The marginal cost of track renewals in the Swedish railway network: Using data to compare methods

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Highlights

  • Railway renewal costs can be analyzed with survival and corner solution models.

  • The two approaches are similar when it comes to estimating the risk of renewal.

  • The corner solution model provides better possibilities to identify cost variations.

  • The survival approach does not model traffic's impact on the size of renewals.

  • The corner solution model is preferred in estimating the marginal cost of renewals.

Abstract

We analyze the differences between corner solution and survival models in estimating the marginal cost of track renewals. Both approaches describe the renewal process in intuitively similar ways but have several methodological distinctions. Using Swedish data for the 1999–2016 period, results suggest the median marginal costs per gross ton-km from corner solution and survival models are SEK 0.0066 and SEK 0.0031, respectively. Since several European countries use information about marginal costs as a basis for track user charges, the choice of estimation method is obviously important. Our conclusion is that the corner solution model is more appropriate in this case, as this method considers the impact traffic has both on the probability of renewal and on the size of the renewal cost. The survival approach does not consider the latter as part of the estimations, which is problematic when we have systematic cost variations due to traffic and infrastructure characteristics.

Introduction

The vertical separation between rail infrastructure management and train operations in Europe during the 1990s generated a need to set track access charges. The rules for these charges are laid down by The Single European Railway Area (SERA) Directive (2012/34/EU), which concerns the management of railway infrastructure and transport activities of railway undertakings in EU's Member States. The Directive establishes that charges for access to infrastructure facilities shall be set at the cost that is directly incurred as a result of operating the train service (Article 31.3), and is based on economic theory that advocates marginal cost pricing for an efficient use of assets. Hence, the marginal cost of infrastructure use needs to be estimated, including both maintenance and renewal costs.

Starting with Johansson and Nilsson (2004), there is now a series of econometric analyses of how railway traffic affects the costs for day-to-day infrastructure maintenance (Andersson, 2008; Link et al., 2008; Wheat and Smith, 2008; Wheat et al., 2009; Odolinski and Nilsson, 2017). This literature has generated estimates of cost elasticities for traffic (which are used to calculate marginal costs) that are relatively stable, both within countries as data accumulates over time and between countries (Nash, 2018).

Assets must at some point of time be replaced as costs for maintenance increase with age and use, including the increased risk for technical failures affecting traffic. This is part of any cost minimizing strategy for infrastructure services and a basis of life cycle asset management in general, where a renewal marks the end of an asset's life cycle. Moreover, replacements of infrastructure assets are costly: Renewal of the Swedish railway infrastructure (defined as major replacements, excluding upgrading) accounted for about SEK 2.4 billion1 in 2016, which is about 25 per cent of the total maintenance and renewal expenditure at SEK 10 billion – a share that has been around 20 to 30 per cent during the 1999–2016 period. Grimes and Barkan (2006) report even higher shares of renewal expenditures (around 20 to 60 per cent) for US railroads in 1978–2002, and Walker et al. (2015) report shares around 40 per cent for the Swiss railway network during 2003–2012.

There are relatively few empirical papers that address railway renewal from the marginal cost perspective, despite its large share of the railway infrastructure managers’ expenditures. One reason may be that renewals on a specific part of the railway is a rare feature, often performed with around 30 years in-between,2 which implies that a long time series is required to capture how changes in traffic affect renewal costs. One solution has been to add renewal to maintenance costs when estimating the marginal cost of rail infrastructure use (see Andersson, 2006; Tervonen and Pekkarinen, 2007; Marti et al., 2009; Wheat and Smith, 2009). But these models do not provide direct estimates on renewal cost elasticities, and any inference on such elasticities are therefore uncertain. Andersson et al. (2012) and Andersson et al. (2016) are however two studies that have access to a long time series and provide estimates of the marginal cost for track renewals using disaggregate data. These papers use different modelling approaches: a corner solution model and a parametric survival model.3 The papers establish a significant difference between the corner solution and survival models in that marginal cost estimates were SEK 0.009 and 0.002 per gross ton-km, respectively.

The purpose of this paper is to consider the qualities of these modelling approaches and – using information about infrastructure renewals in Sweden from 1999 to 2016 – estimate the marginal costs using the respective models. This makes it possible to recommend the best method or indeed to establish that either approach can be used for the measurement of marginal costs. The choice of method is policy relevant considering the difference in marginal cost levels and since several European countries use econometric information about marginal costs for charging track users.

In the literature, the two modelling approaches are linked via censored regression models. For example, a textbook treatment of the survival model usually describes issues with censored data (missing information on time to an event) which is common in any duration analysis (see Kiefer (1988) for an accessible description). The corner solution model is also connected to censored regression models as the econometric techniques are similar (cf. Tobit regression and section 2.1 below) but is applied to a different situation which formally does not concern censored data. The reason is that the individuals/agents are solving an optimization problem with a corner solution that provides a lower bound which is (often) a zero value and a higher bound that is a continuous (observable) variable that can take any positive value (Wooldridge, 2002). The focus of the corner solution model is thus on the various outcomes of an event, while the survival approach focuses on the time to event.

In our case, we are interested in both. That is, we want to analyze the time to (or risk of) multiple kinds of events that is represented by a continuous variable taking positive values. To the authors’ knowledge, the differences and similarities between these two modelling approaches has not been investigated empirically in the context of infrastructure cost analysis. We thus consider the present paper to contribute to the existing literature by spelling out the similarities and differences in their application to infrastructure costing. Indeed, the impact of covariates on time-to-event, as well as on the cost of these events, is relevant for infrastructure assets in general and not only railways. For example, models for road deterioration due to traffic and costs of resurfacing have been used to analyze pricing and investment policies, often building on the seminal work by Small et al. (1989). See Bruzelius (2004) for a survey of the different methods used to measure the (marginal) cost of road use.

The rest of the paper is organized as follows. Section 2 presents corner solution and survival models. Data and descriptive statistics are described in section 3. Results are presented in section 4. The last section of the paper comprises a discussion and conclusion.

Section snippets

The modelling approaches

The timing and frequency of renewal activities depend on the intensity of traffic, and an increase in traffic may therefore cause a deviation from the original cost minimizing plan for renewals (and maintenance4). Specifically, a renewal can be rescheduled to account for more traffic than originally planned and this affects the present value of renewal costs. This is

The structure of available information

The Swedish Transport Administration (Trafikverket) is responsible for the maintenance and renewal of 14 100 km of railway infrastructure in Sweden. This network is divided into 260 sections, which provide disaggregate information about maintenance and renewal costs. These sections are the track individuals’ in our model estimations. In addition, renewal costs are reported for different asset categories on each section, such as track superstructure (rail, sleepers, fastening system, switches),

Results

The similarities between the first part of the (two-part) corner solution analysis and the (continuous time) survival analysis were described in section 2.3. To explore the empirical qualities of these similarities, we present results from the probit and survival models in section 4.1, estimated with random effects and standard errors adjusted with respect to track section clusters. The way in which the hazard rates are linked to marginal costs varies between the approaches, and the

Discussion and conclusion

The efficient use of railway infrastructure requires a charge that is based on the marginal cost of using it. To estimate the marginal costs for track renewal using econometric techniques, the significance of a traffic variable explains how the renewal process generates different results. Our paper has compared two different approaches for establishing a value for marginal costs.

One approach comprises the corner solution (two-part) model, which uses traffic and other covariates to explain the

Statement of contribution

Directive (2012/34/EU) instructs European countries to set track access charges at marginal costs in order to create an efficient use of the railway infrastructure. The date for track renewal is affected by traffic, meaning that this cost category is one marginal cost component. Previous econometric analyses have used either a corner solution or a survival model for estimating the marginal renewal cost. Since the two approaches generate significantly different cost estimates, it is important to

CRediT authorship contribution statement

Kristofer Odolinski: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Data curation, Writing - original draft, Writing - review & editing, Supervision, Project administration. Jan-Eric Nilsson: Conceptualization, Writing - original draft, Writing - review & editing, Supervision. Sherzod Yarmukhamedov: Conceptualization, Writing - original draft, Formal analysis. Mattias Haraldsson: Conceptualization, Funding acquisition, Formal analysis.

Declaration of competing interest

None.

Acknowledgements

This paper has been financed as one part of an assignment (N2017/01023/TS) from the Government Offices of Sweden to review and develop the understanding of social marginal costs for infrastructure use. We are grateful to Phill Wheat for comments and suggestions for improvements on an earlier version of this paper, which has also been presented on a seminar at VTI, Stockholm, 25 May 2018 and on the ITEA Annual Conference and School on Transportation Economics, Hong Kong, 29 June 2018. Special

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