Econometric Modelling of Competition Between Train Ticket Types

Econometric Modelling of Competition Between Train Ticket Types


M Wardman, J P Toner, ITS, University of Leeds, UK



Since the 1970?s, rail ticket sales data in Great Britain has provided a means by which rail travel behaviour can be examined. These aggregate direct demand models have been developed to examine the impact on rail demand of factors external to the rail industry, such as the levels of income, employment, car ownership and competition from other modes, as well as the impacts of fare and service quality which are directly under the control of train companies.

Fare is a central determinant of the revenue earned by train companies and this, along with the traditionally strong interest in Britain in using price differentiation as a means of increasing revenue, has resulted in a considerable amount of empirical analysis in this area. Most research has been based on econometric analysis of ticket sales data and within this the typical approach has been to examine the market as a whole to the neglect of segmentation according to the different types of ticket on offer.

The usual means of representing fare in these models has been to use revenue per trip, an average across the fares of the different types of ticket. However, not only does this fail to provide valuable information on differential price sensitivity across ticket types, but switching between tickets by travellers in response to differential fare changes or changes in travel restrictions can lead to seriously biased estimates of fare elasticities.

In recognition of these shortcomings, attempts were made in Britain in the 1990?s to extend these econometric models to examine competition between different types of ticket and to estimate elasticities specific to particular categories of ticket. Studies were conducted of commuting trips into London, where choices existed between traditional point-to-point rail season tickets and multi-modal but higher priced tickets, and of London based inter-urban trips, where travellers could choose between first class tickets and a range of standard class tickets which differed in terms of their time of travel restrictions and advance purchase requirements.

These studies did not meet with a great deal of success. The cross elasticities were often statistically insignificant and in some cases were the wrong sign. A major contributory factor was the high degree of correlation between the fares of different tickets, largely due to the common practice of applying the same percentage fare increase to all tickets.

A way forward is to harness relationships from economic theory, a procedure which has often been neglected in the empirical analysis of travel demand data. Two relationships are of particular use here. The Slutsky symmetry equation expresses the relationship between two (income compensated) cross fare elasticities as:

Eji = Eij(ViFi/VjFj)

where ViFi is the revenue (volume V times price F) of ticket i and hence the ratio term is simply the relative revenue of the two relevant ticket types. This relationship admittedly relies upon the assumptions of conventional neo-classical economic theory. However, an additional relationship between cross and own elasticities that is true by definition takes the form:

Eij = Ejj(Vj/Vi)Dji

The cross elasticity of demand for ticket type i with respect to the price of ticket type j (Eij) can be deduced from the own price elasticity of demand for ticket type j (Ejj), the relative share of the two ticket types (Vj/Vi) and what is termed the diversion factor (Dji) which denotes the proportion of those who divert from j to i when j changes.

In the study reported here, both these relationships have been exploited to successfully estimate own and cross fare elasticities by ticket type as part of a system of demand equations. The technique of seemingly unrelated regression was used to estimate the system of equations, with the relevant constraints between elasticities imposed. Separate models have been estimated according to distance band for a large number of flows to and from London using annual data which covers the period 1990 to 1998. The system includes equations for the demand for first class tickets, the demand for standard class tickets with no restrictions on time of travel, and the demand for standard class with travel time restrictions. Advance purchase tickets are quota controlled and were dealt with using quantity cross-elasticities.

This paper reports the developed models which, along with own and cross elasticities by ticket type, also provide separate income elasticities for each product. The consequences of not using the theoretical relationships to assist estimation are clearly spelt out. The results have been incorporated into the recently issued fourth edition of the Passenger Demand Forecasting Handbook which contains a demand forecasting framework and recommended parameters that are widely used in the railway industry in Great Britain.

The paper also reports additional research, undertaken for the Strategic Rail Authority as part of its review of how it regulates fares in Great Britain. This extended the analysis to cover flows in the South East based on fresh market research evidence relating to diversion factors between ticket types. It also extended the demand framework to be able to handle changes in time of travel restrictions as well as the introduction of completely new ?generic? tickets.


Association for European Transport