Economies of Scale and Scope in

Urban Public Transport

Matthias Walter∗

July 6, 2009

Abstract

Local public transport in Germany is characterized by highfragmentation and formative changes in market structure with mergersand competitive tendering. In this paper we estimate cost functions inorder to estimate economies of scale and scope. The unbalanced paneldata set for the analysis consists of 573 observations of single- andmulti-output German bus, tram and light rail companies from 1997to 2006. This is the first empirical application of such a unique dataset to Germany’s local public transport. We apply Stochastic Frontierpanel data models to align the estimations at optimal cost curves.The results suggest increasing global, bus-specific as well as tram- andlight railway-specific economies of scale favoring mergers and tenderingin large output volume. Furthermore we find slight diseconomies ofscope in particular for smaller companies accompanying the increasedcomplexity of providing different modes of transport. The results areconsistent for both a Random and a True Random Effects model (whichis used to account for unobserved heterogeneity) which are preferredto a Fixed Effects model.

Keywords: Public transport, Stochastic Frontier Analysis, Economies ofscale, Economies of scope

∗Dresden University of Technology, Faculty of Business and Economics, Chair ofEnergy Economics and Public Sector Management, 01062 Dresden, Germany. Phone:+49-(0)351-463-39762, Fax: +49-(0)351-463-39763, matthias.walter@tu-dresden.de

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1 Introduction

Germany’s urban public transport is undergoing industry consolidation atthe same time that changes in structure and market rules are occurring. Afragmented market comprising almost 1000 companies has begun to alterdue to the mergers and acquisitions of neighboring companies and efforts byfirms with strong capital bases seeking opportunities for growth. Moreover,tenders have become an instrument for introducing market competition.Mergers that exploit size and synergies are most visible for multi-outputcompanies in urban agglomerations with tram or light railway operationson a common network, such as RNV (created by the merger of local publictransport companies from Mannheim, Heidelberg and Ludwigshafen in theRhine-Neckar area) and Meoline (local public transport companies fromEssen, Mulheim and Duisburg in the Ruhrgebiet). Large urban operatorshave acquired small-scale companies in the surrounding area (DVB ofDresden acquired VGM of Meißen). Companies in Koln and Bonn haveproposed mergers twice in the past that have not been successful for politicalreasons. Two examples of companies with strong capital bases searchingout growth opportunities are “Hamburger Hochbahn” which was involvedin operations in Hessen, and DB Stadtverkehr, the subsidiary of DeutscheBahn for local public transport,1 which intensively applies for tenders andsearches for acquisition candidates. The question remains, however, whethera geographically random acquisition strategy can exploit economies of scale.Tenders were established as a form of competition for the market mainlyin the federal state of Hessen (with its economic heart, Frankfurt)and for regional services around the second- and third-largest Germancities, Hamburg and Munchen, prior to the replacement of EU regulation1191/1969 by 1370/2007. These tenders have indicated savings potential aswell as increased quality and have shown that small-scale private operatorscan also be competitive (Beck et al, 2007), potentially by reducing wages.However, there is little substantiated knowledge about whether tendersproduce real savings.In the past, large shares of local public transport services have beenfinanced by subsidies from public authorities. In Germany, the public serviceobligation of local public transport is determined by the regionalization lawfor local public transport (Regionalisierungsgesetz - RegG)2. According tothis, local public transport services must be geographically accessible for the

1 Additionally, DB Stadtverkehr is responsible for the S-Bahn in Hamburg and Berlin.2 Gesetz zur Regionalisierung des offentlichen Personennahverkehrs.

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whole population. However, in the present budgetary crisis, public transportis under pressure to operate as efficiently as possible. The purpose of thispaper is to determine these structures from two angles: first, to evaluatescale economies, i.e. if existing services in larger entities could be producedat less cost; second, to determine the appropriate economies of scope, i.e. thecost savings from the combined services or products. There are various typesof economies of scope in transport. Here we refer to economies of scope fromproducing bus services on the one hand and tram and light railway serviceson the other hand together.3 The approach to the estimation of economiesof scale and scope applied in this paper follows three guidelines:

1. Econometric cost functions are applied. The major requirement forsuch an analysis is the availability of a consistent and sufficiently largeenough panel data set containing information about cost items andproduction quantities of urban public transport operators. Such adata set has not been available in the past. This paper is the firstempirical application of this kind for Germany.

2. Historically, analysis (see Berechman, 1993, pp. 112, for anintroduction) relied on the estimation of average functions withordinary least squares or panel data models. Employing StochasticFrontier Analysis (SFA) allows researchers to estimate for theoptimal (frontier) cost levels, and acknowledge the presence of firms’inefficiency. Since economies of scale and scope are used to determinethe optimal market structure, it appears natural to do this withoptimal cost curves.

3. SFA also allows the use of panel data models. These models shouldbe preferred to a pooled model (Aigner et al, 1977) because a pooledmodel treats each observation independently from other observationswhich is obviously not satisfied in a panel data set. In such a case,panel data models exhibit estimation advantages over techniques forcross-sectional data (Kumbhakar and Lovell, 2000, p. 255). A basicSFA panel data model is the Random Effects (RE) model by Pittand Lee (1981) which treats all heterogeneity as inefficiency. Theresults can then be compared to a True Random Effects (TRE) modelby Greene (2004, 2005a) which is able to account for unobservedheterogeneity and separates this effect from inefficiency. Unobserved

3 This paper does not address economies of scope in the sense of potential savingsbetween the tram network and the actual service provision, as is often performed forrailways. This paper assumes integration (status quo in Germany).

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heterogeneity is not recorded through structural variables in the dataset but is likely to be present in local public transport through networkcomplexities, i.e. differences in network configurations, stop densities,altitudes, etc.

An econometric study relying on an average cost function on economies ofscale and scope in Switzerland’s local public transport was carried out byFarsi et al (2007). Their results for the provision of trolley-bus, motor-busand tramway systems indicate such significant increasing returns of scaleand economies of scope that the authors favor integrated operations overunbundling. Di Giacomo and Ottoz (2007) find fixed cost savings based oneconomies of scope for Italian urban and intercity bus transit operators.Viton (1992, 1993) evaluate economies of scale and scope for differentmeans of transport in the San Francisco Bay Area with a cross-sectionalSFA, and determine that the extent of the savings potential depends onfirm size, type of transport modes and level of wages.The investigation of scale economies and cost efficiency of single-modetransport systems appears more frequently in the literature because of theease of modeling and data availability. Odeck and Alkadi (2001) evaluatethe performance of Norwegian bus companies with Data EnvelopmentAnalysis (DEA), finding an average input saving potential of about 28%.Farsi et al (2006) emphasize the need to distinguish between inefficiencyand heterogeneity and therefore also apply Greene’s TRE model (2004,2005a). The same model is used by Nieswand et al (2008) to evaluate thecost efficiency of rural and regional bus operations in Germany. Similarly,Hirschhausen and Cullmann (2008) find significant economies of scalein Germany’s rural and regional bus operations using DEA. DEA isalso used in the case study by Walter and Cullmann (2008) to identifypotential gains from mergers of bus, tram and light railway operators basedon physical inputs and outputs in a specific federal state of Germany,Nordrhein-Westfalen, a densely populated area.

The remainder of this paper is structured as follows: Section 2 provides themodel specification and the econometric methods and Section 3 presentsthe calculation scheme for economies of scale and scope. Section 4 describesthe data, Section 5 discusses the results and interpretations, and Section 6concludes.

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2 Model specification and econometric methods

The total cost (C) frontier

C = f(Y, Q, wL, wK , N, t) (1)

applied in this paper is dependent on the two outputs (Y ) and (Q), on twofactor prices for labor (wL) and capital (wK), on the network length forrail-bound services (N) and on a time trend (t). To evaluate the economiesof scope the output is split into output of bus services (Y ) and outputof rail-bound services (Q), i.e. tram and light railway services. We donot differentiate among the different rail-bound services since there are nodistinctive criteria available for separation; e.g., one could use average speedas well as the existence of tunnels. The outputs are represented by thenumber of seat-kilometers (including both sitting and standing room). Usingseat kilometers is preferable to using vehicle kilometers because the latterdoes not account for size of vehicles. However, both measures representa pure supply side consideration. A long-standing debate exists aboutwhich output variables to use (see e.g. De Borger et al, 2008, De Borgeret al, 2002,4 or Berechman, 1993). Other applicable output variables arepassenger-kilometers, the number of passengers or even revenues. In order toestimate economies of scope between different types of services, the outputshave to be available separately for each transport mode. In the data setat hand, passenger-kilometers and revenues are only available as aggregates,the number of passengers is not at all reported.5 If output-oriented measureswere available, a comparison to supply-oriented output measures wouldbe interesting. However, there are still reasons to rely on supply-orientedmeasures (Roy and Yvrande-Billon, 2007; Farsi et al, 2006; Margari et al,2007). Considering the nature of public service obligations, local publictransport firms are obliged to provide certain services. Since management’sinfluence over scheduling, pricing, etc., may be limited, this paper gives

4 De Borger et al, 2002, observe that the majority of studies uses supply side measures.5 Whereas local public transport companies know the number of vehicle- and

seat-kilometers from their operation schedules, there is limited knowledge about theother measures. Customers who buy single tickets do not reveal their destinationsbecause the tariff system is organized in zones with fixed payment tariffs. Moreover,buying a bus ticket can involve transfers. Monthly and seasonal passes do not reportthe actual trips taken. This distinguishes local public transport from airlines, and toa lesser extent from railways. Additionally, buses do not distinguish between classesof service, unlike rail and air.

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full intervention possibilities by management only for the input side; thus,the estimation of a cost function with assumed cost minimizing behavior6

and supply-oriented output measures appears reasonable (Farsi et al, 2007;Gagnepain and Ivaldi, 2002). Nevertheless, passenger-kilometers and thenumber of passengers are further important indicators, and the same numberof seat-kilometer can generate different amount of revenues, dependingon the tariff system, the percentage of monthly tickets, the subsidies fortransporting pupils and disabled people, the amount of paid advertising onvehicles etc. However, demand would take as far from measures of costefficiency and productivity, to measures of effectiveness (De Borger et al,2002), and further to the question whether the companies actually achieveto maximize their revenues. Though, the purpose of this paper is to evaluatethe adequate supply structures for local public transport. Demand andrevenues are beyond the scope of this paper.Generally, transport studies identify one input as personnel expenditures.Farsi et al (2005a) suggest two additional inputs: energy expendituresand capital expenditures, with the latter calculated as residual costs aftersubtracting personnel costs and energy costs from total costs. When theshare of energy costs is low, and thus coefficients of parameters could beinsignificant, the literature suppresses the energy input and summarizescapital costs and energy costs as a common second input (e.g. Farsiet al, 2007). Since this paper’s data set lacks information about energyconsumption, we use two factor prices: one for labor (wL) and one forcapital (wK).From an economic point of view, other factor price specifications maybe useful, e.g., the substantial difference in capital costs for bus servicesand rail-bound services could be modeled. Usually, the provision ofrail-bound services is preferred to the provision of bus services, becauseof increased customer attractiveness and increased capacity. On the otherhand rail-bound services clearly have higher infrastructure costs. However,in the absence of detailed information about the companies’ cost structureconcerning bus and rail-bound capital costs, it is difficult to implement sucha differentiation. A common allocation with the same split for all companiescan lead to collinearity problems in the estimation procedure. This paperomits this possibility.In addition, I am confident that reliable results are produced by the acceptedapproach that introduces two factor prices for labor and capital, the assumed

6 This implies input orientation. Outputs and input prices are assumed to beexogenously given.

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exogeneity of factor prices, and the rich data set.However, we do include track length of the tram and light rail network (N) asan additional network characteristic and control variable because it heavilyinfluences a company’s cost. This variable can also serve as a quality proxybecause users often prefer trams because of their superior comfort. We alsotest the influence of two other possible structural variables: network lengthincluding line length of bus services and track length of rail-bound servicesand a density index calculated by the number of inhabitants in the influencearea divided by the network length. Neither show significant coefficientsin the estimation procedure. However, it is probable that more networkheterogeneity (different shapes, number of stops etc.) is of substantialinfluence. This makes it important to model this unobserved heterogeneitywith the TRE model explained below. A linear time trend (t) captures theshift in technology representing technical change.To evaluate economies of scope in a multi-output context, it is crucial touse a quadratic cost function because it allows the incorporation of zerooutputs.7 This is not possible with a logarithmized Cobb-Douglas nortranslog functional forms where all outputs are given in logs.8 The quadraticcost function can be written as:

Cit = α + βY Yit + βQ Qit + βK wKit + βL wLit

+12

(βY Y (Yit)2 + βQQ(Qit)2 + βKK (wKit)

2 + βLL (wLit)2)

+ βY Q Yit Qit + βY K Yit wKit + βY L Yit wLit

+ βQK Qit wKit + βQL Qit wLit + βKL ln wKit wLit

+ βN Nit + βt t + εit

(2)

with subscript i denoting the company and subscript t denoting the year.The βs are the coefficients to be estimated. The specification of α and εit

are dependent on the applied econometric model, explained below. Linearhomogeneity in input prices is an important property of cost functions. Forthe actual estimation, the linear homogeneity can be imposed by dividing all

7 The name “quadratic” refers to the presence of quadratic terms of outputs and factorprices; it does not impose any a priori assumption of the trend of the cost curves.As Formula 11 shows, the estimation of economies of scope demands cost predictionswhere specific outputs are set to zero.

8 We follow Baumol et al (1988, p. 453) and Mayo (1984). See Pulley and Humphrey(1993) for an explanation of why a quadratic specification should be preferred to atranslog specification when some outputs can be zero. See Farsi et al (2007, 2008) fora technical discussion on the choice of the functional form.

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cost measures (i.e. the dependent variable total costs and the factor prices)by an arbitrarily chosen factor price, here the price for labor (Featherstoneand Moss, 1994; Martınez-Budrıa et al, 2003; Farsi et al, 2007):

C∗it =

Cit

wLit

= α + βY Yit + βQ Qit + βKwKit

wLit

+12

(βY Y (Yit)2 + βQQ(Qit)2 + βKK

(wKit

wLit

)2)

+ βY Q Yit Qit + βY K YitwKit

wLit

+ βQK QitwKit

wLit

+ βN Nit + βt t + εit .

(3)

Additionally, flexible cost functions like the quadratic or the translog requirethe approximation at a local point, here chosen by the mean. Consequently,all explanatory variables except the time variable are divided by their meansbefore the estimation.The evolution of SFA can be summarized in the following steps (see alsoCoelli et al, 2005, Greene, 2008, and Kumbhakar and Lovell, 2000). Aigneret al (1977) propose a pooled model ignoring the possible panel characteristicof data. Its composed error term (ε) includes noise (v) and inefficiency (u).Disregarding firm-specific unobserved factors can lead to inaccurate results(Farsi et al, 2006). Treating each observation independently is eliminatedby using the RE model developed by Pitt and Lee (1981) and with theFixed Effects model developed by Schmidt and Sickles (1984). In contrastto the RE model, the Fixed Effects model allows correlation of firm-specificeffects with the explanatory variables. We perform a Hausman test thatconfirms the non-correlation in favor of the RE model at a significance levelof 1%. Hence the cost function’s coefficients (our major determinant forestimating economies of scale and scope) of the RE model can serve as anunbiased benchmark. The Fixed Effects model is therefore not used in thefollowing. The RE model parallels the random effects panel data model,which estimates average functions, and can be specified as:

C∗it = α0 + x′

itβ + vit + ui (4)

with x′itβ standing for the parameter vector and the coefficients to be

estimated (cp. Equation 3). Together with α = α0 it represents thedeterministic part of the cost function. In this model, the composed error

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term is defined so that εit = vit +ui. vit ∼ iid N (0, σ2v) is normal distributed

and represents a time-variant, firm-specific stochastic error term (also callednoise, e.g., data measurement errors). ui ∼ iid N+(0, σ2

u) represents thetime invariant, firm specific inefficiency and is truncated normal distributed.Because of this, the model is estimated using maximum likelihood. Theinefficiency is estimated calculating the conditional mean of the inefficiency(ui) as proposed by Jondrow et al (1982), i.e. E[ui|εi1, εi2, ..., εiT ] = E[ui|εi],with εi = (1/Ti)

∑Tit=1 εit.

The TRE model avoids at least two shortcomings of the RE model. AsGreene (2005a) noted, the assumption of time-invariant inefficiency mightbe questionable in long panels, and the RE estimator forces any timeinvariant heterogeneity in the inefficiency term which is likely to result inan overestimation of inefficiency. The TRE model can be specified as:

C∗it = α0 + αi + x′

itβ + vit + uit (5)

with α = α0 + αi and αi ∼ iid N (0, σ2α) being independent and identically

normal distributed and representing a time invariant, firm-specific randomintercept term introduced to capture unobserved heterogeneity separate fromthe actual production technology (e.g. firms situated in geographicallyunfavorable regions, network complexities etc., for which data is notavailable). The composed error term is again made up with noise andinefficiency εit = vit + uit. Precisely, vit ∼ iid N (0, σ2

v) is independent andidentically normal distributed and represents the time-variant, firm-specificstochastic error term and uit ∼ iid N+(0, σ2

u) is independent and identicallytruncated normal distributed representing the time-variant, firm-specificinefficiency. The cost of having a third stochastic term for unobservedheterogeneity is that the inefficiency is underestimated. The “true”inefficiency might hence lie somewhere between the prediction of the REmodel and the TRE model. The TRE model is estimated using SimulatedMaximum Likelihood. The conditional expectation of the inefficiency termE[uit|rit] with rit = αi + uit + vit is calculated by Monte Carlo simulations(Greene, 2004, 2005a) to be able to approximate the maximization ofthe log-likelihood (Greene, 2005b). The differences of the RE and theTRE model in treating heterogeneity and inefficiency makes it necessaryto estimate both models to get a consistency check.

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3 Definition of economies of scale and scope

This paper follows Baumol et al (1988, pp. 50, 68, 73). Global economiesof scale in the two outputs case are defined as:

SLGlobal =C∗(Y, Q)

Y (∂C∗/∂Y ) + Q (∂C∗/∂Q)(6)

with Y representing the amount of seat-kilometers provided in buses and Qrepresenting the accumulated amount of seat-kilometers provided in tramsand light railways.9 The derivatives used are deduced from Equation 3 as:

∂C∗

∂Y= βY + βY Y Y + βY Q Q + βY K

wKit

wLit

. (7)

and

∂C∗

∂Q= βQ + βQQ Q + βY Q Y + βQK

wKit

wLit

. (8)

The production technology implies increasing global returns to scale ifExpression 6 is greater than one and decreasing global returns to scale ifthe expression is smaller than one. When global returns to scale are equalto one, the technology exhibits constant returns to scale. Increasing returnsto scale imply decreasing average costs when increasing outputs whereasdecreasing returns to scale imply increasing average costs with increasingoutputs. Global economies of scale indicate the ratio of a proportionalincrease in all outputs to the increase in costs.Bus-specific economies of scale are defined as:

SLY =C∗(Y, Q)− C∗(0, Q)

Y (∂C∗/∂Y ). (9)

They indicate the ratio of an increase in bus output (with rail-boundoutput fixed) to the increase in costs. The numerator hereby represents theincremental costs of producing bus services. The interpretation of results

9 We do not differentiate between economies of scale and density. This would requirenetwork variables to be included with cross and squared terms in the cost functionwhich, for a quadratic function, heavily affects the estimatability of the model.

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proceeds equally to global returns to scale. Rail-bound-specific economiesof scale are defined and interpreted similarly:

SLQ =C∗(Y, Q)− C∗(Y, 0)

Q (∂C∗/∂Q)(10)

Economies of scope in the two-output case are defined as:

SC =C∗(Y, 0) + C∗(0, Q)− C∗(Y, Q)

C∗(Y, Q). (11)

Economies of scope display savings from the joint production of severaloutputs. Economies of scope exist if the expression above is greater thanzero. SC then report the relative increase in cost from a separate production.For values smaller than zero there are diseconomies of scope.Obviously there is interaction between global economies of scale,product-specific economies of scale and economies of scope. The extentof global economies of scale depends on the specific measures of economiesof scale as well as on economies of scope. A consideration of a simultaneousincrease in both outputs implies that some of the scope effect is picked up.Whereas product-specific economies of scale can be used to evaluate whethera firm is a natural candidate for mergers in the single-product case, globaleconomies of scale is a measure in the multi-product case.

4 Data

The unbalanced panel data set consists of 573 observations for the years1997, 1998, ..., and 2006. The majority of observations (316) are frommulti-output companies. The exact data structure is given in Table1. In total the data set includes information on 82 companies from allfederal states in Germany except Berlin, resulting in approximately sevenobservations per company on average. All except five of the smallercompanies10 are organized in regular public transport associations with zonetariffs. Although these public transport associations usually share marketingand ticketing, the exact assignment of tasks differs among the federal states.All cost data is collected separately for each observation from annualreports and from balance sheets published in the Federal Bulletin

10 These companies are situated in Arnstadt, Eisenach, Gera, Muhlhausen andMagdeburg in the federal states of Thuringen and Sachsen-Anhalt. They are organizedin less-sophisticated tariff associations that mainly charge for kilometers traveled.

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Table 1: Data structure: observations

Year Total Multi-output Single-output1997 46 26 201998 51 27 241999 50 27 232000 63 32 312001 71 37 342002 68 38 302003 58 35 232004 53 31 222005 59 34 252006 54 29 25Total 573 316 257

Source: Own calculation

(Bundesanzeiger).11 All physical data is obtained by extracting the yearlypublished statistics of the Association of German Transport Companies(Verband Deutscher Verkehrsunternehmen, 1998, VDV, also for thefollowing years). Total costs comprise material costs (also called purchases,consisting of expenditures for raw materials and supplies, purchased goods,inter alia energy, and purchased services), personnel costs,12 depreciations,other operating expenses and interests on borrowed capital as well ashypothetical interests on equity. These interests on equity are estimatedas interest on corporate bonds plus two percentage points of risk premium(Source for interest rates: Deutsche Bundesbank, 2007). All companiesconsidered in 2006 exhibit costs of over four billion euros (see Table 2).Cost and price information are given in 2006 prices and are deflated with theGerman producer price index (Destatis, 2008). The factor price for labor iscalculated as personnel costs divided by the number of full-time equivalents(FTE). As capital prices are not directly observable, capital costs have tobe divided through some measure of capital quantity, i.e. assets or capitalstock (Coelli et al, 2003, p. 85). The majority of capital costs paid by localpublic transport firms relate to rolling stock, i.e. buses and railcars.13 An

11 For recent years there is an online version: https://www.ebundesanzeiger.de.12 Including salaries and wages as well as social insurance contributions and expenditures

for pensions.13 For rail-bound services, the network is a further source of capital commitment. Costs

however could be misleadingly reported because the land for stops and the road bed isvery often on public property. Furthermore in the companies’ profit and loss accounts,

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even more accurate measure is the number of seats in buses and railcars.Again, this includes the size of vehicles in the analysis.14 Hence, capital costsare calculated as residual costs (total costs subtracted by personnel costs)divided by the number of seats. This implies that material costs and otheroperating expenses are assumed to represent payments for capital services(Friedlaender and Chiang, 1983). Establishing one more factor price foroperations would be another option. This factor price could be calculatedas material costs and other operating expenses divided by some measureof operations which is obviously output. But output in turn is alreadyincluded in the cost function and, in the presence of cross terms with factorprices, this will lead to multicollinearity problems if additionally employedfor calculating factor prices.

5 Results and interpretation

5.1 Regression results

Table 3 shows the regression results for the RE model and the TRE model.The coefficient estimates across the two models are quite similar. Thissimilarity confirms observations by Farsi et al (2005a,b). All coefficients, inparticular for outputs and capital price, show the expected signs and aresignificant. The results for the TRE incorporates an additional estimateσα characterizing the random intercept term. The output coefficients forbus services are much higher than for rail-bound services which is explainedby the positive and significant coefficient of the rail-bound network in bothmodels, and shows that the network is a substantial cost factor and thatnetwork extensions produce higher total costs. This variable picks up someof the costs related to tram and light railway services. The time trendsshow negative significant signs, suggesting that the restructuring that hasalready occurred15 is successful and that total costs tend to be lower inrecent years.16 Furthermore, σu relates to the standard deviation of the

costs are not broken down into expenses for railing stock and network expenses. Hence,the network is included as a structural variable assumed to be fixed at least in theshort run.

14 The number of seats was approximated by the number of seat-kilometers multipliedby the number of buses and cars divided by the number of vehicle-kilometers. Theunderlying assumption is that the deployment of each bus and railcar is uniformlydistributed.

15 Particularly in some of the larger companies like Rheinbahn (Dusseldorf).16 A detailed strategic efficiency analysis of individual firm scores could further evaluate

these trends.

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Table 2: Descriptive statistics

Suma Min. Mean Median Max. S.D.Total cost (C) 4313 1 85 60 391 86

[m EUR]Share personnel costs 0.05 0.46 0.46 0.69 0.11Share capital costs 0.31 0.54 0.54 0.95 0.11Labor price (wL) 17 135 48 388 49 298 164 079 11 689

[EUR/FTE]Capital price (wK) 544 1704 1514 5078 784

[EUR/seat]Output [m seat-kilometers]Bus (Y ) 34 256 0 705 586 2402 486Rail-bound (Q) 34 716 0 1212c 654c 6187 1347c

Network length (N)b 1656 0 58c 39c 155 43c

VehiclesBus 8745 0 184 148 1003 148Rail-bound 3525 0 137c 85c 605 125c

aSum values for 2006 bFor tram and light railway servicescCalculated for all non-zero observations

Source: Own calculation

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inefficiency and σv to the standard deviation of the noise. For both models,σu is reasonably higher, as indicated by λ in Table 3.

Table 3: Regression results

Model RE TREParameter Estimate Estimateα −29.89∗∗∗(6.32) −27.61∗∗∗(2.29)σα — 10.51∗∗∗(0.36)βY 45.75∗∗∗(5.60) 51.58∗∗∗(1.97)βQ 23.74∗∗∗(4.73) 31.66∗∗∗(1.37)βK 27.87∗∗∗(4.96) 27.21∗∗∗(2.52)βY Y −12.60∗∗∗(3.24) −14.22∗∗∗(1.23)βQQ −1.57∗(0.89) −4.23∗∗∗(0.27)βKK −8.13∗∗∗(1.79) −7.89∗∗∗(1.25)βY Q −4.08∗∗∗(1.40) −0.06(0.38)βY K 3.71∗(2.14) 2.13∗∗(0.99)βQK 8.05∗∗∗(0.60) 8.25∗∗∗(0.38)βt −1.40∗∗∗(0.11) −1.15∗∗∗(0.07)βN 15.28∗∗∗(3.08) 7.20∗∗∗(0.98)σu 22.35∗∗∗ 15.33∗∗∗

λ = σu/σv 2.34∗∗∗ 4.72∗∗∗∗∗∗significant at 1%, ∗∗significant at 5%, ∗significant at 10%standard errors in parentheses

Source: Own calculation

5.2 Economies of scale and scope for representative outputlevels

Table 4 shows all defined measures of economies for the RE model andthe TRE model. The results are given for four hypothetical firms: a firmproducing outputs at the 25%-quartile of all sample firms, a firm producingat the median of all sample firms, a firm producing at the mean output anda firm producing at the 75%-quartile.17 The network variable is also set atthe corresponding quartile and mean levels. The firms in the sample with norail-bound services are excluded from the quartile calculation of rail-boundoutput and network. According to Farsi et al (2007) the capital price and

17 The determination of an output at the 25% quartile means that 25% of all firms inthe sample produce less output.

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Table 4: Economies of scale and scope for representative output levels

Fleet size Bus-specific SL Rail-bound specific SLOutput level Bus Rail RE TRE RE TRE25% quartile 83 46 1.21 1.18 2.04 1.46Median 148 85 1.35 1.32 1.74 1.31Mean 184 137 1.48 1.41 1.32 1.1175% quartile 237 189 1.62 1.62 1.29 1.08

Fleet size Economies of scope Global economies of scaleOutput level Bus Rail RE TRE RE TRE25% quartile 83 46 -0.35 -0.26 1.16 1.04Median 148 85 -0.15 -0.14 1.35 1.16Mean 184 137 -0.06 -0.09 1.29 1.1175% quartile 237 189 -0.02 -0.07 1.39 1.15

Source: Own calculation

the time trend are kept at their mean values. The intercept term for theTRE model is not varied and kept constant at α.Looking at the specific scale economies one can observe increasing returnsto scale for bus and for tram and light railway services (see Table 4). Theseresults are in line with the literature (Farsi et al, 2006, 2007). While thebus-specific economies of scale are increasing from low to high output levels,the rail-specific economies of scale are decreasing. Further calculations foroutput levels beyond the 75%-quartile (not shown in Table 4) suggest athreshold around the 85%-percentile of output where rail-bound specificeconomies of scale turn into diseconomies of scale. For bus-specific economiesof scale this is not the case. However, as an econometric estimation alwaysattempts to reflect the data as accurately as possible, the boundaries shouldbe interpreted with care. The increasing returns to scale indicate the savingspotential resulting from an increase in output levels or by a merger ofadjacent single-output companies. The savings potential can be increasedby sharing maintenance facilities or by a joint procurement that extends theexisting cooperation among operators. An exact identification of the sourcesfor these economies of scale is beyond this paper.The estimates for economies of scope are negative for both models at alloutput levels, i.e. it is more costly to operate bus and rail-bound servicesas one company than as separate entities. This, in connection with lowerrail-bound economies of scale for higher output levels, would also encourage

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competitive bidding for tram and light railway services. Diseconomies ofscope are present to a greater extent for low output values. Thus, itappears more complex for smaller firms to operate bus and rail-boundservices as one company, especially when ticketing and marketing arealready centralized in the local public transport associations. Anotherpossible explanation is the lack of specialization in firms where employeesare unable to focus on one mode of transport. Farsi et al (2007) on theother hand find positive economies of scope for urban public transport inSwitzerland. The observational difference can partially be explained bythe authors’ data set that includes only one single-output company. Aconsiderable part of the German observations consists of single-output buscompanies, giving a realistic image of their cost structure. The Swiss data setdifferentiates between motor- and trolley-bus services. While determiningcosts of single-output tram companies Farsi et al (2007) as well as thispaper’s application must rely on the econometric predictions.Global economies of scale are present for both model specifications. Sincethey depend on both product-specific economies of scale and economies ofscope, it is obvious that larger companies with zero economies of scope willexhibit greater global economies of scale. Two implications follow: Firstmergers of multi-output companies should be enhanced. Second, in the shortterm, assuming the existing industry structure as fixed, large multi-outputcompanies can still realize savings potential by increasing their output.Developing new customer segments, for example, will increase demand.

5.3 Economies of scale and scope for real firms

Comparing the results for the RE model and the TRE model forrepresentative output levels reveals no substantial differences. One reasonmay be that the firm-specific random intercepts (αi), one characteristic forthe TRE model, did not enter the calculations, because the only meaningfulestimate for representative output levels is the constant α for all firms.It is however meaningful to use the firm-specific random intercepts whenlooking at real companies. Table 5 shows quartile and mean levels ofeconomies of scale and scope of the real multi-output companies includedin the data set. Hence, for each single observation with different outputlevels, factor prices, network lengths, points in time and random intercepts,economies of scale and scope have been calculated. This calculation is onlyperformed for multi-output companies because the defined measures foreconomies of scale and scope apply only to them and adding hypotheticaltram outputs to pure bus companies would not give a true picture. The

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comparison between the estimates of economies of scale and scope forrepresentative output levels on the one hand and real companies on theother hand is somewhat difficult because the order structure is dissimilar.For representative companies, it is output levels, for real companies, it isscale and scope levels. However, some tendencies are comparable. Thegeneral implication holds also for real companies: Global economies of scaleare driven by substantial product-specific economies of scale and slightdiseconomies of scope. The product-specific economies of scale appear tobe present in lower amplitudes compared to the representative companies(e.g. an interquartile range of 0.21 for bus-specific economies of scale of realcompanies in the RE model compared to 0.41 for representative companies).For economies of scope and global economies of scale it is the reverse:Higher amplitudes for real companies compared to representative companies.Comparing the results for the RE and the TRE model, one can observe thatthe quartile range is always greater, except for bus-specific economies of scalefor representative companies, for the RE model. Following this, unobservedheterogeneity appears to remove a prediction bias in differentiating thecompanies.Interestingly, a detailed look at the individual estimates for real companies(not shown here) reveals some patterns: Strong diseconomies of scope inparticular can be observed for smaller East German companies like Gera,Jena, Plauen or Schwerin. Strong global economies of scale driven byeconomies of scope are present for larger municipal companies in the Ruhrarea like Dusseldorf, Essen or Koln. But other large companies like those inStuttgart in the West or Dresden in the East also exhibit substantial globaleconomies of scale. One more observation is of interest: Some mean valuesabove the upper quartile levels (e.g. global economies of scale of 2.27 forthe RE model compared to 1.81 for the upper quartile level) are driven bysome very strong values above the upper quartile level.Based on the results given, companies can manage their mergers andacquisitions (M&A). For single-output companies, a value of economies ofscale above one indicates that the business should be expanded by eitherM&A or generic growth. For multi-output companies a correspondingnegative value for economies of scope at the new output level should notprevent such mergers but is an indication that separation of divisions wouldbe useful even if this is politically unenforceable. The savings potentialshould always be compared with the cost of merging, i.e. economies of scaleshould substantially exceed one for mergers to be pursued.

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Table 5: Economies of scale and scope for real companies

Bus-specific SL Rail-bound specific SLScale and scope level RE TRE RE TRE25% quartile 1.05 1.06 1.71 1.30Median 1.10 1.11 1.83 1.39Mean 1.19 1.26 1.91 1.9675% quartile 1.26 1.25 2.03 1.51

Economies of scope Global economies of scaleScale and scope level RE TRE RE TRE25% quartile -0.33 -0.39 1.06 0.88Median -0.15 -0.16 1.28 1.06Mean -0.25 -0.30 2.27 1.2375% quartile 0.03 -0.04 1.81 1.37

Source: Own calculation

6 Conclusions

In this paper, we estimated both Random Effects and True Random EffectsStochastic Cost Frontier models for urban public transport in Germany, toevaluate the extent of economies of scope and global and product-specificeconomies of scale. The RE model can serve as a benchmark for unbiasedcoefficients while the TRE model supplies unobserved firm heterogeneity.Rich data sets with a time frame of at least five to six years, and including asmany firms as possible, are a prerequisite for useful estimations to representthe dynamic nature of the economies of scale and scope. The modelsapplied in this paper evaluate general industry trends. The product-specificestimates for economies of scale and, even more important, the globaleconomies of scale, are positive, suggesting that the high fragmentationin the German market is not economically justified and that mergers andacquisitions should be politically supported, particularly for companies ingeographical proximity. In an international context, the results can enrichthe discussion about the optimal firm size in local public transport, e.g.there are no bus-specific diseconomies of scale observable in this paper,favoring large companies. From the finding of slight diseconomies of scopewe conclude that bus and rail-bound services should not be integrated onthe cost side. This encourages the use of a competitive bidding process fortram and light railway services. An oligopoly structure appears preferable

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since high fragmentation will again lead to the unexploited economies ofscale problem. The presence of rail-bound increasing returns to scaleand diseconomies of scope points to a structural problem for small tramand light railway systems in Germany. Small tram networks with fewlines are expensive to operate; any expansion can prove too costly whendemand fluctuates. Small networks can be replaced by bus services (as hashappened often in the past), or can be connected with the regional railnetwork according to the Karlsruher Modell,18 where the traction units areequipped with two power systems, one for inner-city operations and theother for interurban operations. Few crossovers between the rail and thetram network, e.g., near the main stations, enable direct connections fromthe rural areas to the inner cities. Such systems can resolve the unexploitedeconomies of scale problem of small tram networks where rail and tramgauge is consistent.

Acknowledgments

This paper is a product of the research program on efficiency analysis in thetransportation sector administered by the Chair of Energy Economics andPublic Sector Management (EE2) at Dresden University of Technology andDIW Berlin. Earlier versions were presented at the 11th European Workshopon Efficiency and Productivity Analysis (EWEPA) in Pisa 2009, the 7thConference on Applied Infrastructure Research in Berlin 2008 and theINFRATRAIN Summer School on Efficiency Analysis in Stockholm 2008. Ithank the participants, in particular Astrid Cullmann, Massimo Filippini,Christian von Hirschhausen, Maria Nieswand, David Saal and AndreasStephan for discussions and suggestions, and the anonymous referees andthe editor of the journal for their helpful comments. Special thanks go toMarika Geissler for support in the data search; the usual disclaimer applies.

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Biography

Matthias Walter is a research associate at the Chair of Energy Economicsand Public Sector Management at the University of Technology Dresden.His focus is on efficiency and competition in network industries, especiallyin public transport. He received his University Diploma in BusinessEngineering from the University of Karlsruhe.

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