Bidder Asymmetries in ProcurementAuctions: Efficiency vs. Information∗

Evidence from Railway Passenger Services

Stefan Weiergraeber†

Christoph Wolf‡

March 8, 2021

Abstract

We estimate a structural model of procurement auctions with private and common value

components and asymmetric bidders using detailed contract-level data on the German market

for railway passenger services. Exploiting exogenous variation in the procurement design, we

disentangle the asymmetries in private costs from asymmetries in information about the com-

mon value. While each asymmetry can rationalize the dominance of a firm, understanding its

source is crucial for the evaluation of the auction design as welfare and revenue implications

depend on the source of dominance. Our results indicate that the incumbent is slightly more

cost-efficient and has substantially more precise information about the common value compo-

nent. If bidders’ common value asymmetry was eliminated, the average probability of selecting

the efficient firm would increase by 40%-points and bid-shading would decrease substantially.

JEL Classification: H57, L92, D44Keywords: procurement with asymmetric bidders, incumbency advantages, structural estimationof auctions, railway passenger services

∗We thank Yonghong An, John Asker, Michael Baye, Estelle Cantillon, Francesco Decarolis, Elisabetta Iossa, MarcIvaldi, Gautam Gowrisankaran, Yao Luo, Georgia Kosmopoulou, Andras Niedermayer, Volker Nocke, MartinPesendorfer, Bernard Salanié, Armin Schmutzler, Johannes Schneider, Katja Seim, Michelle Sovinsky, AndréStenzel, Konrad Stahl, Hidenori Takahashi, Frank Wolak, Ruli Xiao, and Christine Zulehner as well as partici-pants at IIOC 2017, CEPR Applied IO School 2017, EARIE 2018, SITE 2018, ASSA 2019, and Berlin IO Day2019 for helpful discussions and comments. We thank Marisol Diaz Aspiazu for capable research assistance andFelix Berschin from Nahverkehrsberatung Südwest for providing us with the data on procurement prices.

†Department of Economics, Indiana University; E-mail: sweiergr[at]iu[dot]edu.‡Bocconi University, Department of Economics and IGIER; E-mail: christoph.wolf[at]unibocconi[dot]it.

mailto:sweiergr@iu.edumailto:christoph.wolf@unibocconi.it

1. Introduction

A substantial part of economic activity is conducted via procurement mechanisms.1 In manycountries and organizations, the procurement of goods and services above a certain thresholdvalue must be awarded competitively. While the advantages of competitive procedures motivatemany procurement regulations,2 concerns have been raised about their effectiveness in severalindustries. One of the most frequent problems is the existence of incumbency advantages thatprevent entrants from submitting competitive bids.3 Understanding the sources of incumbencyadvantages and designing procurement mechanisms well is important not only because of the sizeof these markets but also because procurers often have a lot of flexibility in the procurementdesign. If used correctly, this flexibility can help to improve procurement outcomes.4 Even thoughthe existence of incumbency advantages is widely acknowledged, the empirical literature analyzingits sources is scarce.

In this paper we combine exogenous variation in the procurement design with a structural auctionmodel to empirically study the sources of the dominance of the former state monopolist DeutscheBahn (DB Regio5) in the German market for short-haul railway passenger services (SRPS). Morethan 20 years after the market’s liberalization, DB Regio still operates the majority of the trafficvolume (67.1% in 2016, Monopolkommission (2019)). The German market for SRPS, with its sizeof around EUR 8 billion in subsidies for 2016, is an important example of incumbency dominancethat shares many features with similar markets in other countries. In the 1990s many Europeancountries started to liberalize several network industries that used to be controlled by state mo-nopolists, for example, telecommunications, retail electricity, and transportation services. In allthese markets asymmetries between firms are prevalent, because entrants that became active inthe market relatively recently compete with established incumbents. While the aim of the liberal-ization was a more efficient provision of publicly subsidized goods through increased competition,the experiences have been mixed.

An explicit concern by the Monopolkommission6 and industry experts regarding the Germanmarket for SRPS is that in many cases competitors of DB do not submit competitive bids. Usingreduced-form regressions, Lalive and Schmutzler (2008) provide evidence that DB has a significantlyhigher probability of winning auctions than its competitors. To assess the effectiveness of this

1For example, public procurement alone amounts to 13% of GDP in OECD countries (Committee 2016).2See, for example, European Commission (1996) for the European Commission’s emphasis on the value of compet-itive awardings for public procurement.

3A recent overview of the topic is provided in OECD (2019). Iossa (2019) discusses the important role of incumbencyadvantages in particular. European Commission (2016) provides a discussion for the transportation sector whichis the focus of our paper.

4For example, Coviello et al. (2018) provide a discussion of the value of flexibility in procurement and show evidencefor potential benefits of additional discretion to procurement agencies.

5For brevity, we refer to DB Regio, the short haul distance passenger service subsidiary of Deutsche Bahn, as DBin the remainder of this paper.

6The Monopolkommission is an independent advisory council to the federal government of Germany focusing oncompetition policy.

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market, it is crucial to understand the sources of DB’s dominance in the auctions, which are runby local procurement agencies. Industry experts and competition agencies regularly bring up twopotential explanations: a more efficient cost structure of DB, i.e., a private value advantage, andbetter information about future ticket revenues, i.e., an informational advantage about a commonvalue.

We show theoretically—in an extension of the model of Goeree and Offerman (2003) to asym-metric firms—that both a cost advantage and an informational advantage about the common valuecan rationalize a dominant firm. Importantly, an informational advantage of a firm creates anamplified winner’s curse for the less informed bidders, which induces them to bid overly cautiously.This can have detrimental effects for both auction revenues and the selection of the cost-efficientbidder.

Therefore, from looking at the aggregate market structure, it is not clear whether DB’s dominanceis justified by an efficient cost structure or whether DB can defend its position due to a stronginformational advantage. As the former state monopolist, DB has more experience in providingservices and, as a publicly held firm, it may have advantages in financing expenditures comparedto its rivals. These factors may result in a cost advantage of DB over its competitors. In addition,ticket revenues from operating a track constitute a common value component and DB might havean informational advantage regarding future demand. The reason is that DB Vertrieb, which isintegrated with the DB holding that owns DB Regio, has access to ticket revenue and passenger dataeven on tracks which it is not operating itself. Entrants—and even procurement agencies—typicallydo not have access to this information. Therefore, DB’s informational advantage is likely to persistover time even after entrants start operating a track.

Competition authorities have raised concerns about DB’s exclusive data access for many years,see, for example, Monopolkommission (2009). Recently, this debate has been reinvigorated by acomprehensive discussion of DB’s data monopoly in Monopolkommission (2019).7 Consequently,it is likely that DB has an informational advantage over its competitors. Ticket revenues typicallycover about 40% of the total cost of a contract and are equal to approximately 67% of the winningbid on average (Rödl & Partner 2014; Monopolkommission 2009); therefore, the common valuecomponent is a substantial part of the value of a contract in our application, and it should affectfirms’ bidding behavior significantly.

To assess the efficiency of the market, disentangling the asymmetries in private and commonvalue components is therefore essential. To the best of our knowledge, we are the first to empiri-cally disentangle these asymmetries allowing us to determine the reason underlying the apparentincumbency advantage.8 Our estimates allow us to compute efficiency measures for different types

7The fact that the competition authority and the competitors regularly argue about and demand the data tobe available to other parties before bidding supports the view that revenues are indeed a common value, i.e.,information that other bidders hold is relevant for a bidder’s assessment of the ex post value of winning theauction.

8While De Silva et al. (2003; 2009) use the model of Goeree and Offerman (2003) to motivate their analysis of

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of auctions and to conduct counterfactual analyses.

Towards this, we make use of a detailed contract-level data set on German SRPS procurementauctions, which covers the period from 1995 to 2011. A key feature of our data is that we observeplausibly exogenous variation in the auction design which enables us to disentangle the two asym-metries. While some local procurement agencies decide to have the train operating firms bear therevenue risk from ticket sales, other agencies decide to bear the risk themselves. If the ticket rev-enues remain with the agency (gross contract) the auction is a standard asymmetric IPV auction.If the train operating company is the claimant of the ticket revenues (net contract), the auction isone with a private value (cost) and a common value (ticket revenues) component.

We use the gross auctions in a first step to recover the cost distributions of the firms usingstandard methods following Athey and Haile (2002). The exogeneity of the contract mode impliesthat tracks auctioned with gross contracts are not systematically different from tracks auctionedwith net contracts; hence, we can extrapolate the cost distribution from gross to net auctionsas well. This allows us to recover the distribution of asymmetric information in net auctions.Intuitively, conditional on the estimated cost distributions, any systematic differences in biddingbehavior between DB and the other firms has to derive from differences in the information aboutcommon values. Assuming that the choice between net and gross contracts is exogenous may seemrestrictive at first sight; therefore, we provide extensive evidence in support of this key assumptionin Section 3.3.9

Our evidence in favor of the exogeneity assumption consists of two components. First, we showthat contract features do not differ systematically between gross and net auctions using statisticaltests and reduced-form regressions. Second, we provide evidence from industry reports and industryexperts who argue that the choice between gross and net auctions by local authorities is driven byidiosyncratic preferences or chosen politically rather than based on characteristics of the track tobe auctioned.

The results of our structural analysis show a systematic cost advantage of DB over its entrantrivals. Importantly though, it is not as large as one may initially expect given DB’s dominancein the market for SRPS. When comparing the cost distributions across bidder types, we find thatDB’s cost distribution is dominated in a first-order stochastic dominance sense in only 27% of theauctions.10 The estimation of the informational advantage of DB over its competitors reveals thatindeed in most auctions DB has significantly more precise information about future ticket revenues.For example, our estimates imply that an entrant’s residual uncertainty, i.e., the variance of the

procurement of highway contracts in Oklahoma, their empirical strategy follows a reduced form approach thatdoes not allow them to distinguish the two asymmetries nor to disentangle which asymmetry induces the observedbidding pattern.

9Note that, for the estimation, we require exogeneity only with respect to the cost characteristics. If the contractmode was chosen based on revenue risk characteristics that are unrelated to the cost structure of the track, ourparameter estimates would not be affected. The interpretability of our counterfactual analyses of changing thecontract mode would be more limited if exogeneity with respect to revenue characteristics does not hold, however.

10Note that if DB’s distribution is dominated in a procurement auction, it has the stronger distribution.

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unknown ticket revenues after having conditioned on the own revenue signal, is on average 2.7 timeshigher than that of the incumbent.

In summary, our results support the concerns of the German competition policy advisory councilin Monopolkommission (2009; 2019) that DB’s dominance is at least partially due to its informa-tional advantage. This may call for regulatory interventions, for example, to symmetrize informa-tion across all bidders. An easier measure to increase efficiency could simply be to award moregross contracts, which eliminates the common value component from the auction. We study thisintervention in a counterfactual analysis and find that entrants shade their bids less than in netauctions. As a consequence, if the net auctions in our sample were procured as gross auctions,the median ex ante efficiency, i.e., the probability of selecting the cost-efficient bidder, increasesdrastically from 19.9% to 80.7%.

To illustrate which channels are likely to be the main drivers of the huge efficiency loss in net auc-tions, we simulate several hypothetical scenarios in which we successively eliminate specific sourcesof inefficiency. We find that both the noise introduced by the revenue signal and asymmetries inthe cost distributions already lead to considerable efficiency losses. By far, the most importantsource of inefficiency, however, is the asymmetric precision of information about the common valuecomponent. This highly inefficient incumbency advantage from superior information in net auc-tions reemphasizes that addressing incumbency advantages in public procurement is important, asdiscussed, for example, by Iossa (2019) and OECD (2019).

Our counterfactuals reveal that gross auctions tend to result in higher agency revenues as well.Assuming that the expected ticket revenues do not depend on who bears the revenue risk, we findthat the required net subsidies11, i.e., the paid subsidies minus the expected ticket revenues receivedby the agencies, are more than 50% lower when net auctions are procured as gross auctions than inthe observed net auction sample. The reason for this is that the common value uncertainty leads tosubstantial bid shading in net auctions. As a consequence, the winning bids are not substantiallylower than in gross auctions. Instead, agencies pay an additional risk premium to the firms in netauctions which reduces the agency payoff.

Overall, our estimates support the view that too many auctions have been procured as netauctions both from an efficiency and a revenue perspective. Therefore, procurers should evaluatecarefully when to use net auctions instead of following their, often ideological, preferences aboutthe contract form in all tenders. On a more general level, our empirical analysis highlights that athorough understanding of the implications of a specific procurement design is essential to enhancethe outcomes of a procurer’s competitive procedures. The crucial role of the buyers on procure-ment outcomes has also been found in a different context, for example, in Decarolis et al. (2018).Therefore, our findings do not only apply to public procurement but they can also inform the de-sign of procurement practices of private companies that often purchase high-value goods or services

11Note that in all of our auctions, the procurement agency pays the winning bid to the winning firm as a subsidyto fulfill the contract. Therefore, we use the terms subsidy and winning bid interchangeably.

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through a variety of mechanisms while also facing asymmetric sellers.

Auction settings with private and common value asymmetries are very common. In principle,our model and estimation strategy can be applied to other settings as well. The only requirement isthat some variation in auction modes is observed that allows the researcher to estimate the privatevalue distribution from one sample and use this distribution to extrapolate private values on thesample with additional common value uncertainty. For example, Li (2020) uses our theoretical andempirical framework to disentangle informational asymmetries from corruption in land auctions inChina to rationalize observed auction outcomes. Other potential applications include oil drillingauctions, procurement auctions with subcontracting requirements, and auctions of objects withresale value. Oil drilling auctions are sometimes in the form of drainage lease auctions next to anexisting tract and sometimes in the form of wildcat auctions.12 While the private value componentis likely to be asymmetric across bidders in both settings due to the use of different technologies,in drainage lease auctions one firm tends to have more precise information about its value thanits rivals while in wildcat auctions information is likely to be symmetrically distributed (see theseminal paper Hendricks and Porter (1988)). Some procurement agencies, for example the NewMexico DOT, require firms to use specific subcontractors for certain projects. If firms possessprivate information about the value of these subcontractors, a model with both asymmetric privateand common value components is likely to be appropriate.

Related literature The German SRPS industry is characterized by bidder asymmetries becausea former state monopolist (DB) that is the incumbent on many tracks competes with new andrelatively inexperienced entrants. Therefore, we build on the theory of asymmetric first-priceauctions. In a seminal paper, Maskin and Riley (2000a) show that stochastically weaker firms bidmore aggressively and stronger firms win with higher profits. Goeree and Offerman (2003) providea tractable framework to study auctions that involve both private and common value components.Our theory relies on their framework and extends their symmetric model to a model in whichbidders have asymmetric private value distributions and have asymmetrically precise informationabout the common value.13

De Silva et al. (2003) analyze data on highway procurement in Oklahoma with reduced formregressions and find that entrants win with lower bids than incumbents. In De Silva et al. (2009) anatural experiment for the same application with more recent data is studied in which an informa-tion release policy makes uncertainty more symmetric. In this paper, the authors find that biddingbecomes more symmetric after the information release. Both papers consider a setting with privateand common values as in Goeree and Offerman (2003) and asymmetries in bidding are explainedby differences in the distribution of the compound private signal. However, the private and com-

12Often mineral rights auctions are modeled as pure common value auctions. However, there may be private valueconsiderations as well, for example, due to differences in extraction technologies, see Sant’Anna (2018) for adiscussion.

13We motivate our choice of this particular model in light of our application in detail in Section 3.3.

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mon value distributions are not modeled separately and therefore the authors cannot disentanglewhich of the asymmetries induces the observed bidding behavior. A key contribution of our paperis that we model private and common value asymmetries explicitly and that the variation in ourdata allows us to disentangle and quantify each of the asymmetries. We theoretically show that itis crucial to understand the relative importance of the asymmetries as they have opposite welfareimplications. Moreover, our structural empirical results allow us to study the efficiency propertiesof the auctions and to conduct counterfactual analyses.

For the estimation of our model, we rely on the large literature on the structural estimation ofasymmetric auctions. Guerre et al. (2000) show how first-price IPV auctions can be nonparamet-rically identified and estimated based on winning bids only. Li et al. (2000) discuss identificationand nonparametric estimation of conditionally independent private information auctions whichcomprise IPV and common value auctions as a special case. Their arguments rely on measure-ment error techniques and require observing all bids and that bidders’ signals are a multiplicativefunction of the private and the common value signals. While there are several papers that analyzeinformational asymmetries in auctions empirically, a common characteristic of this literature isthat they rely on observing the full bid distribution. For example, in recent work, Somaini (2020)shows how common values can be identified in a structural model from the full bid distributionand observable variation in bidder-specific cost shifters. Since we only observe winning bids, wecannot rely on any of the existing methods for asymmetric common value auctions discussed inthe next paragraphs. To be able to shed light on an important policy question in spite of ourdata limitations, we use an empirical strategy that relies only on winning bid data and exogenousvariation in the contract design.

In the same multiplicative framework as Li et al. (2000), Hong and Shum (2002) estimate aparametric model with both private and common value components and symmetric bidders usingprocurement data from New Jersey. They argue that the winner’s curse effect can outweigh thecompetition effect so that more bidders can result in less aggressive bidding. Their focus is onestimating the relative importance of private and common values for specific types of auctions.They find that highway work and bridge repairs contain a substantial common value componentwhile paving services are mostly private values auctions. In contrast to their study, we have preciseinformation about which parts of the contracts correspond to private and which to common valuecomponents. Furthermore, we observe exogenous differences in the design of auctions that eliminateor add specific parts of risk for the bidding firms. These features allow us to focus on separatingthe effects of asymmetric cost distributions and asymmetric information about the common valueacross different bidder types.

Hendricks and Porter (1988) demonstrate that informational asymmetries across bidders haveimportant implications for bidding behavior in offshore drainage lease auctions. Similarly to ourapplication, they analyze a setting in which one firm is more precisely informed about a commonvalue than its rivals. They find that on drainage tracts that are adjacent to a firm’s existing

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tract, competition seems to be less and profits of participating firms, that are better informed,are higher than in auctions in which information is more likely to be symmetric, for example,tracts with no neighboring firm or wildcat auctions. In contrast, we structurally quantify theinformational asymmetry without prespecifying which firm is more precisely informed. Moreover,we allow for an additional private value asymmetry across bidder types. Li and Philips (2012)analyze the predictions of the theoretical asymmetric common value auction model in Engelbrecht-Wiggans et al. (1983) in a reduced form analysis. They find evidence for private informationof neighboring firms in drainage lease auctions. Hendricks et al. (1994) extend the frameworkin Engelbrecht-Wiggans et al. (1983) to allow for reservation prices of an informed seller andtest the model’s predictions on equilibrium bid distributions. In particular, they focus on a purecommon value setting with informed bidders and uninformed bidders who do not observe a privatesignal. Our focus, however, lies on disentangling the asymmetries in both the private and thecommon value dimension. Moreover, we aim at quantifying the differential precision in the commonvalue signal. Hong and Shum (2003) develop an econometric model for ascending auctions withasymmetric bidders in a setting with a multiplicative value consisting of a private and a commonvalue component. While their common value signal is symmetrically distributed, the private valuesignal is drawn from bidder-specific distributions. Hence, the two components directly interactin the bidder’s value. In our setting, the private and common value are additively separable asthe former corresponds to the cost and the latter to revenues. Thus, our formulation allows forseparate forces of asymmetries in contrast to theirs where different realizations of the private valuedirectly alter the valuation of a given common value. Additionally, in contrast to their setting, weanalyze a first-price sealed bid auction for which we only observe the winning bids, preventing usfrom employing their methodology.

Several papers analyze and compare different auction formats for public procurement. Atheyet al. (2011) estimate a structural model of timber auctions to study entry and bidding behaviorwhen firms are asymmetric in their private value distribution. They analyze the effect of differentauction formats (sealed bid versus open auctions) exploiting exogenous variation in the auctionmode across different auctions similar to our analysis of gross versus net auctions. While Atheyet al. (2011) focus on an asymmetric private value model, we study a model with both private valueand common value asymmetries. Flambard and Perrigne (2006) employ a nonparametric estimationstrategy exploiting the full bid distribution to quantify bidder asymmetries in snow removal auctionsin Montreal. As in Athey et al. (2011), they focus on a pure private value model and evaluatevarious bid preference experiments such as discriminatory reserve prices. Branzoli and Decarolis(2015) compare auction outcomes of first-price auctions with bid screening to those in averagebid auctions in Italian procurement auctions using a difference-in-differences approach. Decarolis(2018) studies the same setting in structural analysis. In a similar framework as Krasnokutskaya(2011), he applies a deconvolution estimator to separate common and idiosyncratic cost componentsand to compare the efficiency under first-price and average bid auctions. These auction formats

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are not used in our application and bidder default which is one of the key elements in his paper,has not been an important issue in the German market for SRPS.14 Finally, our approach sharessome features with the growing literature on procurement auctions with multi-dimensional signals,see, for example, Luo and Takahashi (2019), who compare different auction formats for highwayprocurement in Florida and find that carefully considering which party bears the risk of costoverruns can significantly increase the efficiency of the market. The focus of this literature is onprivate value settings with risk-averse bidders, while we concentrate on the role of an asymmetriccommon value component. In Section 3.3, we argue and provide evidence that the former channelis much less relevant in our application than the latter.

Hunold and Wolf (2013) study the German market for SRPS using a similar data set. They usereduced form regressions to understand how the auction design affects the likelihood that DB winsan auction, the number of bidders, and the resulting subsidy. Their results indicate that DB ismore likely to win longer contracts and contracts that are larger as measured by the number oftrain-kilometers. Moreover, they find that DB has an advantage in net auctions which supports ourhypothesis of an informational advantage of DB. Their results on the subsidies, i.e., the winningbids, are weak and rely on a lower number of observations than our analysis. The only effect theyfind is that net contracts yield lower subsidies, which is intuitive as the winning firm receives theticket revenues in addition to the subsidy.

Lalive et al. (2015) analyze the respective benefits of auctions and negotiations in the contextof our application. While they focus on the trade-off between competitive auctions and non-competitive negotiations with one firm, we focus on the specific contract design, once the agencyhas decided to run a competitive procurement auction. To the best of our knowledge, we are thefirst to analyze the effects of multidimensional bidder asymmetry and the role of gross and netcontracts in this industry using structural econometric methods.

The remainder of the paper is structured as follows. We develop the theoretical auction model inSection 2. In Section 3 we describe the industry and our data set. Moreover, we provide extensiveevidence to support our assumptions and modeling choices. The identification arguments and theestimation strategy are outlined in Section 4. We discuss our estimation results and counterfactualsin Sections 5 and 6, respectively. Section 7 concludes.

2. Auction Model and the Effects of Asymmetries

In this section, we present our model of procurement auctions for gross and net contracts andstudy the effects of two asymmetries on bidding behavior: first, the effect of asymmetric privatevalue (cost) distributions, and second, the effect of asymmetric precision of the common value14Our application is also reminiscent of the theoretical literature on auctions of fixed price versus cost-plus contract

as in Laffont and Tirole (1986) and McAfee and McMillan (1986). While they focus on asymmetric informationbetween the procurement agency and bidders and moral hazard after a contract has been awarded, we abstractfrom the latter and focus on informational asymmetries between competing bidders during the auction stage.

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(revenue) signals. The main purpose of our theoretical analysis is to provide an intuition about theunderlying economic channels that drive bidding behavior and to put our empirical results aboutthe magnitude of the different asymmetries into perspective.

All auctions are first-price sealed-bid auctions. The value of a contract and the bidding behaviordepend on whether a gross or a net contract is tendered. For a

• gross contract, the valuation consists solely of the firm-specific cost of fulfilling the contract(ci), because the firm’s revenue is fully determined by the winning bid.

• net contract, the valuation consists of the firm-specific costs of the contract (ci) and the ticketrevenues R, which are unknown to all firms when bidding for a contract.

We first present our model of the bidding stage, in which the number of actual bidders is fixedand known to all firms. Afterwards, we present an entry model based on Levin and Smith (1994) sothat ultimately the number of bidders is endogenous.15 Throughout, we index bidding firms by i,i’s bid by bi, and we denote the number of bidders by N . We assume that N is common knowledgeamong firms.16

The cost component, ci, is drawn from distribution Fci and is privately observed. The ticketrevenue, R, is an unknown common value for which firms observe only a private signal, ri, which isdrawn from distribution Fr. We allow Fci to differ across firms to model systematic cost differencesacross incumbent and entrants. The differential information about expected revenues comes fromthe precision of the revenue signals which we discuss below. All signals are independent acrossfirms and cost signals are independent of revenue signals for each firm. We assume that biddersare risk neutral.17

Gross contract auctions. Firms compete for a single indivisible item (a contract for one track).Each firm submits a bid bi, which is the subsidy that bidder i requests for fulfilling the contract.Firm i’s ex post value of winning (πi) and the expected value of winning with a particular bid aregiven by the formulas for an IPV first-price procurement auction

πi(bi, ci) = bi − ci(1)

E[πi(bi, ci)] = (bi − ci) · Pr(mini 6=jbj ≥ bi|ci, bi).(2)

15The main focus of our study is on informational asymmetries in the bidding stage. These can in principle beanalyzed without an entry model. The main purpose of our entry model is to quantify (potentially heterogeneous)entry costs for different auction modes. Higher entry costs are one potential explanation for observing a smallernumber of bidders in net auctions, see also our discussion in Sections 3 and 5.

16We believe that for our application the assumption of a known number of competitors is reasonable. For example,before the auction, there tend to be media reports about train operating companies signaling their interest inparticular tracks. Allowing for an unknown number of bidders, as for example in recent work by Freyberger andLarsen (forthcoming) goes beyond the scope of our paper.

17We believe that risk-neutrality is plausible in our setting as almost all active firms in the industry are large andoften internationally operating companies (see Section 3).

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For technical reasons discussed below, we assume that each Fci is logconcave.18

We assume that there are two bidder groups: the incumbent and the entrants.19 This yields anasymmetric auction with two bidder types and we build on the theoretical work on asymmetricIPV auctions, in particular, Maskin and Riley (2000a).

In a gross contract, there is only ex ante uncertainty about the operating costs ci. Before bidding,a firm receives private information about its cost, which is distributed according to Fci with strictlypositive density, fci , on support [cL, cH ]. Each firm i chooses bi to maximize its expected profit

πi(bi, ci) = (bi − ci)∏j 6=i

(1− Fcj (φj(bi))

),(3)

where φj(bi) is bidder j’s inverse bid function evaluated at i’s bid. From Maskin and Riley (2000b)it is known that an equilibrium in pure and monotonic strategies with almost everywhere differ-entiable bid functions exists in our setup. The equilibrium is implicitly defined by the first-orderconditions which constitute a system of differential equations in inverse bid functions with thestandard boundary conditions. Denote by 1−Ggri,Mi|Bi(mi|bi, N) the distribution of the opponents’minimum bid mi given own bid bi and a set of bidders N , i.e., 1 − Ggri,Mi|Bi(mi|bi, N) ≡ Pr(mi ≤minj 6=iBj |Bi = bi, N), and by ggri,Mi|Bi(mi|bi, N) the corresponding density in a gross auction.Then, bid functions have to satisfy

(4) bi = ci +1−Ggri,Mi|Bi(bi|bi, N)ggri,Mi|Bi(bi|bi, N)

.

We borrow the definition of conditional stochastic dominance20 and the following result fromMaskin and Riley (2000a), both adapted to the procurement setting.

Lemma 1 (Maskin and Riley (2000a), Proposition 3.3 and Proposition 3.5.). If the private valuedistribution of bidder i conditionally stochastically dominates the private value distribution of bidderj, then i is the weak bidder and bids more aggressively than bidder j. The bid distribution of istochastically dominates the bid distribution of j.

Lemma 1 shows that a bidder with a stronger cost distribution will also have a stronger biddistribution and therefore win the majority of auctions. Hence, observing a dominant bidder in anIPV auction is an indicator for a bidder with a stronger value distribution. However, the weaker18Many commonly used distributions satisfy logconcavity, for example, the normal distribution, the log-normal

distribution, and the beta distribution (see Bagnoli and Bergstrom (2005) for an overview). In addition, we findempirically that the vast majority of our estimated cost distributions are logconcave as well.

19We use DB and incumbent synonymously because it is the historic incumbent and we rarely observe the sametrack procured twice.

20Conditional stochastic dominance is defined as follows. There exists λ ∈ (0, 1) and γ ∈ [cL, cH ] such that1−Fi(x) = λ(1−Fj(x)) for all x ∈ [γ, cH ] and ddx

1−Fi(x)1−Fj(x)

> 0 for all x ∈ [cL, γ]. Note that conditional stochasticdominance is slightly stronger than FOSD so that if a distribution conditionally stochastically dominates anotherit also first-order stochastically dominates it but not vice versa.

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Figure 1: Private value bidder asymmetry: Illustration of bid functions

Cost Signal

Bid

Symmetric Bidders

Weaker Bidder

Stronger Bidder

Notes: When bidders are symmetric, their bid functions coincide. When bidders are

asymmetric, the weaker bidder will bid systematically lower markups to compensate for

its cost disadvantage.

bidder will bid more aggressively (see Figure 1 for an illustration). As a result, the auction may beinefficient and the strong bidder wins too few auctions from an efficiency perspective. This resulthas been generalized by De Silva et al. (2003) to hold also in the Goeree and Offerman (2003) setup,i.e., in the presence of an additional (symmetric) common value component. Hence, it also holdsfor net auctions if firms have equally precise information about the common value component.

Net contract auctions. When net contracts are procured, the bidders’ values of a contract consistof a private cost and a common value (revenue) component. Therefore, we develop an asymmetricfirst-price auction model with both private and common values. The private cost of fulfilling thecontract, ci, is drawn from distribution Fci , and we denote the common value component, the ticketrevenues, by R. In addition to their private value signal, ci, firms receive a private signal aboutR, ri, which is drawn from distribution Fr with mean R̄ and variance σ2r on support [r, r]. Allsignals are drawn independently within and across bidders. For technical reasons discussed below,we assume that both Fci and Fr are logconcave.

Our model of net auctions builds on Goeree and Offerman (2003). A key problem in auctions withprivate and common values is that each bidder’s private information is two-dimensional, consistingof both the private and the common value signal. The strategic variable, the bid, is only one-dimensional. In general, there is no straightforward mapping from two-dimensional signals intoa one-dimensional strategic variable such that the expected value of winning is monotonic in the

11

private information. However, under the assumptions that the common value equals the sum ofthe signals, i.e., R =

∑Ni=1 ri, and that the revenue signal distribution is logconcave, Goeree and

Offerman (2003) show that such a mapping exists. In this case, the expected value of winningcan be written as a linear combination of the private signals, ri and ci, as ρi ≡ ci − ri, andterms independent of a bidder’s private information. Therefore, standard auction theory methodsfollowing Milgrom and Weber (1982) can be applied. In our application, this scalar statistic, ρi, canbe interpreted as a net cost signal (costs minus revenue) and is sufficient to capture all of bidderi’s private information in one dimension.

We extend the model by Goeree and Offerman (2003) to accommodate asymmetric precision ofthe common value signal of different bidder types. Instead of taking the sum of revenue signals,we model the common value as the weighted sum of signals, i.e., R =

∑Ni=1 αiri. If R =

∑Ni=1 αiri

with the normalization∑N

i=1 αi = 1, it follows directly from their analysis that the expected valueof winning the auction is monotonic in ρi ≡ ci − αiri, and αi can be interpreted as a measure ofbidder i’s revenue signal precision. The ex post value of winning, πi, and the expected value of abid are then given by

πi(bi, ci) = R− ci + bi(5)

E[πi(bi, ci)|bi, ci, ri] =

bi − ci + αiri +∑j 6=i

αjE [rj |ρj ≥ φj(bi)]

Pr(bi ≤ mini 6=jbj |ci, ri, bi),(6)where φj(bi) is bidder j’s inverse bid function.21

This model allows us to study the effect of differential precision of common value signals. Whileevery firm draws its signal ri from the same distribution, the asymmetry between incumbent andentrants is captured by their weights αi. We denote the incumbent’s and the entrants’ weights by αIand αE , respectively. We treat αi as a structural model parameter that measures the informationalvalue of i’s signal. Intuitively, a higher αi indicates a more reliable revenue signal for bidder i.Conditional on a private revenue signal ri, the expected value of the common value is given by

E[R|ri = r] = αir +∑j 6=i

αjE[rj ] = αir +∑j 6=i

αjR̄

due to independence of the revenue signals {rj}Nj=1. The conditional variance can be written as

var[R|ri = r] =∑j 6=i

α2jσ2r .

21Note that inverse bid functions differ between gross and net auctions. For notational convenience, we omit thisadditional dependency.

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As αi = αE for all entrants and αi = αI for the incumbent, we can simplify this to

var[R|rE = r] =((N − 2)α2E + α2I

)σ2r for the entrant(7)

var[R|rI = r] = (N − 1)α2Eσ2r for the incumbent(8)

and hence var[R|rE = r] > var[R|rI = r] if αI > αE . Note that the vector α = (αI , αE) effectivelyconsists only of one parameter, since, without loss of generality, we can normalize αI+(N−1)αE =1.

Bidding behavior is monotonic and characterized by a system of differential equations as shownin the following Lemma (see Appendix A.1 for the proof).

Lemma 2. The following system of differential equations constitutes a monotonic Bayesian Nashequilibrium of the first-price auction with asymmetric cost distribution and asymmetric signal pre-cision

bi = ci − αiri −∑j 6=i

αjE [rj |ρj = φj(bi)] +1−Gneti,Mi|Bi(bi|bi, N)gneti,Mi|Bi(bi|bi, N)

,(9)

where Gneti,Mi|Bi(bi|bi;N) = Pr(bi ≤ minj 6=iBj |Bi = bi, N) and gneti,Mi|Bi denotes the corresponding

density function. φj(·) denotes the inverse bid function of bidder j.

The intuition is analogous to bidding in the gross auction. Players bid their expected valuation ofwinning the auction plus a bid shading term. In the net auction the expected value of winning alsodepends on the other players’ revenue signals and bidders therefore face a winner’s curse motive.This can be seen in the conditioning set of the expectation of the other players’ revenue signalsE [rj |ρj = φj(b)]. If bidder i wins with bid b, then it must be the case that the compound signalsof the other players, ρj , were not too good. Hence, when computing that expectation, the playershave to take the winner’s curse into account.

While theory gives strong predictions about how bidding behavior differs across asymmetric par-ticipants in private value auctions, this is less clear in our net auction setting due to the additionalasymmetric common revenue component. We give an intuition for the effect of the asymmetric pre-cision in the following Lemma that assumes a symmetric and known cost component (see AppendixA.2 for the proof).

Lemma 3. Assume there are N ≥ 2 bidders with one bidder having precision parameter αI and theremaining N − 1 bidders having precision parameter αE. Moreover, assume that all bidders havethe same cost c. Denote by Hi(b) the equilibrium bid distribution of bidder group i. If αI > αE,then, HI(b) ≥ HE(b), i.e., the bid distribution of bidder I is stochastically dominated by the biddistributions of bidders with αE, with strict inequality for all interior bids b when N > 2.

Lemma 3 shows that less precisely informed bidders are affected more by the winner’s curse and

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will shade the equilibrium bid more than the more precisely informed bidder. As a consequence, ifall bidders have the same costs, the more informed bidder will have the stronger bid distributionand will win the majority of the auctions (see Figure 2 for an illustration).

Figure 2: Common value bidder asymmetry: Illustration of bid functions

Cost Signal

Bid

More Informed Bidder

Less Informed Bidder

Notes: If costs are symmetric, the less precisely informed bidder (red curve) shades

the bid more than the more precisely informed bidder for the same cost and revenue

realization.

Net auctions are likely to be inefficient for several reasons. First, even if the common valueprecision is the same for all bidders and private value distributions are identical, the bidder withthe lowest private value realization does not necessarily win the auction. The bidder with the lowestprivate value realization might have received an unfavorable common value signal and, therefore,might bid cautiously. Hence, a high-cost bidder can win if she has received a high common valuesignal. Second, even if both bidders have the same private and common value signal realization,they will not submit the same bid, if the precision of the common value signals is asymmetric.The less precisely informed bidder will shade the bid more than the more precisely informed oneand the bidder with more precise information is more likely to win with high cost realizations thanthe other bidders. Finally, as in gross auctions, cost asymmetries across bidder types introduce asource of inefficiency.

It is important to keep in mind that we do not directly test Lemma 1 and Lemma 3 empirically.The main purpose of our theory results is to provide an intuition about the underlying economicchannels and to interpret our empirical results about the respective importance of the two asym-metries. Our estimation relies only on the model structure, in particular its first-order conditionsfor gross and net auctions. However, we generally do not directly impose the assumptions of theLemmas, such as log-concavity or (conditional) FOSD, in our estimation strategy. Instead, we find

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empirically that the model assumptions are typically satisfied at our estimated parameter values.

Entry model. Our entry model fits into the framework introduced by Levin and Smith (1994) andis only played among entrants, i.e., DB enters with probability 1 in all auctions.22 Denote the set ofpotential bidders including DB by N and the set of actual bidders by N .23 Denote the cost of entryto an auction by κ. In light of the industry evidence discussed in Section 3, we judge selective entryto be unlikely in our application. Therefore, we assume that firms do not observe their specific costand revenue signals before making an entry decision. Instead they only know the distribution ofcost and revenue signals based on which they compute the (symmetric) expected profits of enteringan auction with N bidders, which we denote by πe(N). As a consequence, equilibrium strategies ofentrants are symmetric. In this setup, Assumptions 1 to 5 in Levin and Smith (1994) are satisfiedand a symmetric Nash equilibrium in mixed entry strategies exists and it is unique. Each bidderdecides to enter the auction with probability q ∈ (0, 1) such that the expected profit from enteringthe auction is zero for any potential bidder. We summarize the equilibrium of the entry game inthe following lemma.

Lemma 4. In the entry game played by N − 1 potential entrant bidders, there exists a uniquesymmetric equilibrium in mixed strategies. Each entrant bidder enters the auction with probabilityq such that

(10)N∑N=2

((N − 2N − 2

)qN−2(1− q)N−Nπe(N)

)= κ.

The left hand side of Equation (10) describes the expected profit (net of the entry cost) of anentrant firm before entering the auction while the right hand side is the entry cost. The summationis taken over all potential bidder configurations that can occur if the entrant under considerationhas decided to enter.24

3. Industry Description, Data, and Discussion of Assumptions

In this section, we provide background information on the SRPS industry in Germany, we describeour data, and we discuss in detail the motivation for our modeling choices based on industryevidence, statistical tests, and reduced form regressions.

22This assumption is justified in our context, as we discuss in Section 3.23Note that when there are N bidders, N − 1 firms have entered through the entry game and the additional firm,

that always enters, is DB.24Our entry model is not central to our analysis of bidder asymmetries at the bidding stage. In particular, the

estimation of the bidding stage is unaffected by the structure of the entry model, because it uses the biddingstage as an input but not vice versa. We believe that the entry model presented here fits our applicationreasonably well. Developing a richer entry model is possible but goes beyond the scope of this project.

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3.1. Industry Background

As many other countries, Germany liberalized its railway sector in the 1990s. This liberalizationimplemented the EU Directive 91/440 Development of the Community’s Railways through theEisenbahnneuordnungsgesetz in 1993. One of the main objectives of this legislation was to inducecompetition in the railway sector. SRPS are part of the universal service obligation of the gov-ernment and are generally not profitable for operators. Therefore, local procurement agencies areassigned the task to choose an operator that provides this service on behalf of the federal govern-ment.25 As these services require high subsidies (around EUR 8.2 billion in 2017, Monopolkom-mission (2019)), the procurement agencies aim at competition for the tracks to keep the requiredsubsidies at a reasonably low level.

As part of the reform, the former state monopolists Deutsche Bundesbahn in West Germanyand Deutsche Reichsbahn in East Germany were merged into Deutsche Bahn AG which to dateremains publicly owned by the Federal Republic of Germany. As a consequence, new entrants inthe market for German SRPS compete with a publicly held operator (DB) that formerly was thestate monopolist.

While the market share of competitors has risen over time, DB still had a market share of 67.1%measured in train-kilometers26 in 2016 (see Monopolkommission (2019)). The competitors of DBconsist of many firms all of which are small in terms of market share in the German market forSRPS. Transdev is the competitor with the highest market share serving 6% of the market followedby Netinera with 4% and BeNEX with 3%.27

When procuring SRPS, the procurement agencies have a high degree of freedom in designing thecontract and the rules of the awarding. The agencies precisely specify almost all components of thecontract, for example, how frequent a company has to run services on a certain line, the duration ofthe contract, and the type of vehicles to be used. Moreover, ticket prices are usually regulated andbeyond the control of the train operating company. Therefore, the degree to which train operatingcompanies can affect ticket revenues is very limited. While some marginal incentives to improveservices may remain, we do not believe that these are substantial relative to the overall cost and thebaseline revenues generated independent of marginal improvements of the service. This suggest thatthe ticket revenues are mainly determined by factors exogenous to the train operating company.

An important additional feature is that the agency also specifies who obtains the ticket revenues:either the agency itself or the train operating company. When the agency receives the ticketrevenues, the contract is called a gross contract. When the operating company receives the ticket25For our sample period, there were 27 different local procurement agencies.26The variable train-km denotes the number of kilometers one train would have to run in order to fulfill the total

required volume of the contract. It is often used as a summary statistic of the overall size of the contract and isa function of contract duration, size of the respective track, and the required frequency of service.

27While our data does not allow us to test for collusion formally, the Monopolkommission regularly publishesextensive reports on this market and collusion has never been raised as a concern. In addition the marketstructure with DB’s dominance and the relatively small share of its competitors does not suggest that collusionis a significant concern.

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revenues, the contract is called a net contract. An important assumption in our empirical strategyis that the contract choice (gross vs. net) is exogenous to the track characteristics. We providedetailed evidence to support this assumption in Subsection 3.3 below.

3.2. Data Description

Our data set consists of almost all procurement contracts from the German market for SRPS from1995 to 2011, which we obtained from the procurement agencies and a consultancy working onSRPS procurement.28 The data contains detailed information on the awarding procedure, contractcharacteristics, the number of participating firms, the winning bid, and the identity of the winningfirm. Moreover, we collected data on characteristics of the track including data on track accesscharges and the frequency of service from additional publicly available sources.29

Table 1: Descriptive statistics by auction mode

Gross (N=82) Net (N=75)Mean SD Min Max Mean SD Min Max

Winning bid (10 Mio. EUR) 7.50 7.33 0.68 55.16 6.61 6.27 0.35 29.99No. bidders 4.82 2.01 2.00 11.00 3.45 1.61 2.00 8.00Access charges (EUR) 3.39 0.44 2.29 4.64 3.32 0.82 1.23 6.10Volume (Mio. train-km) 0.80 0.61 0.13 3.79 0.86 0.74 0.09 4.17Train frequency (per day) 33.25 15.79 14.59 112.57 31.07 10.76 14.49 67.26Size of network (km) 69.01 43.15 8.85 231.48 79.83 64.55 10.44 317.17Duration (Years) 10.23 2.61 2.00 16.00 10.43 4.07 2.00 22.00Used vehicles (Dummy) 0.59 0.50 0.00 1.00 0.59 0.50 0.00 1.00

Notes: This table compares descriptive statistics of the most important auction characteristics acrossdifferent auction modes (gross vs. net). Volume captures the size of the contract in million train-km,i.e., the total number of km that one train would have to drive to fulfill the contract, Train frequencyindicates how often a train has to serve the track per day, Size of network describes the size of thephysical track network to be covered (in km), Duration is the length of the contract, Used vehiclesindicates whether the contract requires new vehicles to be used on the track with 1 indicating that usedvehicles are permitted. Access charges denotes the regulated price (in EUR) that a firm has to pay everytime a train operates on a one km long stretch of a specific track.

Table 1 displays descriptive statistics for our sample split up by gross and net auctions. Wediscuss the essential characteristics of the data and how they support our modeling choices in thenext subsection.

While this data set contains relatively few observations, it is to our knowledge the most com-prehensive data on the German market for SRPS available. After dropping a few awardings withunreliable or missing information for some variables, the estimation of gross (net) auctions is based

28For a few tenders during our sample period we do not have access to the relevant data, in particular, the winningbid.

29In particular, we used the Trassenpreisprogramm software of DB that allows us to compute characteristics, suchas the length and the regulated access charges, for each track in our sample.

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on 82 (75) awardings, respectively. A limitation of our data is that we do not observe all bids butonly the winning bids.

Since tracks are typically procured for a very long time (on average 10 years) we rarely observethe same track being procured twice. Therefore, panel data methods cannot be applied and wetreat our data as a pure cross section. As different tracks are often geographically separated andhave different technological features, for example, different vehicles, urban versus rural areas, etc.,we argue that the scope for network effects or learning across lines is limited. Therefore, we treatbidding behavior as time-invariant. With a substantially longer time dimension, panel methodscan allow for the analysis of additional aspects such as the effects of entrants’ learning about themarket. Given that there are usually less than 25 awardings per year and the contract duration ison average 10 years, we suspect that a reasonable panel analysis requires at least 15 to 20 additionalyears of data.

3.3. Relation between application and model framework

In this subsection, we provide evidence that our model, presented in Section 2, is well suitedfor analyzing the German market for SRPS, and similar procurement settings. Towards this, wesupport our main assumptions with industry evidence, statistical tests as well as reduced formregressions.

Comparison of bidding patterns. Table 2 displays the results from OLS and count data re-gressions of the winning bid and the number of bidders on various contract characteristics. Theregressions confirm the patterns observed in the raw data summarized in Table 1. Winning bidstend to be lower in net auctions, which is not surprising because bidders factor in the additionalrevenues from ticket sales from a net contract. Moreover, the larger the contract (in terms ofduration or volume), the larger the winning bid. Gross auctions generally attract more biddersthan net auctions (on average 4.8 and 3.5, respectively; see Table 1). Since the incumbent (DB)participates in all auctions, variation in the number of bidders is purely driven by variation in thenumber of entrants. This pattern is confirmed in our regressions (see Columns (2) and (3) of Table2), in which the net auction dummy is negative and highly significant. Observing systematicallyfewer entrants in net auctions can be interpreted as evidence that this auction format is more prob-lematic for entrants. An additional notable difference between gross and net auctions is that thenumber of bidders has a negative effect on the winning bid in gross auctions (-0.17) but a positiveeffect in net auctions (0.27; see Column (1) of Table 2), although both coefficients are insignificant.In line with Hong and Shum (2002), these estimates suggest that there could be a winner’s curseeffect in net auctions that outweighs the competition effect associated with more bidders.30 Forboth dependent variables, a linear-quadratic time trend is generally insignificant which supports

30Pinkse and Tan (2005) show that this observation is not necessarily indicative of a common value setting. Instead,an affiliation effect can result in winning bids that are increasing in the number of bidders.

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Table 2: Reduced form regressions: Winning bids and number of bidders

(1) (2) (3)Winning bid No. of bidders No. of bidders

Net auction -2.9421∗ -1.7284∗∗∗ -0.4363∗∗∗

(1.5396) (0.2435) (0.0575)No. bidders-gross -0.1745

(0.2270)No. bidders-net 0.2741

(0.3197)Access charges 14.1498∗∗∗ -4.8861∗∗∗ -1.4178∗∗∗

(5.0204) (1.7575) (0.4504)Contract volume 8.1860∗∗∗ -0.2400 -0.0473

(1.3761) (0.1842) (0.0437)Contract duration 4.7269∗∗∗ 0.6498∗∗ 0.1386∗

(0.7278) (0.3166) (0.0776)Used vehicles 0.4257 -0.4361∗∗ -0.1042∗∗

(0.6495) (0.2083) (0.0459)Frequency (log) -0.2462 0.9827∗∗ 0.1618∗∗

(0.6663) (0.4925) (0.0746)Adjusted R2 0.759 0.535Notes: Heteroskedasticity-robust standard errors in parentheses. Models (1) and (2)are estimated by OLS. Column (3) is a negative binomial count data regression.No. bidders-gross and No. bidders-net denote the number of bidders in the auctioninteracted with dummies for gross and net auctions, respectively.Net auction is a dummy for net auctions. Frequency (log) is the logged averagenumber of times the train has to operate on the line per day. All other variabledefinitions are as in Table 1. Number of observations: 157.* p < 0.1, ** p < 0.05, *** p < 0.01.

19

our conjecture that during our sample period learning is not very important.

Column (1) in Table 3 presents the results of a reduced form logit regression of a dummy indicat-ing whether the incumbent won the auction on various track characteristics. While most structuraltrack characteristics, such as contract size or track access charges, do not have an effect on theprobability of the incumbent winning, procuring a track in a net auction has a large, positive, andsignificant effect. We interpret these estimates as further evidence that the net auction formatfavors DB. We next discuss evidence for the two types of bidder asymmetries that are likely todrive our model predictions.

Table 3: Reduced form logit regressions: Incumbent winning and net auction choice

(1) (2)DB wins Net auction

Net auction 5.1355∗∗

(2.5312)Access charges -3.2533 -1.5853

(4.1045) (2.8356)Contract volume 0.2424 -0.3729

(0.3551) (0.6523)Contract duration 2.2152∗∗ 0.3444

(1.1105) (0.4946)Frequency (log) 0.5300 -0.0388

(0.8019) (0.6872)Notes: Heteroskedasticity-robust standard errors in parentheses.Both models are estimated using binary logit regressions. DB winsdenotes a dummy indicating whether the incumbent won the auction.Net auction is 1 (0) if the auction is a net (gross) auction.All other variable definitions are as in Table 2.Number of observations: 157. * p < 0.1, ** p < 0.05, *** p < 0.01

Evidence for private cost asymmetries. First, we consider costs to be a private value becausefirms have different access to vehicles, funding opportunities, and they can pay different wages.Naturally, there are common cost components like electricity and infrastructure charges. However,these factors can typically be anticipated by all firms in advance and, therefore, do not result insignificant cost uncertainty.31 Most importantly, we expect the cost of DB to be different fromthe entrants’ costs. First, DB owns a large pool of vehicles that it can easily reuse for variousservices. Entrants typically have to buy or lease vehicles. Expenditures for vehicles are a substantial

31Note that common value components only result in winner’s curse problems if bidders possess private informationabout these factors. Common cost or revenue characteristics that are public information do not create a winner’scurse.

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component of the costs of serving a contract. Also, DB is likely to have cheaper access to fundingas it is a publicly held firm. Altogether, we expect DB to have a cost advantage. Most entrantsare large firms that are active in several markets and have similar capital structures, infrastructurenetworks, and technological equipment. Therefore, and given that DB is 14 times larger than itsbiggest competitor (Veolia Transdev, see mofair and Netzwerk-Privatbahnen (2011)), we judge itreasonable that systematic cost differences among entrants are negligible; therefore, we treat allentrants symmetrically.

Evidence for informational asymmetries and the presence of common values. Second, weexpect systematic differences between DB and its competitors regarding the information aboutthe ticket revenues. DB Regio (the branch of DB that operates in the SRPS sector) is verticallyintegrated with DB Vertrieb GmbH. Almost all tickets, even when DB is not operating the trackitself, are sold through DB Vertrieb GmbH. Therefore, DB possesses an informational advantageabout demand conditions, while its competitors cannot access the information that DB VertriebGmbH has (see Monopolkommission (2009; 2019)).32 Instead, entrants have to rely on their ownmarket research which is usually much less reliable than the information of DB.33

The German Monopolkommission, has explicitly raised the concern that DB Vertrieb does notmake reliable demand data accessible for the agencies and DB’s competitors (see Monopolkom-mission (2019)). This has sparked a debate about the underlying reasons for DB’s dominance, inparticular, whether there are features in the procurement process that reinforce the dominance ofDB or whether DB is simply the efficient firm in the market. We contribute to this importantpolicy debate by taking our auction model to a detailed data set on SRPS auctions.

The long-standing debate by both the entrant firms and competition authorities that DB shouldmake its private revenue data public (see, for example, Monopolkommission (2019) or Monopolkom-mission (2009)), strongly indicates that private signals about future revenues are informative forother firms about the ex post value of winning a net contract; therefore, we model the future ticketrevenues as a common value.

Moreover, we find in reduced form regressions that in net auctions the number of bidders tends toincrease the subsidy paid, while in gross auctions the winning bid tends to decrease in the numberof bidders (see Table 2). In line with the findings in Hong and Shum (2002), we take this as furtherevidence for a common value setting in our net auction sample. Both of these features are typicallynot present in a setting with known revenue streams or ex post uncertainty about revenues as, forexample, analyzed in Luo et al. (2018).

32Note that, while ticket prices are typically available online, the realized passenger volume as well as the compositionof the different types of tickets sold, is never publicly available.

33The current report of the Monopolkommission on the railway market (Monopolkommission 2019) features a sectiondevoted to the data monopoly of DB. In particular, they state on page 121: Through data exclusivity it is possiblethat additional barriers to entry are generated. For example, specific information that DB holds exclusively couldcause disadvantages to non state-owned railway operating companies at the registration of rail lines, in tendersin the short-haul railway passenger services (in particular, in net contracts), and in traffic contracts.

21

Consequently, in our model, the only difference between net and gross contracts is the presenceof a common value component in the form of the ticket revenues. Most features of the contract thataffect demand are pre-specified by the agency, for example, the frequency of the service, the typeof vehicles to be used or the ticket prices. Hence, we consider the level of demand by passengersto be independent of the firm operating the service and do not consider a model with price andquality as, for example, in Asker and Cantillon (2010).

Finally, one might be concerned that differences in the observed bidding patterns are driven bydifferences in the type of bidders participating in the respective auctions modes. For example, netauctions may potentially attract larger and therefore less risk-averse firms. To mitigate this concernwe provide evidence that the set of entrant firms is similar across auction modes. Table 4 providesseveral statistics of the winning firms other than DB34 and compares them across the gross and netformat. As we only observe the identity of the winning firm, we can only study differences in thecharacteristics of the winning firms. First, it could be that net auctions attract more public firms,which in our case are held by federal states, large cities, or foreign countries, because these might beless sensitive to revenue uncertainty compared to private companies. Table 4 shows that our datacannot reject equality of the share of public firms winning net and gross contracts, respectively.Second, it is conceivable that net auctions attract larger firms. We use two proxies for the sizeof a firm (yearly revenues and number of employees) and, again, find no significant differences inthese firm characteristics across the contract modes. In conclusion, we interpret these test resultsas evidence that gross and net contracts do not attract a different set of entrant firms.

Table 4: Summary statistics of characteristics of winning firms (excluding DB) in gross and netauctions

Gross NetMean Mean Difference p-value

Public company dummy 0.681 0.718 -0.0371 0.663Revenues (billion EUR) 4.61 4.95 -0.34 0.975Number of Employees 2690.3 3262.7 -572.4 0.926

Notes: This table summarizes the results from testing the equality of the means of winning firms’characteristics across different auction modes (gross vs. net). Note that we have excluded DBfrom this analysis.

Implications of both asymmetries in the German SRPS industry. In our application, two asym-metries crucially affect bidding behavior. First, on average, DB is potentially more efficient thanthe other bidders. Second, DB is potentially more precisely informed about the common value. Webriefly summarize the implications of the theory for our application in the following paragraph.34Note that industry experts agree that DB participates in all auctions.

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Both asymmetries in isolation can explain the dominant position of DB in the market for SRPSin Germany according to Lemma 1 and Lemma 3 (see Figure 3 for an illustration). However, theassessment of the market structure depends on the relative importance of the asymmetries andhence on which of the two is mainly driving DB’s dominance. If it is dominant due to a bettercost distribution, the outcome is desirable and from an efficiency perspective DB even wins toofew auctions. If it is dominant due to more precise information, the outcome can be undesirable,because DB might win the auction although it is not the most cost-efficient firm.35 When bothasymmetries are present, they can potentially offset each other. If DB is both more efficient andmore precisely informed, as many industry experts suggest, the aggressiveness of the entrants dueto the weaker private-value distribution can be partially offset or even overturned by the reducedaggressiveness due to the winner’s curse as illustrated in the right panel of Figure 3. The overalleffect on the efficiency of the auction is therefore an important empirical question.

Crucially, if one neglects the common value component from the analysis, as is often done inempirical studies, the assessment of the observed market outcome can be misleading. A dominantfirm will necessarily be rationalized with a stronger cost distribution. Hence, the dominance wouldnot call for regulatory intervention. However, the dominance can also be rationalized by moreprecise information, which may call for market interventions.

Figure 3: Both asymmetries: Illustration of bid functions

Cost Signal

Bid

Cost Signal

Bid

Cost Signal

Bid

Notes: Left panel: Under symmetric cost distributions, a bidder with substantially less precise information (red

curve) shades her bid more than a more informed bidder (green curve) and might lose even when the less precisely

informed bidder has a lower cost realization. Middle panel: If a bidder has a weaker cost distribution and is less

precisely informed (red curve), the two asymmetries can partially offset each other moving bid functions closer to

symmetry. Right panel: When a bidder has a weaker cost distribution and is only slightly less precisely informed

(red curve), the bid functions may reverse their relative positions and yield the opposite inefficiency than in the previ-

ous panels. Note that the horizontal axis only depicts the cost signal and assumes the same revenue signal for both bidders.

35Note that also in this case entrants might win the auction even if DB is more cost-efficient because of the additionalnoise introduced by the revenue signal. However, the more precisely informed bidder will win the auction moreoften when she is not the efficient bidder than the less precisely informed bidder.

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Advantages of the GO (2003) model setup. While we are aware that the model by Goeree andOfferman (2003) and our asymmetric version of it is not the standard common value model, webelieve that it is the best framework for our purposes for the following reasons. First, we haveknowledge about which of the components refer to common values (revenues) and which to privatevalues (costs) –unlike, for example, in Hong and Shum (2002)– and in our application firms’ profitfunctions are additively separable into revenues and costs. Moreover, these two components relate todifferent sides of the market, future demand and costs, and it seems plausible that the firms receivetwo distinct and independent signals about revenues and costs, respectively. In general, this leadsto the difficult problem of mapping two-dimensional private information into a one-dimensionalstrategic variable. Goeree and Offerman (2003) show how this problem can be overcome by theirmodel under the assumptions of log-concave signal distributions. Finally, our approach allows usto estimate the model using only data on winning bids, which is not the case for more standardmodels of affiliated private value or common value models. Hence, we consider this model to be thebest choice for the research question, the industry, and the data set used in our empirical analysis.

Evidence for the exogeneity of the contract mode. A key assumption for our empirical strategyis that the procurement agency’s choice between net and gross contracts is exogenous to a track’scost distribution, i.e., conditional on observed track characteristics, the cost distribution shouldbe independent of the choice of contract mode. In general, one might be worried that the choicebetween gross and net contracts is driven by selection and endogenous procurement decisions ofthe agencies. In our application, this would be problematic if agencies decide on the contract mode(net versus gross) based on unobservable cost characteristics. We argue that the role of endogenouscontract mode is negligible in our setting for two reasons. First, industry experts proclaim thatthe main procurement features are mostly determined by agency preferences that generally areuncorrelated with the structural cost and revenue characteristics of a track (see, in particular, theextensive discussion in Bahn-Report (2007)). Most agencies have a preferred auction mode (gross ornet), and procure tracks almost exclusively under this regime. In Bahn-Report (2007) it is arguedthat even on tracks for which it is apparent that the revenue risk is high, agencies with a preferencefor net contracts do not switch to gross auctions.36 In other cases, the decision is not even madeat the agency level but at a higher political level that can span several regional agencies. Forexample, the planning document for regional transportation services (Sachsen-Anhalt Ministeriumfür Landesentwicklung und Verkehr (2011)) mentions explicitly that for all SRPS contracts grossauctions should be used. In such cases the contract mode cannot even be adjusted to the trackunder consideration.

36The article explicitly states: “The individual preferences of individual agencies are so pronounced that experiencedbidders could sort anonymized tenders without problems to the agencies based on their corresponding ideologies.At the BEG [the Bavarian agency], there is an irrefutable net principle, i.e., there are absolutely only contracts inwhich the train operating company carries the entire revenue risk. (...) In contrast, in Hessen and Brandenburg,there is an irrefutable gross principle just like that (...). Many activities like these have the character of lighthouseprojects in which agencies try this or that because they like it. Economic rationality is rarely involved, however.”

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Second, there does not seem to be a significant difference in the track and contract characteristicsbetween gross and net samples, which we interpret as further support for our assumption that theauction mode is exogenous to a track’s cost characteristics. Table 5 displays the results of t-testsfor the equality of the means of the most important track and contract characteristics: track accesscharges (the costs for using a 1-km long stretch of a specific track network), size of the contract (inmillion train-km), the prescribed train-frequency (per day), the size of the physical track networkto be covered (in km), contract duration (in years), and an indicator whether used vehicles arepermitted for operating the track. None of the differences in means is statistically significant,which further supports our exogeneity assumption.

Table 5: Statistical comparison of contract characteristics across gross and net auctions

Gross Net(N=82) (N=75)Mean Mean Difference p-value

Access charges (EUR per net-km) 3.3949 3.3164 0.0785 0.4620Volume (Mio. train-km) 0.7985 0.8587 -0.0602 0.5785Train frequency (per day) 33.2530 31.0742 2.1788 0.3106Size of network (km) 69.0087 79.8341 -10.8254 0.2233Duration (Years) 10.2317 10.4267 -0.1950 0.7243Used vehicles (Dummy) 0.5854 0.5867 -0.0013 0.9869

Notes: This table summarizes the results from testing the equality of the means of the most im-portant track characteristics across different auction modes (gross vs. net). Variable definitionsare as in Table 1.

To support our assumption of an exogenous procurement mode further, we regress a dummyfor net auctions on our standard set of contract characteristics. None of the included regressors isstatistically significant (see Column (2) of Table 3). In both regressions, we control for a linear-quadratic time trend.37 In line with our assumption of time-invariant bidding behavior, thesevariables have no significant effect.

Non-selective entry. In our entry model, only entrants decide about entering the auction. Weassume that DB is not active in the entry game because industry experts agree that DB is partici-pating in all auctions (see Frankfurter Allgemeine Zeitung (2011)). Moreover, we do not considerselective entry as, for example, in Sweeting and Bhattacharya (2015). In the German SRPS market,it seems plausible that competitors of DB do not hold private information before deciding to investinto entry. Firms have to make considerable investments into learning about auction-specific infor-mation. For example, they hire specialized consultants to acquire information about the details of

37Using year fixed effects instead of time trends resulted in qualitatively similar results.

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their cost structure, including garages, schedules, and specific vehicle financing. Moreover, theseconsultancies support firms in estimating the future revenues. Hence, firms incur a considerableamount of sunk entry cost before they know about their cost and the expected future revenues.

4. Empirical Strategy

In this section, we discuss our identification strategy and how we estimate the model.

4.1. Identification

The cost distributions in our gross auction sample, which we model as an asymmetric IPV model,are nonparametrically identified from the winning bid, the number of bidders, and the identity ofthe winner (see, for example, Athey and Haile (2002)).38 The identification of a common valuecomponent is more complicated. In general, identification of the joint distribution of the commonvalue and all the signals requires observing the full bid distribution and either exogenous variationin the number of bidders or the ex post value of the auctioned object. Identification of just thejoint distribution of all common value signals fails if some bids are not observed. In principle, therealized ticket revenues are observable and the full bid distribution is (temporarily) recorded bythe agencies. Unfortunately, we do not have access to this data.The starting point for our identification strategy of the informational asymmetry is the first-order

condition for bidding in net auctions, which we derive in Section 2 and can be written as

bI = cI − αIrI − (N − 1)αEE [rE |ρE = φE(bI)]︸ ︷︷ ︸PI

+1−GnetI,MI |BI (bI |bI , N)gnetI,MI |BI (bI |bI , N)︸ ︷︷ ︸

MUI

bE = cE − αErE − (N − 2)αEE [rE |ρE = φE(bE)]− αIE [rI |ρI = φI(bE)]︸ ︷︷ ︸PE

+1−GnetE,ME |BE (bE |bE , N)gnetE,ME |BE (bE |bE , N)︸ ︷︷ ︸

MUE

,

where Pi and MUi denote the compound net cost signal and the markup for bidder type i,respectively. As a first step, note that the structure of our model is very similar to that of astandard asymmetric IPV auction; therefore, the net cost signals P are directly identified fromthe (winning) bid distributions and the winner’s identity in the net auction sample. The net costsignals can be decomposed as

PI = cI − αIrI − (N − 1)αEχE(Fr, α)(11)

PE = cE − αErE − (N − 2)αEχE(Fr, α)− αIχI(Fr, α),(12)

38Ideally, we would test the assumption of independent bids. However, because we only observe winning bids, wecannot perform such a test.

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where χI and χE denote the conditional expectations about rivals’ revenue signals for the incumbentand the entrants, respectively (see the first-order conditions above). To identify the asymmetryparameters α we need to decompose the compound net cost signals P into the effect of the revenuesignal distribution Fr and the asymmetry parameters α. Towards this, we exploit that our systemof first-order conditions consists of two equations (one for the incumbent, one for the entrant) sothat the data provides us with enough variation to identify two primitives (Fr and α).39 For thenet auction sample, we can treat the cost distributions as known because they are estimated fromthe gross auction sample. The parameters of the revenue distribution Fr, which is assumed to beequal for incumbent and entrants, can then be identified from variation in (winning) bids acrossnet contracts with different characteristics (physical track characteristics and number of bidders).Finally, the asymmetry parameter αI is identified by how often we observe the incumbent winningrelative to the entrants when holding all contract characteristics that affect costs and revenuesfixed.

Intuitively, identification of the parameters of the net auction model comes from contrastingdifferences between the incumbent’s and the entrants’ bidding strategies across gross and net auc-tions.40 If the procurement mode is orthogonal to a track’s cost characteristics, any systematicdifferences in bidding behavior that are not explained by differences in the cost distributions canbe attributed to differences in the revenue uncertainty in net auctions.

For our identification strategy to work, several assumptions need to be satisfied. First and mostimportantly, we require that the procurement mode is orthogonal to a track’s cost characteristics.This allows us to use the gross auction sample, in which there is no revenue risk, to estimate thecost distributions and extrapolate them to the net auction sample. While we cannot directly testthis assumption, we provide extensive evidence from both industry reports and our data in supportof this orthogonality assumption in Section 3.

Second, we maintain the assumptions of the model of Goeree and Offerman (2003), in particular,that the common value equals the (weighted) sum of the revenue signals. Furthermore, our identifi-cation argument requires several arguably mild functional form assumptions on the distribution ofthe cost and revenue signals. Specifically, we assume that the revenue signals r and the cost signalsc are drawn from logconcave distributions and are independent across bidders and each bidder’srevenue signal is independent of her cost signal. We discuss the advantages and disadvantages ofthis model structure in Section 3.

Finally, we implicitly assume that firms value the same revenue stream identically. This assump-tion could be violated, for example, if some bidder types value money differently than others orif they exhibit different degrees of risk aversion. While, in principle, both informational asym-metries and risk aversion could rationalize the observed data, all industry evidence supports that

39Note that our vector of asymmetry parameters effectively contains only one parameter because by constructionαE = (1− αI)/(N − 1).

40One could interpret our empirical strategy as a difference-in-differences approach, where the first difference istaken across bidder types and the second difference is taken across auction modes.

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the asymmetric information problem is much more relevant than issues related to pure revenuerisk. In particular, even the small entrants in our application often belong to large internationalconglomerates that are active in many markets, and often other industries as well, so that it isplausible that entrants value a given revenue stream in the same way as the incumbent (see alsoour discussion in Section 3). To illustrate that the additional uncertainty in net auctions doesnot affect the selection of firms into the auction, we provide a comparison of the characteristics ofwinning firms in Table 4, which does not display any systematic differences across contract modes.

4.2. Estimation Strategy

In the following, we elaborate on the details of our estimation algorithm and the model specificationthat we take to the data. Our estimation proceeds in two steps. First, we estimate the asymmetricIPV model using data on gross auctions. This allows us to compute the distribution of costsfor a track with given characteristics. Second, we estimate our model with private (cost) andcommon value (ticket revenue) components using data on net auctions. Since we extrapolate thecost distributions from the first step, we can isolate the common value parameters in the secondstep using a convolution approach.

We assume that there are two types of bidders: DB as the incumbent, that participates inall auctions, and N − 1 symmetric entrants. Asymmetry complicates the estimation since thedifferential equations in the first-order conditions generally do not have a closed form solution. Anadditional complication is that under asymmetry the markup term has to be computed for eachbidder configuration, i.e., for each number of bidders, separately. With a sufficiently large sample,we could follow a nonparametric approach.

Since the total number of procured tracks is still relatively small, a fully nonparametric estimationis not feasible in our application; therefore, we employ a parametric approach. As in Athey et al.(2011) and Lalive et al. (2015) we estimate the parameters of the bid distribution using maximumlikelihood assuming that the bid distributions for contract type j of bidder type i, Hji , follow aWeibull distribution with distribution function

Hji (bi|X,N) = 1− exp

−( biλji (X,N)

)νji (X,N) ,(13)where λji and ν

ji are the bidder-specific scale and shape parameters. Both vary across incumbent

and entrants and the contract mode (gross or net). We model these parameters as a log-linear

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function of observed contract characteristics and the number of bidders N

log(λjI(X,N)) = λjI,0 + λ

jI,XX + λ

jI,NN

log(λjE(X,N)) = λjE,0 + λ

jE,XX + λ

jE,NN

log(νjI (X,N)) = νjI,0 + ν

jI,XX + ν

jI,NN

log(νjE(X,N)) = νjE,0 + ν

jE,XX + ν

jE,NN,

where I and E denote the incumbent and the entrants, respectively. To keep the number ofparameters reasonably low, we include only the most relevant contract characteristics based onthe reduced form regressions presented in the previous section: the track access costs, a dummyfor whether the auction requires new instead of used vehicles, and three measures of contract sizeand complexity (contract duration in years, contract volume as measured by the number of totaltrain-kilometers, and the size of the track network serviced).41 The track access costs are a directmeasure of an important cost component. The contract duration captures that firms might valueshort-term contracts differently than long-term contracts. Finally, the total volume of the contractand the size of the track network that the train has to cover are plausible proxies for the overallsize and complexity of