Scotland-wide Older and Disabled Persons Concessionary Bus Scheme - Further Reimbursement Research
4 Reimbursement Factors and Elasticities
4.1 Concepts and terminology
4.1.1 The number of bus journeys made by passholders depends at least in part on the fare that is paid. Some bus journeys would be made by passholders even if the full "commercial" fare had to paid, but more will be made if journeys can be made for free. The concessionary journeys that would not be made without the concession are regarded as being generated by the concessionary fare.
4.1.2 Reimbursement for revenue forgone is the product of the number of non-generated concessionary journeys and the average fare forgone. Since the number of non-generated journeys cannot be directly observed, it has to be estimated by reference to the observed number of concessionary journeys. This is calculated using the Reimbursement Factor - the ratio of non-generated journeys to the total number of concessionary journeys i.e. non‑generated / (non-generated + generated).
4.1.3 The volume of journeys generated by the concession will depend upon the level of the commercial fare - or more precisely on the average fare forgone (that is, the average fare per journey that would be paid by passholders in the absence of the concession). Just as higher fares lead to fewer commercial passengers, higher fares will also reduce the number of journeys that would be made by concessionary passholders in the counter-factual. Since higher commercial fares will not influence the observed number of concessionary passengers travelling for free, higher fares imply higher levels of generation, and should be associated with lower Reimbursement Factors i.e. the proportion of observed concessionary journeys that would have continued to use the bus in the absence of the free scheme will decrease.
4.1.4 For a given increase in fares, the change in the number of non-generated journeys will depend upon the overall relationship between the demand for bus services and the price of using them. This relationship is simulated by a "demand curve" - a mathematical expression which determines the number of bus passenger journeys as a function of the fare, and associated parameters. The sensitivity of demand to changes in fare is often described in terms of the elasticity of demand with regard to fares. Elasticity values are frequently expressed as the ratio of a percentage change in demand to a percentage change in fares: so if a 10% change in fares leads to a 3% reduction in bus journeys, the elasticity would be calculated as -0.3. Since journeys generally decrease as fares go up, the fare elasticity is usually a negative number, but it is often convenient to discuss comparisons of elasticities in absolute terms, so it might be said that an elasticity of -0.4 is "larger" than an elasticity of -0.3.
4.1.5 Different forms of demand curve imply different relationships between the elasticity at particular points on the curve (the "point elasticity") and the fare at which it is measured. Unfortunately the one form of demand curve in which the point elasticity is constant cannot be used for calculating concessionary travel reimbursement factors. Various alternative forms have been considered and that used most widely, known as the "damped exponential model", has been adopted here. The key characteristic of this form of model is that the point elasticity rises (in absolute terms) with the fare, but less than proportionately. It requires two parameters, labelled here as Beta and Lambda, which jointly determine the point elasticity at any given fare.
4.1.6 One issue is whether short run or long run elasticities should be used to calculate reimbursement factors. It is generally accepted that some changes in travel behaviour arising from changes in fares will not happen instantly and may take time to occur; for example, changes in car ownership levels or the places individuals travel to and from. Short run elasticities are intended to reflect the short-term consequences of a change in fares, and long run elasticities are generally regarded as reflecting all associated changes, at a new "equilibrium" level. To some degree differences between short and long run fare elasticities can be identified by examining changes in journeys immediately after a change in fare (e.g. in the year following a major change), and comparing them to changes over longer time periods such as three to five years. The length of time that has now passed since free local authority-wide travel was introduced in Scotland in 2002 is such that all significant long run reactions to the change can now be considered to be reflected in observed concessionary journey patterns.
4.1.7 Some practitioners have argued that short term elasticities are appropriate for concessionary travel reimbursement, because they will best represent a counter-factual of a sudden withdrawal of the concession. However, in our view it is more logical to base reimbursement on a counter-factual which represents an equivalent equilibrium position as the observed concessionary passengers. This appears to be the position adopted by the DfT, in that the elasticity values recommended to English Travel Concession Authorities (TCAs) reflects the position three years after free travel was implemented. Long run elasticities would also be consistent with the calculation of additional costs that include substantial allowance for the cost of additional capacity and peak vehicles. Our view is that in principle long run elasticities are the most appropriate basis for calculating "no better off, no worse off" reimbursement.
4.1.8 An additional issue in calculating the Reimbursement Factor is the price base that should be used to relate fare levels in a given reimbursement period (e.g. 2012-13), to the price level at the time when elasticities were established (e.g. 2002). Passenger responses to changes in fares will clearly be influenced by general perceptions of consumer prices, but there are different options for measuring price levels which are discussed in the final section of this Chapter.
4.2 Sources of elasticity parameters
4.2.1 The Reimbursement Factor incorporated in the All-Scotland National reimbursement rate was set at 61.5% at the time the All-Scotland concession was introduced in 2006-7, and has remained unchanged ever since. The value was calculated by combining information on the Reimbursement Factors used by individual Scottish Local Authorities prior to free travel being introduced (in October 2002), with data on the change in concessionary journeys in the year before and after free travel. The origins of the pre-free Reimbursement Factors are not known, and any analytical basis for them is largely un-documented. However, the 61.5% (together with other components of the reimbursement calculation) provided an acceptable basis for the Scottish Government and Scottish bus operators to successfully establish the National Scheme.
4.2.2 Although not calculated from explicit elasticity assumptions, it is possible to work backwards from the commercial fare in 2006-7 to identify the elasticity values implied by the 61.5% figure. This approach was taken in Scottish Government analysis of reimbursement arrangements in 2009 which concluded that the 61.5% rate was consistent with a point elasticity of -0.348 at 2007-8 prices.
4.2.3 Since the Reimbursement Factor in the National Scheme has not changed, similar calculations can also be carried out at more recent fare levels, such as the projected 2012-13 average shadow fare.
4.2.4 In making comparisons across years, it is important to properly take account of changing levels of prices. The discussion above about higher fares leading to lower demand presumes that fares are measured in "real" or "constant" prices, i.e. after allowing for general inflation of price levels. To aid comparability, and for reasons discussed later, the elasticities implied by the current National Scheme Reimbursement Factor of 61.5% have been calculated in terms of 2001-2 prices, as measured by the All-Items Retail Price Index. These values are summarised in Table 4.1.
4.2.5 The Table shows how the average shadow fare in 2006-7 and 2012-13 respectively is used to derive the average fare forgone, which is then converted to 2001-2 prices (in this instance using the Retail Price Index). For the purposes of this illustration, a Lambda value has been selected from estimated All-Scotland Long Run elasticity calculations. These allow a Beta value to be calculated, set at 2001-2 prices.
4.2.6 "Full fare" elasticities have been calculated relative to the estimated All-Scotland average commercial fare of 2001-2. These suggest point elasticities of -0.287 and -0.247, but (as with all the point elasticities quoted here) are intended only to illustrate relative elasticity values, and not for direct calculation of reimbursement.
4.3 Evidence on concessionary fare elasticities from outside Scotland
4.3.1 Short run fare elasticities (i.e. elasticities reflecting short term changes in travel patterns arising from a change in fares) for all bus passengers as a whole are typically quoted as being of the order of -0.4. The DfT-sponsored collaborative study on elasticity evidence reported elasticity values for the elderly ranging from -0.35 to nearly -1.0, with a mean value of -0.5, although the -1.0 figure is a topic of some debate.
4.3.2 The collaborative study also revealed that there was little firm evidence on the differences between short and long run bus fare elasticities, although such long run elasticities as were found were substantially higher than accepted short run values. One reading of the evidence, reported in the DfT Study discussed below, suggested that the long-run uplift to concessionary elasticities in moving from the short run was in the range of 30% to 50%. The DfT assumption at the time was that a 50% uplift was appropriate.
4.3.3 All of the research reported on by the collaborative study predated analysis of the impact of free concessionary travel in the UK on travel volumes. Greater certainty about concessionary travel elasticities has now been achieved, to some extent, with the analysis of the impacts of the introduction of free travel in the UK, although, so far as we know, only one contemporary study at a national level was carried out, in Wales from 2001 to 2003. Although focussed on reimbursement rates rather than elasticity values, the Study derived a point elasticity at full fare (assumed at the time to be £1.00) of -0.365, in 2002 approximately.
4.3.4 Following the introduction of statutory free travel in England in 2006, there were a very large number of disputes between TCAs and bus operators regarding reimbursement. In order to address the issues raised, the DfT sponsored a major research study in 2009-10 which included a substantial amount of work on elasticity values, and which created a comprehensive framework for updating reimbursement calculations. The current project for Transport Scotland is partly in response to the availability of the fresh evidence exposed by the DfT work.
4.3.5 Strands of the DfT research included development of ideas about the shape of the demand curve, which have informed the adoption of the damped exponential demand model as discussed above. Elasticity values were explored in a number of separate workstreams which generated a "zone of reasonableness" for elasticity values. However, the precise values that were recommended by ITS, and then adopted by the DfT, were based on analysis of concessionary journey data before-and-after the introduction of free fares in England in 2006, from four PTE areas and seven non-PTE areas. These areas were selected principally because they offered most likelihood of access to the detailed data necessary for reliable before-and-after analysis, including information on the pre-free concessionary scheme, passholder numbers, and other confounding factors.
4.3.6 The DfT default values are summarised in Table 4.2, together with the point elasticity at an illustrative 2001-2 fare of £0.859.
|DfT Default Elasticities||PTE||Non-PTE|
|Deindexed Beta (2001-2 prices)||-0.665||-0.795|
|Illustrative point elasticity at 2001-2 All-Scotland fare of £0.859||-0.431||-0.462|
4.3.7 It can be seen that the point elasticities are significantly greater than those implied by the current All-Scotland Scheme Reimbursement Factor. This is partly, but not completely, accounted for by the fact that they were derived by comparisons between 2005-6 (the year before free travel was introduced in England) and 2008-9, three years afterwards; they therefore reflect longer-run changes in travel behaviour following the change in the concessionary fare, although the extent to which all longer-run responses have been captured is difficult to judge.
4.3.8 There are reasons for expecting that concessionary passholder elasticities in Scotland would be lower than in England, principally lower levels of car availability in Scotland, and a larger proportion of the elderly population living in rural areas. One of the strands of the DfT study was the development of an econometric model using NTS (National Travel Survey) data covering the period from 1995 to 2008. Although based on English data, the model can be used both to derive elasticities for Scotland directly, and to estimate the impact of differences in characteristics on elasticities in Scotland and England. The direct estimate of the elasticity in Scotland (drawing on the econometric model parameters, but using Scottish values of the independent variables) is a full fare point elasticity of -0.62 in 2002. This appears rather high, but there are some uncertainties about the precise interpretation of these elasticities, in particular the extent to which the analysis will have captured short run or long run elasticities.
4.3.9 However, of the variables included in the econometric model, the most significant differences between England and Scotland are in car availability (lower in Scotland), and the proportion of the elderly population living in rural areas (higher in Scotland). In combination, these are estimated to reduce the magnitude of elasticities by about 25%, implying that the DfT default elasticities adjusted for Scottish characteristics would be equivalent to point elasticities in 2001-2 (at the 2001-2 full fare) of -0.32 and -0.35.
4.4 Deriving Elasticities from Scottish 2002-3 Data
4.4.1 The current study has reviewed the literature to ascertain whether there were robust estimates of Scottish concessionary fares elasticities that could be used to underpin the reimbursement formula in Scotland. It concluded that with one exception in Strathclyde, discussed below, there were not existing estimates, and that estimation of Scotland specific elasticities was required. New research has therefore been undertaken to estimate Scotland specific fares elasticities, by revisiting Scottish data from 2002 and 2003, around the time when free travel was introduced on 1st October 2002.
4.4.2 In general, the most reliable way to estimate fare elasticities for concessionary travel reimbursement is to draw on evidence of passenger reaction to a major change in fares. The introduction of free travel provided a unique opportunity to do so, by comparing travel volumes "before" and "after" the change. However, to ensure a proper like-with-like comparison, information about the "before" situation needs to be as robust and comprehensive as for the "after" situation. This is difficult to achieve on a retrospective basis, since the information required is much more than simply the change in concessionary journeys. Other information needed includes:
- the average concessionary fare charged in the period immediately before free travel;
- the characteristics of the pre-free and post-free concessionary schemes for each of the local schemes;
- the number of passholders and how this changed when free travel was introduced; and
- information on any other "confounding factors" that need to be taken into account so that only the effect of the change in fare on journey numbers is identified.
4.4.3 Achieving certainty on all of these fronts is difficult, and becomes much more so with the passage of time since free travel was introduced. Moreover, local authorities ceased responsibility for concessionary travel in April 2006, when administration was taken over by Scottish Government, and therefore there is no continuity of organisation or personnel to allow historical data to be retrieved or sense-checked.
4.4.4 The exception to the general lack of evidence on Scottish concessionary elasticities is Strathclyde. In 2003, four bus operators applied to Scottish Ministers ("appealed") for a modification of the Strathclyde Passenger Transport (SPT) reimbursement arrangements. The person appointed to determine this application, on behalf of Scottish Ministers is one of the authors of the current report, and is therefore uniquely well placed to draw upon this experience. As part of the formal Determination process, it was necessary to obtain sufficient information to enable elasticity estimates to be derived, leading to the conclusion that at the then commercial fare in Strathclyde of £0.905, a point elasticity of -0.523 could be justified. However, the methodology used during the Determination predated various technical developments (in particular, with regard to the shape of the demand curve), and the value just quoted is not necessarily consistent in terms of definition with others quoted in this report.
4.4.5 However, of great relevance to the current study is the fact that the Determinations led to the collection of a considerable archive of data (the "Determination archive"), to which the current study team have had access. The archive was created in 2004 and therefore was close to the time of the introduction of free travel, is of known provenance, and was subject to close scrutiny by the interested parties at the time. The archive includes data on all the factors listed above, often documented in terms of its originator and the date provided, as well as other incidental information that has helped provide a more complete picture of the situation in Strathclyde before and after free travel was introduced.
4.4.6 Since the current National Concessionary Scheme operates on the basis of a single Reimbursement Rate, it should ideally be informed by a single set of elasticity parameters that fully reflect "average" characteristics of Scotland as a whole. However, the evidence base for the rest of Scotland is somewhat weaker than that for Strathclyde, although extensive efforts have been made to reduce areas of uncertainty. Moreover, the SPT Scheme was the largest in Scotland contributing over half of all Scottish concessionary passengers in 2002. Where necessary, Strathclyde data has been used as a proxy for the rest of Scotland, allowing Scotland-wide elasticity estimates to be made.
4.4.7 The scope of analysis has been limited to comparisons between annual data for the following:
- year ending 30 September 2002, just before free travel was introduced;
- year beginning 1 October 2002, just after free travel was introduced (short run impact); and
- year ending 31 March 2007, the year just after the National Concession was introduced, and administration was taken over by the Scottish Government (long run impact).
4.4.8 The comparison of the pre-free year and 2006-7 will pick up both long run impacts from the 2002 change, and also the short run impacts of the extension of the concession associated with the National Scheme, i.e. national travel (as opposed to just resident local authority-wide travel), and the removal of the morning peak restriction. It is therefore more appropriate for elasticities that reflect the full change to the current concession. However, the greater gap between 2002 and 2006-7 introduces more scope for debate about various "confounding factors" i.e. other contextual changes that could influence the number of concessionary journeys made. The comparison which is most robust in this respect is with the year immediately following free travel.
4.4.9 Where data is limited, it is recognised that there is scope for different interpretations of the information that is available, as well as about assumptions where it is necessary to make them.
4.5 Data sources
4.5.1 Concessionary journeys: for the local authorities outside Strathclyde, in 2002 and 2003, the only source of information of which we are aware is a spreadsheet file that was provided to us by CPT (the "CPT concessionary journey data"). CPT has said that it was passed to them by Transport Scotland, having been initially compiled by ATCO (the Association of Transport Coordinating Officers) as part of the process to inform the implementation of free travel in the 2002-3 period. We have no reason to doubt the accuracy of this data for outside Strathclyde, although equally we have nothing with which to independently corroborate it.
4.5.2 The CPT data also includes figures for Strathclyde, where the Determination archive offers an alternative source of information. In both cases, the information will originally have been supplied by Strathclyde Passenger Transport (SPT), since only SPT will have been in a position to compile the information from operator reports. However, whereas the Determination archive data was supplied direct to the Determination by SPT, as part of the semi-judicial Determination process, at known dates, it is not known when SPT passed the data reported by CPT to ATCO.
4.5.3 This issue is of importance because the Determination data and the CPT data for concessionary journeys in Strathclyde show significant differences. CPT data gives higher journey numbers in the year before free travel and lower journey numbers in the year after, and consequently implies that free travel had a smaller impact on the concessionary journeys than the Determination data. The alternative sets of figures are set out in Table 4.3, which shows quarterly older and disabled concessionary journeys.
4.5.4 The higher growth in journey numbers shown in the Determination data will imply larger elasticities, and lower reimbursement totals, than the CPT data, all other things being equal.
4.5.5 We believe that the reason for this discrepancy is that the data reported by CPT reflects preliminary estimates of quarterly data that were widely circulated by SPT in its consultations about post-free travel reimbursement arrangements in 2002 and 2003. Similar but not identical data was submitted by SPT in the initial stages of the Determination process. However, in October 2004 SPT explained that errors had been found in the initial dataset, and corrected data was provided. The corrected data was used to make the Determination, and we regard it as the best available estimate of journeys in Strathclyde, in the absence of more detailed information about the provenance of the CPT data.
4.5.6 There is some scope for comparison of the Determination data with concessionary journeys data published by Transport Scotland. The latter is only available in financial years (and therefore straddles the period when free travel was introduced), and does not distinguish between local authorities that already provided free travel prior to October 2002. However, it quotes separate data for Strathclyde, which because the Determination data is available on a quarterly basis, can be related to the Transport Scotland financial year totals. For consistency, and at the suggestion of CPT, we have adjusted the Determination concessionary journey numbers to align with the Transport Scotland data, involving an 0.1% increase to the Determination data that fell into the 2001-2 Financial Year, and adjustments of -0.5% and -1.1% for the 2002-3 and 2003-4 financial years respectively.
4.5.7 We have no equivalent checks on the data provided by CPT for concessionary journeys in Scotland outside Strathclyde in the 2002-3 period, and have therefore accepted them at face value.
4.5.8 With regard to 2006-7 concessionary journeys, Transport Scotland's Scottish Transport Statistics 2011 clearly identifies an all-Scotland value for free concessionary journeys of 155.71 million which can be corroborated by reference to the detailed data held by the Transport Scotland Concessionary Travel and Integrated Ticketing Unit ("CT&ITU"). However, this information is not available by local authority area, and consequently there is not a Strathclyde figure that can be contrasted directly with the values quoted above.
4.5.9 When contrasting the "before" and "after" data, one further complication is that Fife, and Dumfries and Galloway Councils already provided a free travel concession on a discretionary basis. Consequently, analysis of "All-Scotland" elasticities needs to be on the basis of excluding data for these areas, which in the case of concessionary journeys is based on the CPT data on concessionary journeys. It has been assumed that the Transport Scotland data on concessionary journeys for 2006-7, which is only available at an All-Scotland level, can be factored down to exclude journeys made in Fife, Dumfries and Galloway using the same proportions as applied in the year ending 30 September 2003. Since it is our view that the Determination data on Strathclyde is more robust that that provided by CPT for Strathclyde, the proportion is based on the Determination data for Strathclyde.
4.5.10 These considerations lead to the estimated "before" and "after" concessionary journeys summarised in Table 4.4.
4.5.11 It should be noted that the absence of distinct concessionary journey data for Strathclyde in the year ending March 2007 means that it is not possible to identify a separate long-run elasticity for Strathclyde which could be contrasted with the short run value that can be estimated.
4.5.12 The pre-free concessionary fare: elasticities are estimated by comparing the change in journeys with the change in fare, and consequently it is necessary to estimate how much concessionary passengers paid for their concessionary journeys prior to free travel being introduced. The situation varied between local authorities, depending on the local view taken as to the appropriate level of concessionary fare within the statutory minimum concession of half the commercial fare.
4.5.13 In Strathclyde, the "standard" concessionary fare adopted by SPT was a £0.40 flat fare, but for concessionary journeys of more than 10 miles, a higher fare was charged based on the sum of £0.40 for the first 10 miles and then an additional element based on the commercial fare increment between 10 miles and the length of the concessionary journey. In addition, in Glasgow some bus operators offered passholders cheaper fares than the "standard" concessionary fare of £0.40, in one case by offering a four-weekly period pass that entitled the purchaser to then make journeys at a flat fare of £0.05 per journey. The estimation of the average concessionary fare paid in Strathclyde has required access to a number of sources of data, some from the Determination archive, some provided through CPT, and some from analysis of Scottish Household Survey data. The end result is an estimated average concessionary fare paid by passholders in Strathclyde in the year ending September 2002 of £0.443.
4.5.14 We are reliant on data provided by CPT for all information on the concessionary fares in Scotland outside Strathclyde, and have also used the estimates made by CPT, for both an average commercial fare in Scotland to which percentage concessions can be applied, and a weighted average fare for the Lothian councils. These values are summarised in Table 4.5.
4.5.15 Note that the journeys shown for Strathclyde (necessary to calculate an overall Scottish weighted average concessionary fare) are based upon the Determination estimate, giving an All-Scotland average concessionary fare of £0.397. A slightly higher value of £0.398 is derived if the CPT estimate of Strathclyde journeys is substituted.
4.5.16 Passholder numbers: changes in the number of passholders stimulated by the introduction of free travel can have a profound impact on the interpretation of data on concessionary journeys. However, data on passholder numbers is often unreliable, because it is difficult to ensure that records are updated when individual passholders die or move away. This is exacerbated if passholders are not required to renew their pass at regular intervals eg every few years.
4.5.17 There is relatively robust data on passholder numbers in Strathclyde, because SPT policy required passholders to renew their passes every four years. SPT data on passholder numbers was the subject of specific inquiries during the Strathclyde Determination. Elsewhere in Scotland, there is some information on changes in passholding in Edinburgh, but this is not regarded as reliable because passes were issued "for life", and figures for the absolute number of passes "on issue" exceeded the eligible population by a substantial margin. It is therefore difficult to interpret the available figures for Edinburgh with any confidence. There is some data for passholder numbers in other local authority areas in 2003, after the introduction of free travel, but we are aware of no equivalent data for the period before free travel.
4.5.18 Consequently, the approach that we have adopted is to assume that the change of passholder numbers that can be inferred from the Strathclyde data should be taken as representative of that for Scotland as a whole. In fact, even the Strathclyde data requires some interpretation, because of a backlog in the processing of pass applications in the period immediately following the introduction of free travel, and the most robust numbers are regarded as those representing the passes issued at 31/3/2002 (336,969) and at 31/3/2004 (386,578).
4.5.19 Transport Scotland has published data on concessionary passes issued by individual local authorities since the National concession was established, and this provides a means through which SPT's data from 2002-3 can be compared with later years. The available data is summarised in Table 4.6. The data selected for use in the elasticity analysis is also identified, with the year of which it is assumed to be representative.
4.5.20 The first two columns reproduce data provided to the Determination by SPT. CPT has noted the likelihood that SPT may have classified male passholders aged between 60 and 64 newly eligible for the pass through the extension of the age of entitlement as "non-elderly", and have estimated that these may have accounted for about 26,000 of the total as at 31/3/2004. The data shown in Table 4.6 has reclassified these passholders as "eligible by age" i.e. reflecting the actual eligibility criteria at the time, although in practice the distinction between the two groups of passholders is not relevant to elasticity estimates beyond the initial year.
4.5.21 For the year ending March 2006, we have used data reported in a Scottish Executive research report published in 2006, but it is unclear precisely to what period it refers, and there are some indications that it may not be defined consistently with the other figures shown here. For the year ending March 2007, we have drawn on data published in "Bus and Coach Statistics" by Transport Scotland. The value shown is calculated from the sum of passholder numbers recorded by the individual local authorities in the former Strathclyde Passenger Transport area, including all of Argyll and Bute. Transport Scotland's published Strathclyde total excluded Argyll and Bute, which is only partially in the Strathclyde Regional Partnership area, whereas prior to April 2006 it was fully included in the SPT area.
4.5.22 Note that since no passholder data is available on a consistent basis for Scotland outside Strathclyde prior to the National Scheme, any allowance for passholder growth in the elasticity estimation process is reliant upon the assumption that Strathclyde is reasonably representative of Scotland as a whole.
4.5.23 Age equalisation: a major complication in the interpretation of data from 2003 is that in April of that year, the minimum age of eligibility for the elderly concession was extended to men aged between 60 and 64, having previously been set at 65. This change ("age equalisation") will have increased the number of concessionary bus journeys included in the data from that time, representing both a transfer to the concession of journeys previously made by bus but paying a fare, and also through additional bus journeys generated by access to free travel. Ideally, to allow for "before" and "after" comparisons of concessionary journeys on a like‑for‑like basis, the numbers of concessionary journeys by these newly eligible passholders should be subtracted from the "after" concessionary journeys, and an equivalent adjustment should be made to reflect the change in passholder numbers brought about by age equalisation.
4.5.24 Research was commissioned in 2003 by the Scottish Executive from Accent Marketing and Research ("Accent") to estimate the additional demand for concessionary travel. Accent conducted 900 telephone interviews just before the change came into effect, and reported on how much respondents would make use of the new concession. Results were expressed in terms of estimated additional concessionary journeys, categorised between those previously made on a fare-paying basis, those made previously by another mode, and journeys that were completely new. Overall, Accent estimated that age equalisation would result in about 443,000 additional concessionary bus journeys in a typical week.
4.5.25 In principle, the Accent work provides a useful starting point for making allowance for age equalisation. However, it is likely to overstate the scale of additional journeys - respondents are inclined to report intentions, some of which do not materialise. The likelihood of this is confirmed by considering that the average number of journeys that would be made per week, according to the stated intentions of respondents, would average about 3.64 per male aged 60-64, in contrast to the overall average (for example, in 2006-7) of 2.662. Evidence from elsewhere suggests that average concessionary trip making by those aged 60 to 64 is lower than those of older concessionary passholders. In addition, the growth in concessionary journeys for men aged 60 to 64 will be from a base position of no concession, whereas for other passholders, the movement is from at least a half fare scheme and in many instances a more generous flat fare concession.
4.5.26 Overall, these represent a complex series of interactions which cannot be fully allowed for with available evidence. CPT has proposed a pragmatic assumption that one third of those increases in concessionary journeys estimated by Accent associated with modal shift and "new" journeys should be allowed for in the estimated number of post-free concessionary journeys. In the absence of firmer evidence, we have adopted this assumption for illustrative purposes in the elasticity estimates that follow. However, in our view it is regarded, on the basis of anecdotal evidence from England, and also some Strathclyde data provided to the Determination by SPT, as more likely to overestimate this impact rather than an under-estimate, and therefore will favour lower elasticity values and higher levels of reimbursement.
4.5.27 Trends in eligibility for disabled concessions: over the period under consideration, the number of passes issued on grounds of disability has increased more rapidly than those for the elderly, reflecting amongst other trends an increase in the underlying number of people eligible for disabled benefits. Since there is good evidence that, on average, disabled concessionary passholders (e.g. those aged under 60) make more use of the concession than older passholders, this would suggest that in the counter-factual a larger increase in concessionary journeys would have occurred than if all passholders were assumed to have the same propensity to make concessionary journeys.
4.5.28 We have used data on the number of claimants for Disability Living Allowance (DLA) to provide a proxy measure of the trends in the number of people who are eligible for concessionary travel on grounds of disability. We have used the total caseload, all rates, of working-age applicants as the proxy measure of growth in disabled passholding and journeys.
4.5.29 The underlying trend in concessionary journey volumes: time-series analysis of concessionary travel in Strathclyde from 1993 to 2003 was carried out by MVA Ltd in research on trends in concessionary travel for the Passenger Transport Executive Group ("pteg"), of which SPT was a member. This identified an underlying long-term decline in concessionary journeys numbers of -0.75% per year, after allowing for a range of explanatory variables including concessionary fare changes, demographic change and increased car availability. Data on bus service levels in Strathclyde was not available to inform the analysis for pteg, but if the all-Scotland trends in bus-kms were representative of Strathclyde, then a larger trend decline would probably have been observed, with the consequence that elasticity estimates would have been modestly higher. The -0.75% pa trend decline has been assumed to apply to the year ending September 2003, and pro-rata to the fiscal year 2006-7.
4.5.30 For Scotland outside Strathclyde, no equivalent analysis is available, and the assumption has been adopted that there was no overall underlying trend. Determination data for concessionary journeys in the year ending September 2003 shows that Strathclyde represents 59.0% of journeys in Scotland excluding Fife, Dumfries and Galloway. The overall trend per year for Scotland excluding Fife, Dumfries and Galloway has therefore been assumed to be -0.443% (0.59*-0.75%) per annum.
4.5.31 Demographic change: even without age equalisation, the elderly population in Scotland is increasing by about 0.5% per year, so that if free travel had not been introduced, both passholders and concessionary journeys could be expected to have increased in similar proportions. General Register Office for Scotland data on the elderly population has been assembled for Scotland and Strathclyde, and used to adjust journey totals pro-rata on the basis that 75% of concessionary journeys are made by those qualified for a pass on grounds of age. Age equalisation added about 13% to the elderly eligible population in Scotland, and about 12% in Strathclyde.
4.5.32 Changes in bus service levels: vehicle kilometres on local bus services in Scotland increased from 2001-2 to 2006-7, and this is likely to have encouraged more concessionary journeys even if free travel had not been introduced. It has been assumed that 10% increase in bus kilometres will lead to a 6.6% increase in patronage. Data has been taken from Transport Scotland's Bus and Coach Statistics. Separate data is not available for Strathclyde, and for the Strathclyde-specific elasticity estimates, it has been assumed that the All-Scotland figures apply.
4.5.33 Impact of free bus travel on concessionary rail demand: in Strathclyde, the introduction of free travel on buses probably led to some transfer to bus of concessionary passengers who had previously used trains (for which a £0.40 concessionary fare continued to be available). The scale of this impact was estimated during the Strathclyde Determination and has been included in our calculations.
4.5.34 Other confounding factors: in addition to the above, there are other influences on the volume of concessionary journeys that will affect the "before and after" comparisons. The most significant are probably changes in car availability amongst the older population, and increased proportions of accessible buses. The former is likely to have led to reduced concessionary journeys, the latter is likely to have increased concessionary journeys. However, evidence on the scale of these impacts is weak, and it is difficult to judge whether the net effect is positive or negative. In our view, the impact of increased car availability is likely to outweigh more accessible buses, but CPT has a different view. Our elasticity estimates have been based on an assumption that, overall, these other confounding factors have a neutral effect on the underlying demand for concessionary travel, but we recognise that these other influences add uncertainty to our conclusions.
4.6 Scottish Elasticity estimates
4.6.1 The various considerations set out above provide the inputs into the elasticity estimation process. Elasticities based upon the comparison between the years ending September 2002 and September 2003 are regarded as providing least scope for error through confounding factors but representative of short-run elasticities; those based upon the comparison of concessionary journeys in 2006-7 with the year ending September 2002 are regarded as long run elasticities.
4.6.2 Our elasticity estimates, and those drawn from other sources, are summarised in Table 4.7. The estimates are as follows:
- the elasticity parameters implied by the current National Scheme Reimbursement Factor of 61.5%, if measured at the average fare forgone assumed by the current National Scheme in 2006-7;
- the elasticity parameters implied by the current National Scheme Reimbursement Factor of 61.5%, if measured at the average fare forgone assumed by the current National Scheme in 2012-13 (note that the difference between these two elasticity parameters arises from the very different fares charged at these different times);
- our estimate of the short-run elasticity implied by contrasting the concessionary journeys in Strathclyde in the years ending September 2002 and September 2003 (just before and after the introduction of free travel);
- our estimate of the short run elasticity, derived from data for the same years as Strathclyde, but for all Scottish local authorities except those that were already providing free travel;
- our estimates of long run all-Scotland elasticities derived from contrasting data for the year ending September 2002 and March 2007;
- CPT's estimates of all-Scotland elasticities, based on contrasting data for the years ending March 2002 and March 2006 (Medium/long run);
- CPT's estimates of all-Scotland elasticities, based on contrasting data for the years ending March 2002 and March 2007 (Long run);
- parameters obtained from DfT's recommended values for PTE areas in England, adjusted for differences between English and Scottish characteristics; and
- parameters obtained from DfT's recommended values for Non-PTE areas in England, adjusted for differences between English and Scottish characteristics.
4.6.3 Table 4.7 shows the elasticity parameters (Lambda and Beta) and as a comparative measure, the point elasticity that would be derived from these parameters at an average fare forgone of £0.859 at 2001-2 prices.
4.6.4 The comparative point elasticities are plotted in Figure 4.1.
Figure 4.1 Comparisons of elasticity estimates
4.6.5 Our (Minnerva/MVA) estimates of Scottish elasticities, for Strathclyde and for Scotland, based on the analysis of the impact of the introduction of free travel in October 2002, are highlighted. It can be seen that the Strathclyde short run value is quite similar to the elasticities implied by the current Scheme Reimbursement Factor, if calculated at 2006-7 fare levels. Our estimate of the Scotland long-run elasticity is higher, and in fact is very similar to the value that would be calculated based on DfT recommended values for English PTE areas, if adjusted for Scottish car ownership and population characteristics.
4.6.6 The values estimated by CPT are lower than our values. Broadly, the CPT and MVA/Minnerva elasticity estimates are based on the same datasets using a largely identical methodology. The fact that there are non-negligible differences in the elasticity estimates, which imply significant differences in reimbursement payments, demonstrates the sensitivity of both the estimation process, and the reimbursement calculation. The principal reasons for differences in elasticity values are the choice of specific years for before and after analysis (and consequent differences in values for all relevant annual averages and indicators) and the values used for end-year passholder data. Our values are preferred because our choice of comparison years before and after the introduction of free travel is more likely to be free of confounding factors that would otherwise distort the analysis, and we have also used different, and we believe more accurate, data on passholder numbers.
4.7 Preferred elasticity values
4.7.1 In our view, the most robust of the various estimates of Scottish elasticities that have been discussed in this chapter is the Strathclyde short run estimate, which draws on a variety of data from sources of generally well known provenance. Most of these data were collected close to the date of the introduction of free travel in connection with the Determination of bus operator appeals, and was subject to scrutiny by interested parties with a considerable stake in their outcomes. A particular strength of the Determination journey data is that the detailed quarterly figures allows Financial Year comparisons to be made exactly with equivalent data published by Transport Scotland, while permitting a choice of analysis years for elasticity estimation from the period immediately before and after the introduction of free travel. Overall, there are far fewer residual uncertainties associated with the Strathclyde estimates (e.g. associated with basic data and confounding factors) than with all-Scotland estimates.
4.7.2 However, the Strathclyde elasticities are not necessarily representative of Scotland as a whole, and are short run only, whereas longer run elasticities are more appropriate for reimbursement. The All-Scotland elasticities are therefore a better basis for an All-Scotland Reimbursement Rate.
4.7.3 There is scope for error arising from the difficulty of fully accounting for confounding factors with the longer run estimates, and our Scottish long run elasticity is only 12% larger than our short run elasticity. Long run increments of between 30% and 50% are commonly assumed, and overall, these Scottish elasticity values are lower than typical values from equivalent analysis of English data. We are aware of areas of uncertainty in which assumptions might err on the side of lower elasticity assumptions, but also know of others which will potentially go the other way. Overall, we are content that our elasticity values fairly represent the implications of the available data.
4.8 Application of Elasticity Estimates
4.8.1 All the parameter values quoted above are expressed relative to price levels in 2001-2: they are determined from the average concessionary fare paid in that year, and hence relative to consumer prices in that year. Prices in 2012-13 are between 30% and 40% higher than in 2001-2, depending upon whether measured by the Consumer Price Index (CPI) or the Retail Price Index (RPI). To calculate a Reimbursement Factor for a given Reimbursement Year such as 2012-13, it is necessary to apply an index to relate the average fare forgone in 2012-13 to prices in 2001-2.
4.8.2 The CPI and the RPI have different technical characteristics, and over the last ten years RPI has tended to increase at a faster rate than CPI. The UK DfT recommends the use of CPI, largely on the grounds that CPI is now the basis on which State Pensions are uplifted and will therefore better track passholder incomes. However, RPI was the basis for pension changes until 2011, and possibly would better reflect the general price changes experienced by older persons between 2001-2 (the year of the concessionary fare from which the elasticity was established) and the year for which reimbursement is being calculated. Since for the majority of the period from 2001-2 onwards RPI was used for pension settlements, it is proposed that this forms the basis of the price index used to apply 2001-2 based elasticity parameters, although it is recommended that Transport Scotland give further consideration to the choice of CPI or RPI in the future.
4.8.3 An additional consideration is that the index used for calculating the Reimbursement Factor (and hence generation) should take explicit account of changes in the costs of alternative modes. Petrol prices have risen particularly rapidly in real terms since 2004-5, and it has been suggested that an index should be constructed as a weighted average of the RPI and the fuel price element of RPI.
4.8.4 Figure 4.2 shows the historic data on these different indices, including a forecast for 2012-13 based on continuation of the rate of change in September 2012. Also included is the motoring expenditure element of RPI, of which petrol forms one component, the others including various fixed costs as well as operating costs. It can be seen that in contrast to petrol and oil, overall motoring costs have tended to rise more slowly than other prices except in the last two years.
Figure 4.2 Potential indices for price adjustment of fare levels
4.8.5 Although not easy to estimate, there will be a proportion of concessionary bus journeys for which the passholder will consider the relative costs of car and bus modes. While the majority of older passholders now have access to a car, this probably does not reflect the availability of car as a viable alternative for concessionary bus journeys, because of the skewed nature of concessionary bus use. Car availability is likely to be much lower amongst frequent bus users than for infrequent bus users in the population of older people and passholders.
4.8.6 The extent to which the car represents a likely alternative mode to bus can be gauged from the stated intention data gathered by Accent during research on the impact of age equalisation in 2003. Respondents, who were all men aged 60 to 64, reported that of the journeys that they would make using the concession once it became available, 37.3% would otherwise have been made by other modes. We believe that this will overstate the extent to which cars are a real alternative to bus for the generality of passholders, for a variety of reasons including the tendency for stated intention surveys to lead to overstated responses. We have therefore proposed making use of the same assumption employed in the elasticity analysis, whereby only a third of the intended "mode shift" and "generated" journeys are assumed to be translated into concessionary journeys. That would imply that potential "mode shift" journeys are 22.0% of the overall number of concessionary bus journeys.
4.8.7 We therefore recommend that a combined index is used to relate Reimbursement Year prices to the 2001-2 price base of the elasticity parameters, with a 78% weight for the general RPI and a 22% weight for the petrol and oil component.
4.9 Conclusions with regard to elasticity values
4.9.1 Elasticity values are essential components of the reimbursement calculation. They reflect the sensitivity of concessionary passengers to changes in fares, and are therefore key both to establishing a Reimbursement Factor at a given point in time, and also to determining how that Reimbursement Factor should change over time if the average fare forgone changes in real terms.
4.9.2 The Reimbursement Factor of 61.5% incorporated in the current National Reimbursement Rate was not calculated explicitly from elasticity estimates. However, the elasticity estimates that would lead to 61.5% can be implied by working backwards from the fare at different points in time. Elasticity values are also available from research elsewhere in Great Britain, particularly that conducted by the DfT in 2009-10. Differences between Scottish characteristics, and those of passholders elsewhere in the UK, limit the direct applicability of this evidence, although we have produced estimates of elasticities based on the DfT results adapted to Scottish conditions.
4.9.3 There was little readily available evidence on All-Scotland elasticities suitable for calculating reimbursement on an All-Scotland basis. Substantial effort has been devoted to making new estimates of Scottish concessionary elasticities based on the change in concessionary journeys experienced in Scotland when free travel was introduced in October 2002. This analysis has relied upon a large volume of data assembled in 2004 for the Strathclyde area, in connection with Determinations of operator appeals, and also information collated by CPT.
4.9.4 Elasticity estimates require information on changes in passholders and various other factors that might influence change in concessionary journeys. Because of the passage of time between 2002-3 and the present day, the available data is limited and requires careful interpretation. Residual uncertainties leave room for debate, although in the case of Strathclyde, the availability of the Determination archive, and some Transport Scotland data, provided robust evidence on many key issues.
4.9.5 The elasticity analysis has resulted in the identification of a range of estimates for Strathclyde, for Scotland as a whole, and for the short and long run. Our preference is for reimbursement to be based on long-run elasticities derived for Scotland as a whole. There remain a number of residual uncertainties and alternative choices could be made, reflecting the nature of many of the judgements required, although on balance we believe that our preferred elasticity estimates fairly represent the elasticity implications of the available data.
4.9.6 The preferred elasticity parameters are summarised in Table 4.8 below, which also shows CPT's estimates, and the compromise values that are an average of these two. Our preferred values are derived from the concessionary journey numbers shown in Table 4.3 above and the passholder numbers shown in Table 4.6.
4.9.7 In applying a given set of elasticity estimates, it is also necessary to choose a price index to allow fares to be expressed in constant prices. Various alternatives have been considered, and our preference is to use the RPI, with added weight given to the petrol and oil component, to reflect the likely significance of petrol prices in passholder mode choice.