilometers in buses (y2) - 7 from Switzerland (1991-2003), source: Structural Variable Swiss Federal Statistical Size of the operating area (z1) Office, annual reports � Supply oriented model - 9 -
Estimation Results (TRE and RCM) Standard Deviation for Model 1 Model 2 random Model 2 parameters (a) RCM p-value TRE p-value RCM p-value Constant 0.62 0.00 Constant -0.10 0.21 -0.13 0.00 ln(y1) 0.11 0.00 ln(y2) 0.07 0.00 ln(x2/x1) 0.19 0.00 0.19 0.00 Trend 0.01 0.00 ln(x3/x1) 0.34 0.00 0.31 0.00 Variation across companies ln(y1) -0.29 0.00 -0.25 0.00 � different economies of scale and density ln(y2) -0.53 0.00 -0.49 0.00 � different technological changes Trend 0.02 0.00 0.03 0.00 RC model can improve the estimates ln(z1) -0.09 0.00 -0.07 0.00 - 10 -
Efficiency Analysis Summary Statistics of Efficiency Estimates Number of Mean Std Dev Min Median Max Observation Model 1 707 0.905 0.061 0.469 0.921 0.987 True Random Effects Model 707 0.926 0.052 0.585 0.942 0.994 Model 2 Random Coefficient Model For Comparison Pitt and Lee 1981 For Comparison Pitt and Lee 1981 Pitt and Lee (1981): mean (0.78) median (0.76)) Pitt and Lee (1981): mean (0.78) median (0.76)) Battese and Coelli (1992): mean (0.80) Battese and Coelli (1992): mean (0.80) � Any unobserved, time-invariant, firm-specific heterogeneity is considered as � Any unobserved, time-invariant, firm-specific heterogeneity is considered as inefficiency. inefficiency. - 11 -
Correlation and Rank Correlation Kruskall Wallis Test Statistics Model I Model II 0.004 1.101 German (616) vs Swiss (91) Companies • Kruskal-Wallis test � no significant difference between Swiss and German • Kruskal-Wallis test � no significant difference between Swiss and German transit companies. transit companies. • Kruskal-Wallis test for Pitt and Lee Model and Battese and Coelli Model � • Kruskal-Wallis test for Pitt and Lee Model and Battese and Coelli Model � significant difference between Swiss and German transit companies. significant difference between Swiss and German transit companies. - 12 -
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. - 13 -
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