The Effects of Park and Ride Supply and Pricing on Public Transport Demand
11 Appendix A4: Modelling methodology for the bus market
11.1 Two surveys were undertaken with regards to bus demand and parking provision at Ingliston (Edinburgh) and Bridge of Don (Aberdeen) with a total of 250 respondents. The first set were current users of bus based park and ride, whilst the second were non users but did not reject park and ride. For current users the questionnaire established:
- what they did prior to the improvement at the car park (Point 1)
- what they would do in response to a series of bus fare increases (Point 2)
- what they would do in response to a series of bus frequency increases (Point 3)
- what they would do in response to a series of increases in the chance of not being able to find a parking space (Point 4)
- what they would do in response to a series of changes in the quality of the car parking. These were presented as (1) the removal of CCTV; (2) the removal of lighting; and (3) the removal of both CCTV and lighting and the absence of a tarmac road surface (Point 5)
11.2 The main analysis was related to 2, 3 and 4 above and the permitted responses to these questions were:
- as now
- use bus but from a different park and ride site
- use another bus service
- use another mode
- not travel
- other
11.3 Adaptive stated intentions questions were asked of every respondent with the aim being to 'hone in' on the change of bus fare, bus frequency and chance of not parking that would result in the current user choosing an option other than 'as now'.
11.4 A process of doubling changes was adopted if a respondent answered As Now (i.e. if they answered As Now when faced with a £1 increase in bus fare they were then asked what they would do if the bus fare increased to £2) and halving the difference if they answered anything other than As Now (i.e. taking the same example if the respondent did not answer As Now at £2 they were then asked what they would do if the bus fare increased to £1.50). This would continue for a maximum of 4 iterations or until a value that was, for bus fares, within 10 pence of the starting price.
11.5 The processes were very similar for both 'chance of finding a parking space' and 'bus frequency'. For the former a starting value set at the respondent's current chance of not finding a parking space (note for this sample of respondents this was primarily 0%) plus 20%. If the respondent answered As Now then the chance increased by 20% or if they did not answer As Now it was reduced by 10%. This process was iterative until a chance within 10% of the starting value was found.
11.6 For bus frequency the starting point was the respondent's current departure pattern plus 10 minutes. If the respondent answered 'as now', then the increase was doubled to 20 minutes but if they did not answer 'as now' it was reduced to 5 minutes. Again the process was iterative until a value for frequency was found that was within 5 minutes of the starting frequency.
11.7 Where suitable, as with price and occupancy changes, the series of questions asks allow for multiple observations per respondent, much as in standard Stated Preference methods, and makes for a much larger data set than if, as is sometimes the case, only a single Stated Intention question is asked.
Analysis of stated intention data
11.8 The Stated Intention data was combined to denote the proportionate changes in demand after some particular increase in bus fare, bus frequency and the likelihood of not getting a parking space. The estimated model contains three primary variables. These are:
- bus fare, specified in constant elasticity form
- bus frequency, specified in constant elasticity form
- the chance of not getting a parking space, specified in difference form (as with variable O in equation 3), since the chance of not getting a space is often zero in the base case
11.9 The models are contained in Table A7.1 and are presented for the base cases (i.e. without disaggregation by purpose or ticket type), relating solely to the bus park and ride market (i.e. the demand affects upon demand for bus services leaving from the Ingliston and Bridge of Don bus park and ride sites). The bus fare elasticity is very high at -1.605 suggesting that for a 10% increase in fare, demand would fall by 16%. Clearly this is too high and is reflective of the nature of Stated Intentions type questioning in that if respondents perceive that fares might be in line to increase, they have every incentive to state that they would no longer park and ride bus if the fares were increased.
11.10 Another factor to consider is that this elasticity relates to demand for the two specific park and ride sites at Ingliston and Bridge of Don, not to the bus market as a whole. A high elasticity is therefore expected since whilst a number of respondents may no longer use a specific park and ride site that doesn't mean to say they will not stop using bus (either a local but slower local service or another park and ride service).
11.11 A further look at the data revealed that a large number of respondents had been offered increases well in excess of 100% of the current fare, with a number of these still choosing the As Now option. This will contribute to the high elasticity estimate and as such a restricted version of the model was estimated which capped the fare increased offered to respondents at £3.40, equivalent to around a 110% increase on the highest fare. The result was a much lower and more plausible fare elasticity of -0.927.
11.12 Two elasticities are presented for bus frequency in Table A4.1, an unrestricted one based upon the whole data set and a restricted one. Again we see that the elasticity for the unrestricted case is considerably higher that one would expect at -1.468 suggested that a 10% increase in bus frequency would result in a 15% reduction in passenger numbers. As with the fare elasticity part of the explanation for such a high number can be attributed to the nature of SI questioning and partly to the fact that the elasticity relates to the specific park and ride market and not the general bus market. Again a number of incremental models (purpose and ticket type) were estimated but the findings were not significant and/or counter intuitive.
11.13 A closer inspection of the data found that the a number of respondents had been offered 'odd' increases in frequency which they might have found hard to translate into actual frequencies, i.e. a bus every 40 minutes is more difficult to conceptualise than a bus every 30 minutes. A restricted model was estimated that only considered those respondents who had been offered the following levels of bus frequency - every 15 minutes, 20 minutes, 30 minutes and 60 minutes. This reduced the sample size by over half but improved the frequency elasticity, although still high, to -0.982.
| Unrestricted Constant |
Restricted Constant |
Unrestricted Constant |
Restricted Constant |
Unrestricted Exponential |
|
|---|---|---|---|---|---|
| Bus Fare | -1.605 (27.6) | -0.927 (9.1) | |||
| Frequency | -1.468 (25.0) | -0.982 (10.2) | |||
| Park Chance | -0.021 (6.8) | ||||
| Adj R2 | 0.60 | 0.59 | 0.58 | 0.50 | 0.20 |
| Obs | 161 | 30 | 172 | 68 | 53 |
Note: Adj R2 is for model with constant included whilst the elasticities reported are from models with no constants.
11.14 The final elasticity reported in Table A4.1 relates to the chance of not obtaining a parking space. The exponential of the produce of the demand parameter (-0.021) and the change in the chance of not finding a parking space (i.e. 10=10-0) indicates the proportionate change in demand after that change in the chance of finding a space.
11.15 Thus moving from a 0 to a 10 percent chance of not finding a space would lead to a 19% reduction in bus demand, whilst a move from a 0 to 20 percent chance of not finding a space would result in a 34% reduction in bus demand at the park and ride sites. These are considerably higher than the figures produced for rail and probably reflect that the current park and ride sites currently have a large amount of spare parking capacity at all times so users will be much more sensitive to any move away from 0%.
11.16 The point has already been made that the demand elasticities reported above are relevant to the specific bus park and ride markets examined and that this is likely to lead to exaggerated elasticities vis a vis those normally associated with general bus use. To investigate whether this is the case a further set of models are presented in Table A4.2 below which look at the general bus market, i.e. do people remain in the bus market (use a slower local bus service or another park and ride service) when faced with changes to their current bus park and ride services.
| Unrestricted Constant |
Unrestricted Constant1 |
Unrestricted Exponential |
Unrestricted Exponential |
|
|---|---|---|---|---|
| Bus Fare | -0.306 (4.8) | |||
| Frequency | -0.285 (4.1) | -0.007 (3.6) | ||
| Park Chance | -0.008 (2.0) | |||
| Adj R2 | 0.024 | -0.069 | -0.080 | -0.146 |
| Obs | 32 | 14 | 14 | 7 |
Note: Adj R2 is for model with constant included whilst the elasticities reported are from models with no constants.
1 This assumes a current frequency of 15 minutes.
11.17 As expected the elasticities reported in Table A4.2 are much lower than those for the park and ride specific market (Table A4.1). The bus fare elasticity reduces from -1.605 to a much more plausible -0.306, suggesting that a 10% rise in bus fares reduces bus demand by 3%. For frequency, a similar picture emerges with a reduction in the constant elasticity from -1.468 to -0.285, suggest that a 10% increase in frequency reduces demand by just under 3%. This elasticity was based on an assumed current frequency of 15 minutes (based on the median average of the sample).
11.18 A further frequency model is reported based upon differences between the current frequency and proposed increases. The exponential of the produce of the demand parameter (-0.007) and the change in frequency (i.e. 10=20-10) indicates the proportionate change in demand after that change. So for example, moving from a 10 to a 20 minute frequency would lead to around a 7% reduction in bus demand.
11.19 A similar exponential model is reported for the impact of parking. Again a reduced impact can be seen from that reported in Table A4.1. A 10% increase in the chance of not being able to park would see demand reduced by 8% as compared to 19% with the model reported in Table A4.1.