Efficiency Analysis Working Papers

WP-EA-16

Potential Gains from Mergers in Local Public Transport – An Efficiency Analysis Applied to Germany

Matthias Walter and Astrid Cullmann

April 2008

Dresden University of Technology Chair of Energy Economics and Public Sector Management Potential gains from mergers in local public transport – an efficiency analysis applied to Germany

Matthias Walter a,∗, Astrid Cullmann b

a Dresden University of Technology, Faculty of Business and Economics, Chair of Energy Economics and Public Sector Management, 01062 Dresden, Germany, [email protected] b German Institute for Economic Research (DIW), Graduate Center of Economic and Social Research, Mohrenstraße 58, 10117 Berlin, Germany, [email protected]

Abstract

We analyze potential gains from hypothetical mergers in local public transport using the non-parametric data envelopment analysis. Our sample consists of 41 public transport companies from Germany's most densely populated region (North Rhine-Westphalia). These companies are merged into geographically meaningful, larger units which are partly operating on a joint tram network. Merger gains are decomposed into individual technical efficiency, synergy and size effects. Our empirical results suggest that substantial gains up to 17 percent of factor inputs are present, mainly resulting from synergy effects.

Keywords: Merger, Public Transport, Efficiency, Data Envelopment Analysis

*Corresponding author: Tel.: +49-351-463-39762; Fax: +49-351-463-39763

1 1 Introduction

Local public transport in Germany is under increasing reform pressure. Up to now the level of cost coverage is far below 100%. Public transport companies operate in monopolistic, historically grown, regional market structures. Recently, public spending has started to decline whereas the number of tenders has steadily been increasing. In this changing market environment, public transport companies run the risk of losing their financial basis. The German market itself is highly fragmented with up to 800 public transport companies being loosely organized in so called public transport associations to secure e.g. a unique ticketing. International studies (e.g. Berechman 1993) indicate that the underlying technology for public transport provision is characterized by increasing returns to scale. Bigger companies have therefore efficiency advantages in comparison to smaller ones. In the United Kingdom, a concentration process had been observed during the liberalization of local public transport (see Cowie 2002) in order to respond on the demanding stress of competition. The fragmentation in Germany seems also not to be efficient and a deeper cooperation, if not outright mergers, is likely to lead to significant cost reductions. The local management of public transport provision in Germany has been eligible. A strong cooperation with local authorities is necessary and local circumstances have to be taken into account. Therefore it is doubtful if a “random” acquisition strategy in geographical distance would be successful.1 Efficiency gains through combined operations can be rather raised where mergers make organizational sense. In this paper, we focus on modeling potential gains from mergers in public transport in Germany’s most densely settled region North Rhine-Westphalia. There, public transport companies have the features that make the realization of merger gains feasible:

• Cities lie very close to each other so that combined operations are possible;

• there are light railway and tram networks with connecting lines, e.g. in Köln and Bonn or in Düsseldorf and Duisburg. That means that up to now there have been two or more public transport companies operating on a common network.

1 There have been examples for failures of such “random” acquisitions, e.g. the Hamburger Hochbahn withdrew from their shareholding in WiBus in Wiesbaden, almost 500 kilometers away from Hamburg, in 2007. 2 Companies have also been proposing mergers in the past (e.g. in Köln and Bonn in 2003 and 2007) but have been hindered by politicians for a variety of reasons. Our empirical analysis is based on deterministic nonparametric efficiency estimates, the data envelopment analysis (DEA). To model the potential gains, we apply a methodology proposed by Bogetoft and Wang (2005). Within this framework, a decomposition of the overall potential gains into three different effects is possible: a technical efficiency, a synergy and a size effect. Therefore, the results allow us to quantify the overall potential gains from mergers for German public transport companies as well as the separate role and magnitude of each of the three components. The framework also allows us to identify the most promising merger combinations and their respective characteristics. Possible merger cases that we analyze include co- operations between up to four neighboring public transport companies in North Rhine- Westphalia. We also test the robustness of our calculations by applying different scale properties and the introduction of structural variables. On an international level numerous studies have analyzed the potential for efficiency improvements through costs reductions or increased technical efficiency at the firm level in particular looking at single output bus companies. Pina and Torres (2000) carried out DEA in order to test if public or private operators are more efficient in the provision of bus services. A good overview for the use of benchmarking analysis, different model specifications and the evaluation of increasing returns to scale is given in De Borger et al. (2002). Multi-output companies are rarely analyzed, especially in Europe; however there is one quantitative study conducted by Farsi et al. (2007) who used Stochastic Frontier Analysis (SFA) to estimate economies of scale and scope of multi-output public transport companies in Switzerland. This paper is to our best knowledge so far the first efficiency analysis analyzing multi-output public transport companies in Germany. Viton (1992) looked at the potential gains from mergers in public transport and analyzed the effects of mergers in the San Francisco and the Bay Area also using SFA. Against this background the motivation of our paper is to empirically study to which extent mergers can improve the technical efficiency level in the German local public transport sector, and how much of the potential gains can be attributed to synergy and size effects.

The remainder of this paper is structured as follows: The next section gives an overview of the methodology. Section 3 introduces the data and model specification and briefly

3 reflects the proposed mergers. We then present average efficiencies for the unmerged firms, compare merger gains under variable and constant returns to scale, reflect merger gains with and without incorporating differences in the production of tram and light railway services and calculate alternative decompositions of synergy and size gains. In Section 5 we present our conclusions and give some policy recommendations.

2 Methodology

2.1 Data envelopment analysis

2.1.1 Analytical Framework Within the empirical literature on productivity and efficiency analysis, we focus on non- parametric linear optimization, the data envelopment analysis.2 This approach relies on a production frontier where the individual efficiencies of the firms relative to this production frontier are calculated by means of distance functions.3 The production frontier can be estimated nonparametrically from a set of observed production units, based on envelopment techniques, e.g. the data envelopment analysis.4 DEA involves the use of linear programming methods to construct a piecewise linear surface or frontier over the data and measures the efficiency for a given unit relative to the boundary of the convex hull of the input output vectors. The determination of the efficiency score of the i-th firm in a sample of N firms in the constant returns to scale (CRS) model is equivalent to the following optimization (see Coelli et al. 2005):

minθ,θ ,λ s.t.

− yi + Yλ ≥ 0

θxi − Xλ ≥ 0 λ ≥ 0

2 The idea of estimating production efficiency scores in a nonparametric framework was originally proposed by Farrell (1957). 3 The concept of distance functions is used to measure efficiency and productivity closely related to the concept of production frontiers. The framework was independently proposed by Malmquist (1953) and Shepard (1953). By defining these functions the concept of radial contradictions and expansions is used, thus an input distance function considers by how much the input vector may be proportionally contracted with the output vector held fix. See Färe and Primont (1995) for mathematical derivation of distance functions. 4 Another technique is e.g. the free disposal hull estimator, which only assumes free disposability and no convexity constraint. We limit ourselves in the analysis to DEA. 4 with λ being an N*1 vector of constants, and X ,Y representing input and output matrices, respectively. θ measures the radial distance between the observation x, y and the point on the frontier is characterized by the level of inputs that should be reached to be efficient is the efficiency score. λ determines the weights for the firms’ inputs and outputs. A value of θ = 1 indicates that a firm is fully efficient and thus is located on the efficiency frontier. To determine efficiency measures under the assumption of variable returns to scale (VRS) a further convexity constraint ∑λ=1 has to be considered.

Data Envelopment Analysis can be carried out with either input or output orientation. Here, input orientation is applied to all calculations. This assumption is realistic in local public transport in Germany because the output volume is mostly predetermined by contracts between local authorities and public transport companies. So the companies’ intention is to use as few resources as possible.

2.1.2 Sub-vector efficiency The radial measure of efficiency commonly used in DEA proposes to reduce inefficiency by a proportional reduction of all employed inputs. This restricts the inefficiency interpretation possibilities. It can be useful to know about the sub-vector or input-specific inefficiency, i.e. how it would be possible to reduce inefficiency by the reduction of only some of the employed inputs. Some inputs may be fixed in the short- term and therefore not reducible or it can be cheaper to focus on the reduction of a specific input. Hence, we calculate sub-vector efficiency additionally to overall efficiency values of the unmerged firms according the methodology proposed by Färe et al. (1994) and for example employed by Lansink et al. (2002). We do that by multiplicating fixed inputs with -1 and transfer these inputs to the output side with all fixed variables. In this context we do not stick to the weak disposability assumption.

2.2 Decomposing merger gains

Following a framework proposed by Bogetoft and Wang (2005) for agricultural services and applied by Bagdadioglu et al. (2007) to the energy sector we decompose efficiency gains from mergers into technical efficiency gains, synergies from joint operation and size gains. The results allow us to quantify the overall potential gains from mergers for

5 German public transport companies as well as the separate role of each of the three components: • A technical efficiency effect: This individual firm effect estimates the improvements made if each single firm in a merger cluster would lie on the frontier, i.e. would be as efficient as its peer with similar size. Note that a merger is not ultimately necessary to realize these effects. • A synergy effect: This effect estimates the economies raised by producing with an improved ratio of input mixture. • A size effect: This effect estimates the improvements possible through the fact that the merged company is operating closer to the optimal firm size.

Let us assume that utilities which are close in a geographic sense merge into larger units. The merged unit is denoted DMU J where J determines the number of merged units. By direct pooling of inputs and outputs we obtain a unit which has used ∑ x j to jJ∈ produce ∑ y j . Based on Bogetoft Wang (2005) a radial input based measure of the jJ∈ potential overall gains from merging the J-DMUs under an input orientation is therefore:

minθ J , θλJ , st. j −+≥∑ yYi λ 0 jJ∈ Jj θλ∑ xXi −≥0 jJ∈ λ ≥ 0

θ J is the maximal proportional reduction in the aggregated inputs ∑ x j that allows the jJ∈ production of the aggregated output ∑ y j . A value below one indicates that one can jJ∈ economize costs by merging the utilities.5 As shown by Bogetoft and Wang (2005) the measure θ J of the potential overall merger gains can be decomposed into several

5 See Bogetoft and Wang (2005) for sufficient conditions about feasible solutions and the requirement of weak gains for arbitrary mergers.

6 effects such as technical efficiency gains, synergy gains and size gains which will be shortly shown subsequently.

2.2.1 Technical efficiency effect (TE) The technical inefficiency of the individual utilities in J may be captured inθ J . These inefficiencies might be eliminated by the new management processes itself, e.g. by imitating the better performers of the same size, sometimes referred to as the peer units, without any benefit from scale or synergy effects. This effect is defined as the technical efficiency effect and it is useful to adjust the overall gains caused by mergers for the potential technical efficiency effect.

Bogetoft and Wang (2005) propose to project the original units to the production possibility frontier and use the projected plans as the basis for evaluating the remaining gains from the merger. Thus, for example, we may project (x jj ,y ) into (θ jjx ,y j ) , where θ j is the standard technical efficiency score under an input orientation for a single decision making unit. Then in a second step the projected plans (θ jjx ,y j ) are used as the basis for calculating the adjusted overall or real merger gains:

*J min Θ , *J Θ ,λ s.t. j − ∑ yi + Yλ ≥ 0 j∈J *J j j Θ ∑Θ xi − Xλ ≥ 0 j∈J λ ≥ 0

Letting T J = θ JJ/θ * we obtainθ J = T JJθ * . T J indicates what can be saved by individual adjustments in the different units in J. We now analyze the two most interesting production economic effects of a merger: First, the synergy effect (H)6 and second, the size effect (S).

6 Bogetoft and Wang (2005) refer to the synergy effect as harmony, scope or input mixture effects.

7 2.2.2 Synergy Effect (H) A merger involves different input and output combinations. This might be advantageous when it leads to a more “productive” way of the product space. We call it the synergy effect (H) in our analysis. Bogetoft and Wang (2005) propose to capture the synergy gains by examining how much of the average input could be saved in the production of the average output, i.e. by the measure (H), which can be expressed in the DEA optimization by:

J min H , H J ,λ

s.t. j α∑ yi + Yλ ≥ 0 j∈J J j j H α∑θ xi − Xλ ≥ 0 j∈J λ ≥ 0 where α ∈[]0,1 is a scalar determining the size of the firm evaluated with the synergy measure. In order to eliminate the size effect, α is typically chosen to be equal to J −1 .

We then consider the mean input and average output over the merged firms. Other values for α can be used for sensitivity testing. HJ <1 indicates a saving potential due to improved harmony, while HJ >1 indicates a cost of harmonizing the inputs and outputs.

2.2.3 Size Effect (S) To analyze the scale effects one has to consider the properties of the underlying production technology. A merger leads to a unit that operates at a larger scale. The outcome depends on the scale properties of the underlying technology. A positive size effect is characterized as follows: Under the assumption that the original productions of firm A=(x1, y1) and firm B=(x2, y2) are efficient and improvement potentials are present in the merged unit A+B using x1+x2 to produce y1+y2, it is sufficient for unit A+B to use in the production process (*(θ x12+ x )) to produce (y1+y2). In the next linear optimization the size gains are captured by asking how much could be saved by operating at full scale rather than at α -scale. This can be reflected by the measure SJ:

8

minS J , S J ,λ st. −+≥∑ yYj λ 0 jJ∈ SH[]0JJj∑θλ x−≥ X jJ∈ λ ≥ 0

SJ <1 indicates that rescaling is advantageous given the synergy improvements, whereas SJ >1 shows that the return to scale property does not favor larger units and therefore merger is costly.

Summarizing the effects, using the definition from the linear optimization, leads to θ *J = HSJJ* and by means of θ J = T JJ*θ * one obtains the basic decomposition θ J = THSJJJ**. This corresponds to a decomposition of the basic merger index θ J into a technical efficiency index T J , a synergy index H J and a size index S J .7

3 Data and model specification

3.1 Dataset

We focus our analysis on a regional sample out of several hundred public transport companies. For this study, the data consisted of 43 local public transport companies in North Rhine-Westphalia. This cross-sectional dataset from the year 2006 is taken from the annual statistics of the Association of German Transport Undertakings (Verband Deutscher Verkehrsunternehmen, VDV) which collects the data from their member companies. The dataset does not include the degree of personnel outsourcing under which the companies have organized their operations. Hence the number of employees (full-time equivalents) in the dataset could be underestimated. However the dataset includes the number of chartered buses which can be used as a proxy for the degree of outsourcing. On this foundation the number of full-time equivalents (FTE) can be updated. According to Leuthardt (1986 and 2005) we assume two additional FTEs per

7 For a survey on alternative decomposition concepts see Bogetoft and Wang (2005).

9 chartered bus.8 After the adaptation of the dataset two of the 43 companies where identified as outliers due to a very low ratio of FTE to employed vehicle capacity. For these companies the FTE numbers are apparently not correctly stated in the statistics. From the remaining 41 companies, 38 are under complete private ownership and three are under mixed, public and private, ownership. 12 of these 41 companies are multi- output companies, i.e. besides bus services these companies also offer tram, metro- similar light railway and in Wuppertal aerial cableway services. 29 of the 41 companies are pure bus operators including trolley buses in Solingen. In order to evaluate the efficiency of mergers under a variable returns to scale technology, the dataset must contain firms of at least similar size in comparison to the mergers. As we want to merge some of the larger firms, we extended our dataset by collecting additional data points of these local public transport firms in Germany that are bigger than those in our original dataset. After eliminating outliers again, we arrived at a dataset of 44 companies in total for the reference technology. The reason of comparability as well as the reduced sample because of outliers limit our maximum evaluated number of merged companies to four.

3.2 Model

In our model we focus on the production process of public transport services based on physical inputs and outputs. The model specifications are limited by data availability. We have no cost and input factor prices in our data sample; thus we focus only on the technical efficiency of the companies. Looking at our dataset, three different input- output specifications are possible, whereby all empirical models base on the international empirical literature for efficiency analysis in public transport. Inputs and outputs differ across the specifications and are summarized in Table 1: 1) The first specification contains the inputs number of seats in the bus fleet and number of seats in the railcar fleet (both including standing room) and the outputs seat-kilometers in buses and seat-kilometers in railcars. 2) The second specification includes the pure number of buses and the number of railcars as inputs and vehicle-kilometers, for buses and for railcars, as outputs. 3) The third specification has passenger-kilometers as single output; both input combinations from the first and second specification are possible.

8 The analyses have also been conducted with 1.5 and 2.5 additional FTEs per chartered bus. No significant different results could be observed. 10 For sensitivity reasons, the analyses have also been carried out with the second input-output-specification. No significant differences in results were observed. 10 Additionally, all input-output specifications have the input number of employees in full- time equivalents (FTE) in common.

[Insert Table 1 here or further back]

We now evaluate the possible input-output specifications: The first input-output specification with seat-kilometer is most appropriate for our analyses because the variables incorporate as much information as it is here possible. In comparison to the second input-output specification with vehicle-kilometers, the capacity of vehicles is included. This capacity can differ substantially, e.g. between articulated buses in urban areas and normal buses in rural areas or between large light railways in Dortmund and the aerial cable cars in Wuppertal for example. The last specification with the one combined output variable passenger-kilometers cannot be used because the model then does not make the economically reasonable distinction between the provision of bus and other services. In the short run, there is no substitutability. In addition, the use of passenger-kilometers would include the demand side in the analysis whereas seat-kilometer and vehicle-kilometer focus on the supply side only. The capacity utilization does often not lie in the public transport company’s area of influence. They are not directly responsible for advertisements, ticketing and traffic planning. So the focus in the model on the supply side is economically justified.10 Additionally to inputs and outputs we pick up the idea of structural variables presenting environmental conditions which are not in the influence of the management or representing specifications of input or output variables not covered yet. We include two different variables through introducing them as additional output variables. This is a valid procedure following Coelli et al. (2005) because we apply input orientation and hold all outputs constants, i.e. all outputs are outside the scope of the management while organizing the merger:11 • The first structural variable is an inverse density index defined as total track length for trams and light railways and line length for buses divided by the number of inhabitants in the operation area of a local public transport provider. We therefore make those providers better off which operate in a less densely populated area. For these companies it is usually

11 Within the DEA framework there is also another approach to capture conditions which are not under the control of the management. It was proposed by Banker and Morey (1986) who formulated a DEA model in which one only seeks radial input reductions over some variables of the input vector, the discretionary set. 11 more difficult to produce their output because of a less intensively coordinated timetable and the network dispersion. With our approach companies operating in these areas will obtain a better efficiency score, because they obtain additional “output”. • The second structural variable is a tram index measuring the tram capacity as percentage of all rail-bound capacity. We therefore favor these companies offering tram12 services in comparison to those companies offering light railway or metro services for mainly two reasons. On the one hand the provision of metro and partly also light railway services require high infrastructure investments which cannot be covered here due to the lack of cost data. On the other hand the average speed of tram services is much lower and therefore output production more difficult with given inputs.13

3.3 Mergers

We now proceed with the simulation of the mergers. In general, the proposed mergers should fulfill two criteria: 1) A tram or light railway network with connecting lines, operated by more than one company at present, shall be operated by only one company after the merger in order to facilitate operations planning and to encourage the use of shared facilities. A network with connecting lines is the case for three mergers.15 2) All other companies are assigned to mergers where it makes geographical sense. The realization of efficiency gains from mergers in public transport relies heavily on the geographical nearness of the cities and companies. Only under this constraint, gains in the production process, e.g. from combined operations,

12 Also aerial cableway because the average speed is similar to trams (approximately 30 km/h) 13 The data for the non-discretionary variables is obtained from the VDV statistics 1998 and 2006, validated by company information. 15 These three mergers are: Köln and Bonn; Düsseldorf, Duisburg, Krefeld and Neuss; Essen, Mülheim, Oberhausen and Moers. Apart from these mergers, there is only one additional tram network in Germany with connecting lines between different cities. Interestingly enough, there is already the joint-venture Rhine-Neckar-Verkehrsgesellschaft between the public transport companies of Mannheim, Heidelberg and Ludwigshafen in the Rhine-Neckar area on this network.

12 seem feasible. North Rhine-Westphalia is in comparison to the rest of Germany the state which best fulfills this constraint.

We select 14 out of 73 potential mergers from our analyses. shows these mergers through different fillings. For Herten, Lüdenscheid, the two companies from Münster and Siegen no adequate merger combinations could be found; thus these five remain unmerged. We get three mergers with trams and light railways operating on a network with connecting lines, four mergers of one tram and light railway operator with several pure bus operators and seven pure bus mergers.

[Insert Figure 1 here or further back]

4 Results and interpretation

In this section we present our results. First we calculate average efficiency estimates for the unmerged companies and analyze input-specific inefficiency as well as the impact of structural variables on the companies’ performance. Then we present merger gains under variable and constant returns to scale. Afterwards we compare technical efficiency and real merger gains without and with a structural variable and calculate alternative decompositions of the real merger gains into synergy and size effects.

4.1 Average efficiencies for the unmerged firms with structural

variables

Table 2 shows the average efficiencies for the unmerged firms with seat-kilometer as output for different model variations. Our intention is to analyze sub-vector efficiency as well as the effects of the structural variables under variable returns to scale (VRS) and constant returns to scale (CRS) and draw conclusions for the impact on the performance level. We start with the base model (Model 1) without the inclusion of any structural variables. The average efficiency for the unmerged firms is 0.851 for VRS and 0.806 for CRS. The average firm therefore would be able to save 14.9% respectively 19.4% of their inputs if it produced on the efficiency frontier. Also the range from 0.575 respectively 0.479 up to 1.000, when looking at the individual scores in the base model, shows that inefficiency is inherent in the sector while still being on a realistic level. Concerning the input-specific efficiency estimates we see that the efficiency value of the input capital (buses and railcars) with 0.838 for VRS is

13 approximately on the level of overall efficiency. On the other hand, the efficiency value of the input labor (FTEs) with 0.680 is significantly below overall efficiency. These conclusions hold for CRS. The technical inefficiency in the sector is thus mainly determined by labor which apparently is not efficiently employed. This corresponds with the trend in the sector to reduce the number of FTEs in the last years while subsequently producing more output. According to this, the trend can be expected to continue in the next years. In Model 2 and 3 we introduce structural variables in order to compare with the overall efficiency of Model 1. In Model 4 we include both structural variables at the same time. In total, VRS and CRS, the impact of the tram index seems to be higher than the impact of the inverse density index. To be more exact, under VRS the impact of the inverse density index with an efficiency value of 0.870 is slightly higher than that for the tram index with 0.863. But under CRS, the impact of the tram index with an efficiency value of 0.841 is substantially above that for the inverse density index with 0.825. When including both structural variables at the same time, we see a significant difference to the Models 2 and 3 with 0.882 as efficiency value for Model 4 under VRS, but no big difference to Model 3 under CRS in Model 4 with an efficiency value of 0.845 and a calculated difference of 0.004. We therefore will discuss the merger gains in the following with Model 1 (without structural variables) and Model 3 (with tram index). We will leave the inverse density index aside, also in order not to over-specify our model regarding the relatively small data set.

[Insert Table 2 here or further back]

4.2 Merger gains under variable and constant returns to scale

We calculate overall potential merger effects for VRS and CRS without structural variables included (Model 1). We decompose these overall effects into real merger effects (synergy and size effect together) and technical efficiency effects. Table 3 shows the results. The mergers are presented in descending order with respect to company size. The most important result is the existence of significant real merger gains, i.e. gains that are only possible in merging the operational processes. Under VRS and CRS the biggest merger 1 with two large bus, tram and light railway operators shows the highest real merger gains: 17%. Under VRS solely, we also find mergers with negative real merger gains, i.e. the mergers result in increased inefficiency in terms of synergy and size. 14 However, mergers 6, 9, 10 and 11 can still have a positive overall impact if the technical efficiency is brought to a frontier level. The negative real merger effects have their explanations. The one for merger 6 is of economical nature. Wuppertal has an aerial cableway with which synergies to bus services are not probable, at least not for maintenance, technology and substitutability. Mergers 7, 9, 10 and 11 compose big bus companies which do not exist in the German market yet.16 So the reason for these negative effects is just the missing references. In reality, however, real merger gains seem possible. In the following we will stick to the VRS assumption because it allows us to further decompose the real merger gains into synergy and size gains. As the overall potential gains shown in Table 3 are always bigger for CRS, the potential gains given in the following analyses will therefore be a rather conservative estimation.

[Insert Table 3 here or further back]

4.3 Merger gains with and without incorporating differences in the production of tram and light railway services Figure 2 visualizes the VRS results from Table 3. We see substantial real merger gains (synergy and size) for the mergers of companies operating on a common tram and light railway network (dark-shaded) and mergers of tram and light railway operators (light- shaded) except merger 6. The mergers of companies operating on a common tram and light railway network are at the same time the biggest in terms of output seat-kilometers (bus, tram and light railway) indicated by the bubble size. The results for smaller pure bus mergers vary and have to be evaluated on a case-by-case basis.

[Insert Figure 2 here or further back]

We now include the tram index as structural variable with the biggest impact in our analysis. Therefore the tram index is calculated for all mergers. As the mergers consist of companies of different sizes, the tram index is input-weighted. Figure 3 shows the results. Comparing them with Figure 2, we see some heterogeneity and can cluster the mergers into four groups. First we have the pure bus mergers 7 and 9-14 with no changes at all. This seems reasonable because the tram index itself is not directly

16 The integrated transport company Deutsche Bahn with its bus subsidiary DB Stadtverkehr is not included in the dataset. 15 affecting the results for bus companies. Second there are the bus, tram and light railway mergers 1, 4 and 8 with no significant changes because the level of tram services differs not very much in comparison to their benchmarks and hence the incorporation of the structural variable does not change the results. Third there are the bus, tram and light railway mergers 2a and 3a which are still favorable but to a smaller extent and with few firms (Neuss taken away from merger 2 and Oberhausen as well as Moers taken away from merger 3). Mergers 5 and 6 are not beneficial any more and hence not included in .

[Insert Figure 3 here or further back]

All these mergers (except merger 6) have been highly beneficial without including the tram index. However, not all the non-beneficial mergers in Model 3 are likely to be really disadvantageous. As we have seen in the illustration of average efficiency estimates for different structural variable specifications, the individual efficiency increases as the number of structural variables increases. So a careful interpretation and evaluation of these mergers seems necessary.

4.4 Alternative decompositions of synergy and size gains

Up to now we only looked at the real merger gains in general. We did not differentiate between a synergy effect from a better input mixture or the common provision of different outputs and a size effect resulting from the production at bigger scale. We want to calculate this decomposition with three different values for α , the scalar determining the size of the firm evaluated with the synergy measure (see Section 2.2). First we follow Bogetoft and Wang (2005) with the default value of 1/n where n is the number of firms merged. In order to conduct a sensitivity analysis we halve and double this value. This gives us some indication on the magnitude of the merger effects if there is a quite small firm operating with this input mixture or if the merger consists of a very big firm and additional smaller firms. Table 4 gives the result for the described decomposition. The most obvious result is the much more advantageous status of synergy gains, in particular for mergers 1, 4 and 9 where this conclusion holds for all the three different values of α . For the scalar values of 1/n and even more 2/n, the synergy gains are in majority higher than the size gains. In general, significant gains (at least 5%) can be expected from six mergers due to synergy gains in the 1/n and the 2/n case and due to size gains in the 1/(2n) case, from three

16 mergers due to synergy gains in the 1/(2n) case and from one merger due to size gains in the 1/n case. This also emphasizes the advantageous status of synergy gains. However, that these input mixtures in the mergers seem beneficial is not purely related to synergy. Size over a specific threshold can be conditional in order to reach this beneficial input mixture, e.g. for automated maintenance activities. Furthermore, the question remains which input mixture or output combination determines the synergy gains. We leave this to further research.

[Insert Figure 4 here or further back]

5 Conclusions In this paper we applied new methods of data envelopment analysis in order to evaluate the potential efficiency gains from mergers in an important sector of the economy: local public transportation. We motivated our approach with prior international research indicating inefficiency, the high fragmentation in Germany and the suitable geography of the proposed mergers. We derived that the incorporation of differences in rail-bound local public transport services is necessary, i.e. the production technology for tram provision is different from the production technology for metro provision, but has to be analyzed on a case-by-case basis. Population and network density plays no substantial role in this already very densely populated area. Substantial merger gains can be expected for bus, tram and light railway mergers and smaller bus mergers. A resilient statement for bigger bus mergers in this case study cannot be given; we leave this to further research. A sensitivity analysis for decomposition of real merger gains showed the mastery of synergy gains against size gains. Nevertheless these two effects can only be addressed together. Following our analysis, the implementation of mergers with companies operating on a common tram and light railway network is of highest priority and should politically be facilitated. Mergers are furthermore a good instrument to prepare the companies for the changing competition constraints with the increasing number of tenders. Companies active in several cities can diversify their risks, no longer being completely dependent on contracts with one city. It is furthermore an issue of transport and competition policy to aim at a framework and measures for a new industry structure. Increasing financial pressure and changes in demography as well as settlement structures will also raise the topic again. There is plenty of room for further research in this sector, especially with monetary data. Revenue and cost efficiency should be

17 analyzed, also in order to come up with more insights into the existence of economies of scale and scope from an allocative point of view.

Acknowledgements

We would like to thank Prof. Dr. Christian von Hirschhausen for his valuable comments. Without his support this paper would not exist.

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20 Table 1: Possible input-output specifications Specification 1 Specification 2 Specification 3

Inputs Number of employees ∗ ∗ Number of Seats in bus fleet ∗ ∗ Either Number of Seats in railcar ∗ ∗ Number of buses * ∗ or Number of railcars * ∗

Outputs Seat-kilometers in buses ∗ Seat-kilometers in railcars ∗ Vehicle-kilometers in buses ∗ Vehicle-kilometers in railcars ∗ Passenger kilometers in total ∗

Structural Variables Inverse density index (∗) (∗) (∗) Tram index (∗) (∗) (∗)

21 Table 2: Average efficiency estimates with seat-kilometers as output

Model 1 Model 2 Model 3 Model 4

Without structural variables With inverse With tram With tram and Overall Labor-specific Capital- density index index inverse efficiency efficiency specific density index efficiency VRS 0.851 0.680 0.838 0.870 0.863 0.882 CRS 0.806 0.583 0.806 0.825 0.841 0.845

22 Table 3: Decomposition of potential merger effects for variable and constant returns to scale (Model 1)

Merger Overall Real Technical Overall Real Technical potential merger efficiency potential merger efficiency effect effect effect effect effect/ effect J J Θ J Θ*J T Θ J Synergy T (VRS) (VRS) (VRS) (CRS) effect (CRS) (CRS) 1) Köln, Bonn 0.70 0.83 0.85 0.69 0.83 0.84

2) Duisburg, Düssel- 0.80 0.94 0.86 0.80 0.93 0.86 dorf, Krefeld, Neuss 3) Mülheim, Essen, 0.79 0.95 0.83 0.73 0.90 0.82 Oberhausen, Moers 4) Dortmund, Hagen 0.77 0.90 0.85 0.77 0.88 0.87

5) Bochum, Herne 0.79 0.95 0.83 0.78 0.93 0.83

6) Wuppertal, 1.00 1.17 0.85 0.80 0.94 0.85 Ennepetal

7) Aachen, 1.03 1.20 0.86 0.77 0.91 0.85 Geilenkirchen

8) Detmold, Extertal, 0.77 0.88 0.88 0.77 0.92 0.84 Bielefeld 9) Troisdorf, 0.90 1.25 0.72 0.69 0.95 0.72 Euskirchen, Düren 10) Gummersbach, 0.80 1.03 0.78 0.76 0.99 0.77 Remscheid, Solingen 11) Dormagen, Gladbach, 0.95 1.11 0.86 0.81 0.96 0.85 Viersen 12) Hamm, Kamen 0.76 0.98 0.77 0.76 0.98 0.77

13) Monheim, 0.88 0.91 0.97 0.88 0.91 0.97 Leverkusen

14) Gütersloh, Soest 0.73 0.96 0.77 0.73 0.96 0.77

Bold: companies with tram / light railway

23 Table 4: Decomposition of potential merger effects for variable returns to scale

Merger Synergy Synergy Synergy Size Size Size merger merger merger merger merger merger gains gains 1/n gains gains gains 1/n gains 2/n 1/(2n) 2/n 1/(2n)

1) Köln, Bonn 0.87 0.84 0.83 0.95 0.98 1.00 2) Duisburg, Düssel- dorf, Krefeld, Neuss 1.02 0.97 0.95 0.92 0.97 0.99 3) Mülheim, Essen, Oberhausen, Moers 0.98 0.93 0.90 0.97 1.02 1.05 4) Dortmund, Hagen 0.94 0.89 0.90 0.96 1.01 1.00 5) Bochum, Herne 1.02 0.97 0.95 0.93 0.98 1.00 6) Wuppertal, Ennepetal 0.96 0.94 1.17 1.23 1.24 1.00 7) Aachen, Geilenkirchen 0.92 0.91 1.20 1.31 1.32 1.00 8) Detmold, Extertal, Bielefeld 1.20 0.97 0.89 0.74 0.90 0.99 9) Troisdorf, Euskirchen, Düren 1.03 0.97 0.95 1.21 1.29 1.31 10) Gummersbach, Remscheid, Solingen 1.03 1.00 0.99 1.00 1.03 1.04 11) Dormagen, Gladbach, Viersen 1.06 0.98 0.95 1.05 1.13 1.00 12) Hamm, Kamen 1.06 1.00 0.98 0.93 0.99 1.00 13) Monheim, Leverkusen 1.00 0.93 0.91 0.91 0.98 1.00 14) Gütersloh, Soest 1.05 0.98 0.96 0.91 0.97 1.00 Bold: companies with tram / light railway

24 Figure 1: Geography of local public transport mergers in North Rhine-Westphalia

Extertal Münster Bielefeld Detmold Gütersloh

Oberhausen Hamm Herten Kamen Soest Herne Moers Dortmund Duisburg Essen Bochum Krefeld Mülheim Hagen Wuppertal Düsseldorf Ennepetal Viersen Solingen Lüdenscheid Gladbach Neuss Rem- Dormagen scheid Gummersbach Leverkusen Monheim Geilenkirchen Köln Troisdorf Siegen Düren Aachen Bonn Euskirchen

Rhein

Legend: Tram or light railway operators in bold font Not merged companies

25 Figure 2: Merger gains decomposition for variable returns to scale without structural variables (Model 1)

30% Technical Efficiency Gains 9

10 12 14

20% 3 1 6 5 4 7 11 2 8 10%

13 Synergy and Size Gains 0% -30% -20% -10% 0% 10% 20% 30%

Legend: Pure bus merger Bus and tram / light railway merger Bus and tram / light railway merger on a common network Bubble size reflecting company size (in total seat-kilometers)

26 Figure 3: Merger gains decomposition for variable returns to scale with a tram index (Model 3)

30% Technical Efficiency Gains 9

10 12 14

20% 3a 4 1

7 11 2a 8 10%

13 Synergy and Size Gains 0% -30% -20% -10% 0% 10% 20% 30%

Legend: Pure bus merger Bus and tram / light railway merger Bus and tram / light railway merger on a common network Bubble size reflecting company size (in total seat-kilometers)

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