The marginal cost of track wear; does more data make a difference?

Abstract

This paper estimates the marginal cost for maintenance of the Swedish rail network, using a unique panel dataset stretching over 14 years. We test different econometric approaches to estimate the relationship between traffic and maintenance costs, and compare our estimates with previous studies using shorter panels. The dynamic model results in this paper are contrasting previous estimates on Swedish data. Our results show that an increase in maintenance cost during one year can increase maintenance costs in the next year. No substantial differences are found for the static models. We conclude that more data made a difference in a dynamic context, but the estimated cost elasticities in European countries are rather robust.

1.0 Introduction The Swedish government has commissioned VTI to summarize state-of-the-art principles for estimating the marginal costs of infrastructure use and to update cost estimates as well as develop new knowledge if and when feasible. While this is a cost appraisal assignment, the ultimate benefit of these estimates is to provide input for the pricing of infrastructure use.

One component of the marginal cost in the railway sector concerns the way in which track maintenance costs are affected by variations in railway traffic. The relevance of this relationship was formally established after the vertical separation of infrastructure management and train operations introduced by the European Commission in 1991 (see directive Dir. 91/440)1, and the White Paper on Fair payments for infrastructure use (CEC 1998) endorsing the use of marginal cost pricing to finance infrastructure.

Note the Swedish reform was made in 1988

Previous estimates on Swedish data are summarized in Table 1; Table 2 comprises the current charges for using Sweden’s railway network. The cost elasticities for maintenance in table 1 are in line with the estimates in the review of best practice by Link et al. (2008), which reports elasticities from 0.07 to 0.26. In additional studies made within the rail cost allocation project CATRIN, the cost elasticities lies within 0.2 and 0.35 (see Wheat et al. 2009).

The purpose of this paper is to present new marginal cost estimates for maintenance of the Swedish rail network. The analysis departs from the models referenced in table 1. A significant difference is, however, that our data covers a much longer period of time than the previous studies. This does per se motivate the research: since previous studies make use of rather short data panels, it is relevant to consider whether longer time series makes a difference to conclusions.

An additional motive for addressing this question is that the maintenance of Sweden’s railways has gone through a far-reaching organizational reform. In 1998, the production unit of what was then the Swedish Rail Administration (Banverket) was separated from its administrative unit, creating a client-contractor relationship. This further led to a political decision to introduce competitive tendering of maintenance contracts, with the first contract tendered in 2002. The exposure to competition was gradual, but almost 95 percent of the network had been tendered at least once as of 2012.

Changes in the definition of activities have also been made, with snow removal defined as a maintenance activity as of 2007. Table 1 shows the operation cost elasticities from previous studies, in which snow removal costs constitutes a major part of the operation cost included in the estimations.

Table 1 - Previous estimates on Swedish marginal railway costs

Output Marginal Marginal costs in 2012 Model Output variable elasticity cost prices using CPI

Maintenance Johansson and Pooled Gross tonnes 0.17 0.0012 0.0014 Nilsson (2004) OLS Andersson (2006) Pooled Gross tonnes 0.21 0.0031 0.0036 OLS

Andersson (2007) Fixed Gross tonnes 0.27 0.0073 0.0084 effects Andersson (2008) Fixed Gross tonnes 0.26 0.0070 0.0081 effects Andersson (2011) Box- Freight gross 0.05 0.0014 0.0016 Cox tonnes Passenger 0.18 0.0108 0.0124 gross tonnes

Operation Andersson (2006) Pooled Trains 0.37 0.476 0.5481 OLS Andersson (2008) Fixed Trains -0.04 0.089 0.1025 effects Uhrberg and Fixed Trains 0.18 0.45 0.4975 Grenestam (2010) effects

Table 2 - Current charges

Track charge, SEK/gross tonne-km Operating charge, SEK/train-km 2013 0.0040 0.10 2014 0.0045 0.18

The present paper makes use of a panel covering 14 years. This includes a re-assessment of the appropriate choice of functional form and the choice between a static or a dynamic panel data model.

2.0 Methodology Different approaches have been used in order to determine the cost incurred by running one extra vehicle or vehicle tonne on the tracks. There are examples of a so-called bottom-up approach that use engineering models to estimate track damage caused by traffic (see Booz Allen Hamilton 2005 and Öberg et al. 2007 for examples). Starting with Johansson and Nilsson (2004) previous studies have, however, mainly used econometric techniques to estimate the relationship between costs and traffic, and can be referred to as a top-down approach. To estimate the marginal costs from trains using railway infrastructure first requires the derivation of the cost elasticity when traffic varies and secondly to establish the average maintenance cost.

Most of the top-down approaches use a double log functional form, either a full translog model or quadratic and cubic terms for the output variables. However, another functional form that has recently gained popularity within this area of research is the Box-Cox model, which also can be used to test the appropriateness of different functional forms. See Link et al. (2008) and Wheat et al. (2009) for a list of these studies and their reported cost elasticities.

In this paper we use the econometric – top down – approach, which is briefly presented in section 2.1. There are some intricate challenges that have to be addressed in order to formulate a model that can be expected to deliver the relevant marginal cost estimates. The first concerns the appropriate transformation of variables. We therefore begin with the Box-Cox functional form, which is presented in section 2.2. Another challenge concerns the choice between fixed and random effects assumptions when dealing with a 14-year panel of data; this is addressed in section 2.3. The static double log model to be estimated is presented in section 2.4.

A hypothesis tested by Andersson (2008) was the cyclic fluctuation of maintenance activities, where costs in year t depend on costs in t-1. Section 2.5 considers a modelling approach with lagged maintenance costs as an explanatory variable, i.e. a dynamic double log model.

2.1 An econometric approach The marginal cost of railway infrastructure wear and tear can be demonstrated to be the product of the cost elasticity of traffic (γ) and average cost (AC). To derive the cost elasticity, a general cost function is given by eq. (1) where there are i = 1, 2,…, N track sections and t = 1, 2,…, T years of observations. Cit is maintenance costs, Qit the volume of output (traffic density as defined below), Nit a vector of network characteristics and Zit a vector of dummy variables.

( ) (1)

We assume there is low variation in input prices, an assumption suggested by Johansson and Nilsson (2004) as well as by Andersson (2009), arguing that salaries for employees are rather similar across the country. Since then, maintenance activities have however been transferred from using in-house resources, including employees, to being competitively tendered. This may have increased the variation in salaries. A proxy for wages did, however, not affect maintenance costs at the contract area level in the model estimated by Odolinski and Smith (2014). Moreover, prices

on the materials used in the production can be assumed to be constant between entrepreneurs (and thus track sections) since the principal, Trafikverket, procures these on behalf of the maintenance producers without any price discrimination. Hence, no factor prices are included in the model.

2.2 Box-Cox regression model Eq. (2) demonstrates a transformation of variable y where λ is a parameter to be estimated, developed by Box and Cox (1964):

( ) ( ) (2)

This functional form does not impose a specific transformation of the data, such as the logarithmic transformation in the double log functional form. Instead, the functional form is ( ) tested with a logarithmic transformation ( ) if and a linear functional form ( ) if . Eq. (3) is the general cost model to be estimated, referred to as the “theta model”:

( ) ( ) ( ) (3)

The dependent variable is subject to the transformation parameter θ and the explanatory variables are subject to a different transformation parameter, λ. is gross tons and a vector of network characteristics. refers to variables that are not subject to a transformation, representing dummy variables and data that include zeroes. A “lambda model” can also be specified where the dependent and explanatory variables are subject to the same transformation parameter (λ), and is therefore more restrictive than the theta model. Likelihood ratio tests can be used to compare different values of the transformation parameters (for example 0 or 1) with the estimated values.

2.3 Modelling unobserved effects With access to data for cross-sectional units observed over 14 years, we can estimate panel data models. Following Baltagi (2008), we first consider the linear model in eq. (4). Here, yit is the dependent variable and Xit is a vector of observed variables that can change across i (individuals,