Scotland-wide Older and Disabled Persons Concessionary Bus Scheme - Further Reimbursement Research

Appendix B - Glossary of terms


Accent Marketing and Research, a market research company that undertook research for the Scottish Government on the likely impact on concessionary journeys numbers of the equalisation of the age of eligibility for the concession to men aged 60 to 64 ("age equalisation").

Additional Costs

Additional costs that bus operators necessarily incur as a consequence of the concession, to which they are entitled to be reimbursed.


See Average Fare Forgone.

Age equalisation

In April 2003 the age at which men became entitled to a concessionary pass on grounds of age was lowered from 65 to 60, to bring it line with the age of eligibility of women.


Association of Transport Co-ordinating Officers. Interest group of local authority public transport officers.

Average Fare Forgone

The average fare per journey that concessionary passholders would pay in the absence of the concession (abbreviated to "AFF").


One of two parameters that determine the shape of the demand curve which is used to simulate the relationship between the fare paid and the demand for bus journeys. The other is known as "Lambda".

Confounding factors

The various non-fare influences on the demand for bus travel which may affect differences in concessionary bus journey volumes before and after the introduction of free travel. To calculate a fare elasticity, it is necessary to fully account for such factors to ensure that the residual change in demand is caused only by the change in concessionary fare.


The hypothetical situation in which there is no concessionary fare (that is passholders have to pay the full, equivalent, commercial fare) but all other things are the same. "No better off, no worse off" reimbursement should leave operators in the same financial position as they would have been in the counter-factual.


The Consumer Price Index, which with the RPI is one of the commonly used measures of consumer price inflation.


Confederation of Passenger Transport. In this report CPT will generally refer to CPT - Scotland, which represents Scottish bus operators.

Damped exponential model

A particular form of demand model used for calculating the Reimbursement Factor, in which the point elasticity increases with fare but less than proportionately. It requires two parameters which between them dictate the point elasticity at any given fare; these are known as Lambda and Beta.


Application of a Reimbursement Factor or Generation Factor to take away generated concessionary journeys from an observed quantity of concessionary journeys.

Demand model or demand curve

A mathematical expression used to simulate the relationship between the demand for bus journeys and the fare that passengers are charged for each bus journey. They are used to calculate the Reimbursement Factor, because they can be used to estimate the relationship between observed concessionary journeys at free fare with the fewer journeys that would be made in a counterfactual in which a non-zero fare is charged.

Determination archive

The archive of data and documents collected at the time of the Determination of appeals by four bus operators against the reimbursement arrangements of Strathclyde PTE in 2003.

Discount Factor

The percentage by which the Reference Fare is reduced to give the estimated Average Fare Forgone.

Discount Tickets

See Period Tickets.


A measure of the extent to which the demand for bus journeys is sensitive to the fare charged. It is commonly described in terms such as the percentage change in demand as a proportion of the percentage change in fare. The point elasticity is one such measure and is used most frequently in this Report.


The concept of the transport system or part of it being in balance, after changes (such as fare increases or changes to transport supply) have been in place for some time and consequent adjustments of demand and supply have evened out.

Exponential constant

The mathematical constant "e", which has particular mathematical properties and is part of the formula used in the damped exponential model.

Generated Journeys

The number or percentage of observed concessionary journeys which are generated, or which would not have been made if there was no concession.


The concept that additional bus journeys are made at the concessionary fare (for older and disabled passholders, zero fare) by concessionary passholders relative to the journeys that would have been made if the average fare forgone had been paid.

Generation factor

A measure of the extent of generation. There are different ways in which it can be defined, and because of the potential scope for confusion it is not used in this Report. A less ambiguous measure of generation is represented by the Reimbursement Factor.


Institute for Transport Studies, University of Leeds, which carried out the study for Scottish Government Social Research reporting in 2010 "Improving the evidence for setting the reimbursement rate for operator sunder the Scotland-wide Older and Disabled Persons Concessionary Bus Scheme". This was the predecessor of the current Study and in particular examined Discount Factors and Additional Costs.


The second of the two parameters that determine the shape of the demand curve which is used to simulate the relationship between the fare paid and the demand for bus journeys. The other is known as "Beta".

Long run

The period of time after a particular change (such as a change in the fare) after which it is considered that consequent change sin travel behaviour will have stabilised so that the relationship between supply and demand is in equilibrium.

Period Tickets

Bus tickets such as day tickets or weekly tickets which entitle the purchaser to make an unlimited number of journeys within the specified period of validity of the ticket e.g. in day or week of purchase. The key characteristic of these types of tickets is that the number of passenger journeys made using each ticket type is typically not recorded with any accuracy, and therefore the average number of journeys made per ticket purchased, and hence the average price per journeys is not known. Such tickets may include 4-weekly tickets and longer-period season tickets. Sometimes known as discount tickets.

Point elasticity

The elasticity at a particular point on the demand curve, as would be calculated from the change in demand arising from a very small change in fare.


The Passenger Transport Executive Group, which represents the Passenger Transport Executives, including Strathclyde Passenger Transport Executive at the time it was responsible for concessionary travel in Strathclyde. pteg sponsored research by MVA Ltd to examine trends in concessionary travel which has been used in the elasticity analysis reported here.

Reference Fare

The fare used to measure the level of fares charged by an individual operator, relative to which the Average Fare Forgone is calculated by application of the Discount Factor. The current Scottish National Scheme uses the Shadow Fare, measured from the adult cash single fare scale, as the Reference Fare.

Reimbursement Factor

The ratio of concessionary journeys that would continue to be made in the counter-factual, to the observed concessionary journeys actually made with the concession.

Reimbursement Period or Reimbursement Year

The particular period (e.g. a given financial year) for which reimbursement is being calculated.


The Retail Price Index, which with the CPI is one of the commonly used measures of consumer price inflation.

Shadow Fare

The fare recorded for individual concessionary passenger journeys by looking-up the adult cash single fare that would have been charged for the journey in the absence of the concession (from the passenger boarding stop, and stated alighting stop. The Shadow Fare is currently used as the Reference Fare in the National Scheme.

Short run

The period of time immediately after a change in the transport system, such as a change in fare, in which short term changes in travel patterns may happen but these may not reflect changes that take a longer period to materialise (which should be fully apparent in the long run).


Strathclyde Passenger Transport, the organisation which was responsible for public transport co-ordination, and concessionary travel, in the Strathclyde Region until April 2006.