The Effects of Park and Ride Supply and Pricing on Public Transport Demand

8 Appendix A1: Rail modelling methodology for revealed preference


8.1 The aim of this aspect of the study is to determine the effects of parking provision, prices and policy directly on the demand for rail travel, rather than simply to estimate, say, the valuation of improved facilities. For this reason, we have developed demand models that link observed and stated behavioural responses to, amongst other things, changes in parking provision, quality and prices. The method of rail demand forecasting set out in the Passenger Demand Forecasting Handbook (PDFH), which is widely used in the railway industry in Great Britain, is an incremental approach of the form:

formula 1

8.2 Where V is the volume of rail demand in the new (forecast) and base period. This proportionate change in demand is driven by proportionate changes in price (P), generalised journey time (GJT) and a range of external factors (E). The terms p, g and e denote the respective elasticities of these variables. We enhance this framework to include station parking policy as follows:

formula 2

8.3 Thus the change in rail demand is now additionally dependent on the change in parking spaces (S), the change in parking charge (C) and changes in other factors (O), such as the quality and security of the parking provision. The latter enters in this form since O is likely to be a dummy variable denoting discrete changes reflecting, say, a change in CCTV provision. The parameter s is the elasticity to parking space provision. It is informative to establish how this varies with:

  • the extent to which the station car park was previously at capacity
  • the extent to which there is other car parking provision near the station
  • the extent to which there are competing stations with differing levels of parking provision
  • whether the rail journeys are for commuting or other purposes
  • whether the rail journeys are short or long distance, with 20 miles typically being used in the rail industry to distinguish the two

8.4 The parameter 'c' is the elasticity to parking charge and ideally the sensitivity of this elasticity to a range of factors would be explored, including:

  • the level of the parking charge
  • charges at alternative parking locations
  • the presence of competing stations with parking provision

8.5 The parameter o denotes the proportionate change in demand after other changes, such as the quality and security of parking.

Overview of the datasets

8.6 Two forms of data are used in estimating the model:

  • tickets sales (LENNON) data denoting actual changes in demand
  • survey data denoting the diversion factors consequent upon changes in parking policy

8.7 In addition, we can combine the two forms of data, in a jointly estimated model, which would be unique since we are not aware of previous studies which have analysed both ticket sales data and survey based data in a single model. The reason for using two forms of data is not only because this provides more data, and hence more precise estimates, but the two forms of data are highly complementary to each other:

  • the ticket sales data has the advantage in that it is based on what people actually do and indeed their perceptions of actual changes. However, as with all revealed preference data, it is limited to the changes that have occurred in the real world, in this case in the context of parking policy
  • survey data can provide more detail and cover changes that we would like to model that do not occur in the real world. For example, we can offer respondents changes in parking charges and parking quality, as well as parking spaces, and we can offer these in different contexts where, for example, there are different degrees of competition from other parking spaces, different likelihoods of getting a parking space, and for the flows and ticket types that are of greatest interest to us. In addition, there is no possibility of confounding effects, such as demand varying for other reasons

LENNON ticket sales data

8.8 The changes in rail demand have been analysed and form a useful starting point to understand the impact of car park extensions on changes to rail demand. We have used a number of data sources to assess how demand has changed. Since period-by-period LENNON data, split by ticket type is only available for the last five years, this duration may not fully represent the before /after period when each car park was extended.

8.9 This yields 91 observations per flow. We have obtained revenue and volume for each flow and time period for season tickets and non-season tickets. The ratio of revenue and volume provides a measure of price. The most popular demand flows were identified using LENNON data, since any changes to parking availability will have the greatest impact on these movements.

8.10 As a result, we have used trip data from MOIRA to enable the time period the LENNON dataset represents to be extended. The following describes the process adopted:

  • review annual MOIRA data for individual flows, for example, Bridge of Allan to Edinburgh or Glasgow
  • examine LENNON data representing total footfall from each station to understand the proportion of journeys made during each four week period throughout the year
  • review overall ticket types, and aggregate for season and non-season tickets to estimate the number of trips for commuting or other journeys
  • use the MOIRA and LENNON datasets to estimate the number of journeys by period, split by ticket type for individual flows for up to 10 years

8.11 Four weekly ticket sales data was derived between 2003/4 Period 1 through to 2009/10 Period 13. In total we have 170 station-to-station flows in the data set. Given 91 time periods per flow, this yields a total of 15,470 flows for modelling purposes.

8.12 Employment data at the destination has been included, to help to explain variations in season ticket demand, and Gross Value Added (GVA) at the origin, to help explain variations in trips on non-season tickets. It was beyond the scope of this study to source historic journey time data but we have included distance between the origin and destination.

8.13 Estimates of the changes in parking spaces were overlaid onto this dataset, with utilisation rates before and after the change in parking spaces and a variable denoting whether there is any local car parking other than the station, ample free local parking or ample local parking at a charge.

Survey data

8.14 This data takes two forms:

  • at Kirkcaldy, Bridge of Allan and East Kilbride where improvements have occurred, car park users were asked what they did prior to the improvement
  • at these improved or indeed any other stations, selected to cover a wide range of parking situations, car park users would be asked what they would do in the event that car parking became less available, became more expensive, or was of reduced quality

8.15 In both cases, the effects of changes in parking policy are not confounded with changes in other factors, such as fares or GDP/employment, which can occur with ticket sales data.

Impact of parking improvements

8.16 At Kirkcaldy, Bridge of Allan and East Kilbride, users were asked how they had changed their behaviour as a result. They were first asked if they were aware of the improvements to the car parking facilities that had been implemented and were told when these were improved. For those who were aware of the improvements, they were asked whether they would have still made the journey by train in the absence of such improvements. If the answer was yes, they were further asked if they would have parked at the station, parked somewhere else nearby or else access the station by some other means.

8.17 Current train users were asked what they would do in response to a series of parking charge increases, a series of reductions in the chances of finding a parking space, the removal of CCTV and of lighting, the removal of both CCTV and lighting and the absence of tarmac road surface, and finally a 10% and a 25% increase in rail fares. Permissible responses were:

  • as now
  • use rail but park elsewhere
  • use rail but use a different access mode
  • use rail but from a different station
  • use another mode of transport
  • not travel

8.18 With the exception of the rail fare increases, permissible responses were to continue with train, use another mode of travel or else not to make the journey.

8.19 If appropriate, a series of questions are presented for multiple observations per respondent, similar to standard Stated Preference methods. This generates a much larger data set compared with the presentation of a single Stated Intention question and helps to make the overall results more robust. Iterative scenarios were presented, comprising increasing parking charges and / or reduced chances of getting a space.

Non user surveys

8.20 There is scope to ask non users whether they would make a train journey if parking provision at a station was improved, but the level of uncertainty surrounding such questions is high. In addition, the cost of contacting a sufficient number of non-users who might possibly make a train journey if the parking at a station was improved was beyond the resources of this study. Furthermore, trying to estimate the proportional increase in rail demand that would result would also be very difficult. Instead, a more straightforward approach was adopted, by discussing possible deteriorations to existing rail users compared with the current train service. Whilst this assumes symmetry between equivalent improvements and deteriorations in travel attributes, this is the default assumption used by most conventional travel demand models.

Modelling approach

8.21 We can estimate three types of model

  • demand model based solely on ticket sales data
  • demand model based on the Stated Intentions survey data where the parking situation is made worse
  • a combined model covering both the ticket sales and the Stated Intentions data, and additionally also the behavioural response data relating to the actual improvements

8.22 Whilst the behavioural response to improvements can be included in the joint model, unlike the Stated Intentions data, there is not enough data to estimate a freestanding model. In order to facilitate pooling of the ticket sales data and the survey data, since the former covers the population whilst the latter is a survey, the model has been specified using ratios, as presented in equation 2. Taking a logarithmic transformation, where 'ln' denotes natural logarithm, for estimation by ordinary least squares regression, yields:

formula 3

8.23 This differs from equation 2 in terms of the exact variables included since historic journey time data is not readily available. Parameters 'C' and 'O' are only included in the Stated Intentions data since these terms do not vary in the ticket sales data.

Analysis of ticket sales data

8.24 The model is specified in ratio form, so 91 observations per flow yields 90 ratios of demand that are independent observations. There are various ways to specify the ratios. If we specified them as 'first differences', reflecting period on period changes, then there would only be one ratio out of the 90 where the car parking variable would change. Alternatively, the ratio could be specified as demand after the change relative to demand before the change, ensuring each period is used at least once.

8.25 The approach adopted compares each period after the additional car parking was introduced with the situation immediately preceding it, and then to compare the situation immediately prior to the change with all previous periods. This gives us a mixture of different scenarios. The actual period when the change occurred was removed, thereby eliminating a small amount of data. After reducing the number of observations from 91 to 89 per flow, and taking account of missing data, 15,120 observations for season tickets and 14,230 observations for non-season tickets remained. These are robust samples for modelling purposes.

8.26 The estimated models for season and non-season tickets are reported in Table A1.1. The goodness of fit achieved by each is reasonable given that the employment data covers a relatively large geographic area. The absence of reliable local income variations, which drive sales of other tickets are further limitations. Data on historic journey times, changes in inter-modal competition or local one-off events are also excluded.

8.27 The employment elasticity calculated produced a non-typical result due to some of the inherent inaccuracies affecting the data. As a result, we have specified dummy variables to represent the impacts relative to the 2003/04 base data. The absence of local income effects meant some dummy parameters were also used in the non-season data model to reduce the reliance on regional GVA statistics.

8.28 Period effects are similarly accounted for by the specification of 12 dummy variables, with period 1 serving as the arbitrary base. The remaining variables relate to fare, represented as revenue per trip, and car parking spaces. The fare elasticity has a 'base' term and incremental variations, denoted by '+'. The incremental effects relate to whether the fare is a reduction (FareRed) and whether the journey was inter-urban, defined as more than 20 miles (FareInter). As a result, the fare term relates to fare increases on urban journeys.

Results from the RP models

8.29 The base fare elasticity for commuting rail trips is -0.641, implicitly relating to fare increases, whereas it falls to -0.144 (-0.641+0.497) for fare reductions. These figures seem reasonable. The corresponding figures for non-season tickets are -1.242 and -0.663. We also observe that inter-urban journeys have lower fare elasticities, by 0.072 for season tickets and 0.177 for non-season tickets. Thus reductions in the price of season tickets for inter-urban travel would generate few extra trips.

8.30 The reason we distinguish between increases and losses in price is that the Stated Intention data relates explicitly to price increases. For comparability purposes, it therefore makes sense to be able to isolate the effect of price increases in the ticket sales data since this is how we assess the quality of the Stated Intentions responses to price increases.

8.31 With regard to spaces, we have a significant incremental effect relating to inter-urban trips for season tickets (SpacesInter) of -0.078. This would imply a wrong sign effect and we are inclined to ignore this, particularly given that inter-urban commuting trips from the origin stations in question will be comparatively rare. There was no significant effect from whether there is ample free local parking (SpacesLocal); perhaps commuters are less inclined to leave their cars 'off-site', although there will be more spaces available earlier in a morning and hence free parking elsewhere is less of an attraction. However, the base effect (Spaces) indicates that increasing provision increases rail demand overall.

8.32 For non-season tickets, increasing spaces does have a significant effect on demand, although neither of the incremental effects were significant. We might expect the impact of increased parking spaces to depend upon occupancy levels prior to improvements. We could not detect any effect from occupancy levels on the demand for either season or non-season tickets.

8.33 It is encouraging that we can recover right sign coefficients estimated with a reasonable degree of confidence for the effect of changes in parking spaces. As far as we are aware, this is the first study to have recovered such effects.

8.34 The base spaces coefficient indicates that a 10% increase in parking spaces would be forecast to lead to:

  • a 0.43% increase in season ticket trips
  • a 0.35% increase in non-season ticket trips

Results from the RP models

Table A1.1: Results of the demand models
Seasons Non-Seasons
Intercept -0.047 (7.8) -0.019 (3.7)
Fare -0.641 (25.6) -1.242 (47.3)
+FareRed 0.497 (14.5)
0.579 (12.0)
+FareInter 0.072 (3.3) 0.177 (5.4)
Spaces 0.043 (4.0) 0.035 (4.6)
+SpacesInter -0.078 (6.2) n.s.
+SpacesLocal n.s. n.s.
Year0304 Base Base
Year0405 0.130 (17.2) 0.110 (16.1)
Year0506 0.184 (27.2) 0.241 (37.8)
Year0607 0.322 (40.1) 0.300 (40.8)
Year0708 0.359 (43.7) 0.331 (44.1)
Year0809 0.451 (48.9) 0.391 (45.2)
Year0910 0.481 (52.8) 0.464 (54.5)
Period1 Base Base
Period2 0.108 (13.1) -0.033 (4.5)
Period3 0.081 (9.8) -0.036 (4.9)
Period4 -0.002 (0.2) -0.071 (8.7)
Period5 -0.066 (8.5) 0.073 (10.8)
Period6 0.126 (18.9) 0.120 (18.2)
Period7 0.234 (28.8) 0.045 (6.2)
Period8 0.284 (36.7) 0.061 (8.8)
Period9 0.231 (24.6) 0.079 (9.5)
Period10 -0.189 (18.2) -0.035 (3.9)
Period11 0.273 (25.1) -0.057 (5.8)
Period12 0.314 934.5) 0.111 (13.7)
Period13 0.207 (19.0) 0.001 (0.1)
Adj R2 0.47 0.40
Obs 15120 14230

Source: Analysis by ITS

Behavioural responses

8.35 The travel market has been differentiated into the following segments:

  • season tickets and urban journeys
  • season ticket and inter-urban journeys
  • other tickets and urban journeys
  • other tickets and inter-urban journeys

8.36 Of the 323 respondents who answered the question about awareness of car parking improvements, 201 (62%) were aware, although this total does not include respondents from Perth. Those who were not aware of the improvement might still have been influenced by the enhanced level of improvement but the question is not relevant to them and hence they have been excluded. There would be others who were not aware since they were not making rail trips at the time of the improvements and thus again the question is irrelevant.

8.37 Table A1.2 shows the different possible behavioural responses. Not using the train is a minor response, as would be expected. Splitting the sample by train station as well as ticket type and distance would mean the sample sizes would be too small.

8.38 With the exception of inter-urban journeys, the impact of car parking improvements has had little impact on demand. The largest impact is for inter-urban other, indicating a 14% demand effect. The effect would still exceed 10%, even if it is assumed all those unaware were not bothered about car parking.

Table A1.2: Response to the retention of existing car park facilities
Urban Seasons Urban Other Inter-Urban Seasons Inter-Urban Other
Total 39 99 58 127
Aware 28 (72%) 55 (56%) 28 (48%) 90 (71%)
Not Use Train
Bus 1 (4%) 1 (2%) 3 (3%)
Car 1 (4%) 6 (7%)
Other 1 (4%) 4 (4%)
Use Train
Park at Station 21 (75%) 44 (80%) 21 (75%) 28 (31%)
Park Nearby 5 (18%) 9 (16%) 2 (7%) 30 (33%)
Use Another Station 1 (2%) 2 (7%) 6 (7%)
Walked to Station 2 (7%) 4 (4%)
Bus to Station 4 (4%)
Taxi/Lift to Station 5 (5%)
Generation 2 (7%) 1 (2%) 1 (4%) 13 (14%)

Source: Analysis by ITS

Table A1.3 provides predicted demand effects based on the ticket sales analysis. There would seem to be a high degree of correspondence between the two sets of results for urban other and inter-urban seasons. For inter-urban other, the behavioural response data seems high whilst for urban seasons the behavioural response data is based on a small sample.

Table A1.3: Predicted response based on ticket sales model
  Urban Seasons Urban Other Inter-Urban Seasons Inter-Urban Other
Bridge of Allan 0.9% 2.2% 1.5% 2.2%
Kirkcaldy 2.4% 5.5% 3.9% 5.5%
East Kilbride 2.2% 1.3% 3.6% 1.3%

Note: Kirkcaldy and Bridge of Allan were defined as having no local parking whereas East Kilbride was defined as having ample local parking. Before and after spaces for each station were 114:146 for Bridge of Allan, 162:287 for East Kilbride and 274:594 for Kirkcaldy. Results for Perth were not collected.

Results from the modelling outputs

Link between parking availability and demand

8.39 The secondary data was examined to understand the relationship between parking availability and resulting demand in accordance with the modelling methodology described. The data indicates a 10% increase in parking spaces would lead to a 0.43% increase in season ticket trips and a 0.35% increase in non-season ticket trips based on the sample of data analysed.

Likelihood of getting a space

8.40 The proportionate change in demand if either the car parking charges or the likelihood of getting a parking space was altered was also assessed. The model results are presented in Table A1.4. The demand parameters included ticket type, inter-urban or local journeys and whether the origin station had no local parking, ample free local parking or ample paid local parking. Ticket type was used as a proxy for differentiating between peak (using seasons and full tickets as a proxy) and off-peak (using reduced as the proxy) results.

8.41 With regard to the availability of spaces, an incremental (add-on) effect relating to inter-urban trips for season tickets was identified, although this was not significant for non-season tickets. However, there is an incremental effect where there is ample local free parking for non-season tickets, although this was not significant for season tickets. This implies commuters are less inclined to leave their cars 'off-site', although there will be more spaces available earlier in a morning and hence free parking elsewhere is less of an attraction. Thus moving from a 0 to 20% chance of not finding a space would lead to a 4.3% reduction in rail demand. If the likelihood of not getting a space increased to 10%, demand would be reduced by 2.2%.

Table A1.4: Results from the stated intention model
Attribute Value
Rail Fare -6.3230 (12.8)
+Season 1.9401 (3.4)
+Inter 2.2078 (3.9)
Chance -0.0022 (4.0)
Park Charge -0.0005 (7.5)
+AmpleFree 0.0002 (1.3)
Adj R2 0.46
Obs 246

Source: ITS calculation. Note: Adj R2 is for model with constant included. A % chance of not getting a parking space is specified as 10 whilst parking charge is specified in pence. The numbers shown in brackets are the t ratios, whilst the other numbers are model coefficients. The results are elasticity values, where an elasticity is defined as a proportional change in demand after an absolute change in fare, expressed in pence

Impact of parking charges

8.42 A range of scenarios were tested to examine the impact of changes to parking charges. These tests include the introduction of a parking charge to £1 for locations where parking was previously free, or increasing the parking charge to a higher value from £1 to £2. Table A1.5 illustrates the change in travel behaviour if parking costs changed. Responses have been used to assess the percentage using rail who would not alter their travel behaviour, and the proportion parking elsewhere or switching to another mode depending on absolute changes to the parking charges. Different ratios are calculated for individual changes in price. The relationship shown is non-linear, since every respondent was not presented with every price increase.

8.43 If the parking charge is increased by £1, park and ride demand would be reduced by 4.9%. A 3.0% reduction in park and ride usage would occur if there is ample free parking available in an alternative location nearby.

Table A1.5: Change in user behaviour in response to pricing changes
Change in Car Parking Costs - Pence Rail Park and Ride Users Rail Users who Park Elsewhere Transfer from Rail
20 33.9% 65.1% 1.0%
40 30.2% 67.9% 2.0%
60 22.7% 74.4% 3.0%
80 47.3% 48.8% 3.9%
100 41.3% 53.8% 4.9%
120 30.8% 63.4% 5.8%
140 24.8% 68.5% 6.8%
160 29.4% 62.9% 7.7%
180 19.3% 72.1% 8.6%
200 30.2% 60.3% 9.5%
220 21.1% 68.5% 10.4%
240 21.6% 67.1% 11.3%
260 14.0% 73.8% 12.2%
280 20.9% 66.1% 13.1%
300 9.3% 76.8% 13.9%
400 19.2% 62.6% 18.1%

Source: ITS calculation