1. The often quoted value for the current "discount factor" is 4.5%, but this is after it has been multiplied by the 61.5% Reimbursement Factor.
2. The elasticity parameters estimated are for two parameters which between them allow calculation of the Reimbursement Factor at a given commercial fare. The elasticity values quoted above are point elasticities at a fare of £0.859 at 2001-2 prices.
3. The Institute for Transport Studies at the University of Leeds.
4. Some of which had joint schemes, most significantly in Strathclyde.
5. "Improving the evidence for setting the reimbursement rate for operators under the Scotland-wide older and disabled persons concessionary bus scheme", Institute for Transport Studies, published by Scottish Government Social Research 2010
6. Note that because the Reimbursement Rate as currently formulated is constructed by adding together the different components, the most quoted value for the discount rate is 4.5%. But this is after it has been multiplied by the Reimbursement Factor ("post-degeneration") i.e. after allowing for generation, which in principle is itself dependent upon the average fare forgone. This circularity provides scope for confusion, and is one reason why we recommend changes to this way of presenting the reimbursement formula.
7. Even if passenger journeys that do not involve a ticket purchase are recorded, they are unlikely to be accurately assigned to the specific type of ticket used.
8. Note that on the basis of this data, return tickets and carnets are priced at more than the equivalent single ticket. This almost certainly reflects a pricing structure in which single tickets tend to be used most for shorter journeys and returns and carnets for longer journeys. Outside Scotland, returns and carnets are usually priced at less than a single ticket.
9. For example, as in the DfT approach to average fare estimation.
10. CPT quoted data from a major bus operator in Glasgow who, prior to the introduction of the free concessionary travel scheme offered passholders a 4-weekly ticket for £8.50 which entitled purchasers to use the bus for a fare of £0.05, in contrast to the standard SPT concessionary fare of £0.40 for each journey. Approximately 40% of concessionary journeys were made using this 4-weekly ticket offer, suggesting a substantial willingness on the part of concessionary passholders to invest in longer-period tickets. However, this is an isolated piece of data which will have been influenced by a number of local factors.
11. As noted in Chapter 2, the National Scheme quotes a value of 4.5% but this is applied additively to the Reimbursement Rate and implicitly includes the 61.5% Reimbursement Factor. The value that is equivalent to those quoted in this Chapter is 0.045/0.615 = 7.317%.
12. Because this particular mathematical expression is not defined at zero fares.
13. "Review of the Scotland Wide Free Bus Travel Scheme", Part 11 Annexe C, May 2009.
14. "The demand for public transport: a practical guide", TRL Report 593, TRL, 2004.
15. E.g. "Report 4 Shape of the Demand Curve" by Phil Goodwin and Andrew Last.
16. "All-Wales Concessionary Fares Reimbursement Study", MVA Ltd, 2003.
17. "The DfT study was commissioned from the Institute for Transport Studies (ITS) at the University of Leeds (in association with Minnerva Ltd and Professor Phil Goodwin). To avoid confusion with the research commissioned by Transport Scotland from ITS, but, in 2009, it is referred to here as "the DfT Study".
18. Prior to the National Concession implemented in 2006, concessionary travel was administered by the individual Scottish local authorities, apart from the area within Strathclyde Passenger Transport and Lothian. There were therefore 13 different schemes, each potentially having more generous concessions than the statutory minimum, but with local variations about how these were specified.
19. To be conservative, we have assumed that all of the correction for 2002-3 should be applied to the two quarters following the introduction of free travel. The adjustments were therefore 0%, 0%, -0.8% and -0.8% for each of the four quarters in the 2002-3 financial year.
20. "Improved Public Transport for Disabled People Volume 1 Report", Table 3.4, Scottish Executive Social Research, 2006
21. Bus and Coach Statistics 2005-6, Table 32. The table quite explicitly states that the quoted passholder numbers are as at 31st January 2007.
22. Based on total concessionary journeys divided by the eligible elderly population. The actual contrast is greater than this, since the journeys numbers will include those made by disabled passholders not included in the population figure.
23. As shown in Report 3 of the DfT Study "Analysis of concessionary passholder data from Lancashire and Nottingham"
24. In other words we have assumed a service-km elasticity of 0.66, based on standard DfT assumptions.
25. As in Tables 10 and 11 of Transport Scotland's Bus and Coach Statistics 2010-11,
26. i.e. multiplying by 1/(1-0.139) = 1.1614
27. Note that this does not conflict with the observation that concessionary journeys are on average longer than those of adult cash single passengers. This arises from the fact that cash single fares will tend to be priced to attract shorter distance journeys, whereas other ticket types are more financially attractive for longer distance journeys. This is demonstrated by the CPT data on the prices of different ticket types, with return tickets and ten-journey carnets priced at significantly more per journey than single tickets.
28. We have taken the reimbursement parameters set out in the spreadsheet "20130104 Reimbursement Scenarios - SDG version.xlsx" as representing the preferred position of CPT's advisors, using long run elasticity estimates.
29. It is recognised that Transport Scotland has implemented various checks on operator fare increases to try to moderate this type of behaviour, but this primarily addresses the symptom rather than the problem.
30. However, alternative methods need not be significantly more complex or difficult to operate. In England, individual Travel Concession Authorities are responsible for calculating reimbursement payments, each potentially for a large number of individual operators, with different rates which may vary from month to month. These arrangements are now generally tried and tested.