Estimating the value of risk reductions for car drivers when pedestrians are involved: a case study in Spain

Abstract

We estimated the benefits associated with reducing fatal and severe injuries from traffic accidents using a stated choice experiment where choice situations were generated through a statistically efficient design. Specifically, the risk variables were defined as the expected annual number of vehicle car-users that suffered their death or were severely injured in a traffic accident. In addition, and differing from previous research, the number of pedestrians that died or were severely injured in traffic accidents per year was also included as a risk attribute in the choice experiment, to attempt at measuring drivers’ willingness to pay to reduce the risk of hitting pedestrians in a crash. The empirical setting was a choice of route for a particular trip that a sample of car drivers periodically undertakes in Tenerife, Spain. Models were estimated accounting for random taste heterogeneity and pseudo-panel data correlation. The median of the distribution of simulated parameters was used to obtain a representative measure for the monetary valuation of risk reductions. We found that the ratio between the values of reducing the risk of suffering a serious injury and that of reducing a fatality was approximately 18 %. Further, and quite novel, we also found that the value of reducing a pedestrian fatality was 39 % of the value of reducing a car occupant fatality.

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Fig. 1

Notes

  1. 1.

    We are explicit in mentioning the level of safety of pedestrians as the cause of altruism instead of the level of welfare. In the former case—paternalistic altruism—, respondents will derive personal utility from knowing that pedestrians walk in a safer road environment; in the latter case—pure or non-paternalistic altruism—, respondents will derive personal utility from any measure aimed at improving the welfare of pedestrian whether this is a road safety improvement or an income transfer. Only if altruism if paternalistic, it will add to the value of safety reduction (Jones-Lee 1992).

  2. 2.

    To encourage participation, two laptops computer were raffled among participants; response rate was nearly 60 %.

  3. 3.

    As Yang et al. (2010) indicate survey data on personal and household income is usually associated with a large amount of item nonresponse.

  4. 4.

    These values were obtained from the following trip operating cost (in euros) expression:\(C = (Consumption\,(S_{1} ) \cdot D_{1} + Consumption\,(S_{2} ) \cdot D_{2} ) \cdot P \cdot h\; + \;0.49\), where consumption is given in litres/km and speed (S) in km/hour. P is the price of fuel, h is a conversion factor that refers to vehicle type and 0.49 represents the estimated fixed cost (insurance, maintenance and taxes) for the reference trip.

  5. 5.

    In the case of fatalities, these averages were based on data about casualties within 24 h after the accident, since disaggregate data on fatalities within 30 days were not available at the time of the survey.

  6. 6.

    If the travel time under congested conditions was zero in choice situation 4, the current route dominated the alternative. The presence of this scenario enabled us to assess whether respondents travelling outside the severe congestion period answered consistently. The analysis of responses showed that almost all individuals responded consistently in this scenario, with only two drivers choosing the dominated alternative. We decided to remove these two inconsistent responses reducing the total number of observations to 4291 for the model estimation stage.

  7. 7.

    The valuation of a fatality reduction involves a risk judgment by drivers. We did not provide respondents with flow estimates allowing them to assess objective risks of being fatally or severely injured. We assumed that people processed risk in a subjective fashion following mechanisms as those suggested by Anscombe and Aumann (1963). For more details about this issue, see Rizzi and Ortúzar (2006a).

  8. 8.

    We are grateful to an anonymous referee for having pointed this out to us.

  9. 9.

    The null hypothesis of equality of the travel time coefficients under severe congestion versus low/moderate congestion produced a t-test value of 0.472 (for a model estimated with the full sample), 0.51 (for the model for frequent drivers) and 1.69 (for the model for occasional drivers), allowing accepting H0 at the 95 % confidence level.

  10. 10.

    The true distribution of each random parameters is obviously unknown; so, in principle, any distribution could be applied (Carlsson et al. 2003; Hensher and Greene 2003). We chose the Normal because it is the most easily applied distribution (Train and Sonnier 2005).

  11. 11.

    The mean of the simulated distribution was computed over values of the WTP less than 10 euros.

  12. 12.

    In Spain, the Manual de Evaluación Económica de Proyectos de Transporte (2010), established a unit value of travel time between 8.30 and 9.90 €/h for non-commuters and commuters travelling by car in short distances in Spain. However, lower values for travel time in Tenerife could be expected as its per capita income level is one of the lowest in Spain.

  13. 13.

    Combining this information with the average annual number of fatalities for car users (drivers and passengers) from Table 2, we can estimate the risk of being fatally wounded in a road accident in the TF5 highway as one fatality per 42.3 million vehicle-km; or equivalently as 2.36 fatalities per 100 million vehicle-km. Thus, if one fatality is reduced, risk is reduced by 4.7 × 10-9.

  14. 14.

    The values reported by De Blaeij et al. (2003) are in 1997 US$. They were updated to 2010 US$ values (36 % increase in CPI, according to http://www.minneapolisfed.org/) and converted to € using an exchange rate of €1 = US$ 1.3138 (http://www.federalreserve.gov/releases/h10/Hist/dat00_eu.htm).

  15. 15.

    The Lindhjem et al. (2011) values were reported in US$ from 2005. We updated them to 2010 and converted that value to 2010 € using the figures in footnote 14.

  16. 16.

    Although there is additional evidence for the value of a statistical life in Spain, it refers to studies carried out in sectors other than transport; for example, estimates were obtained on the basis of correlating the risk of a fatal working accident and the observed workers’ salary. In these studies, the value of a statistical life varied between 2.6 and 3.9 million € for the year 2010 (Albert and Malo 1995).

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Acknowledgments

The authors acknowledge the financial support provided by the Project PT-2007-027-01CAPM from the public call: Convocatoria de Proyectos I+D+i - 2007 del Centro de Estudios y Experimentación de Obras Públicas (CEDEX), Ministerio de Fomento de España. We are also grateful for the support of the Institute in Complex Engineering Systems (ICM-FIC: P-05-004-F; CONICYT: FBO816), the Centre for Sustainable Urban Development, CEDEUS (Conicyt/Fondap/15110020) and the Alexander von Humboldt Foundation. The authors would like to thank Prof. Kip Viscusi and two anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

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Correspondence to Rosa Marina González.

Appendices

Appendix 1: Proposed choice situations for the SC experiment

Attributes Choices
1 2 3 4 5 6 7 8 9
Current route
 Travel cost C C C C C C C C C
 Travel time under severe congestion T1 T1 T1 T1 T1 T1 T1 T1 T1
 Travel time for low/moderate congestion T2 T2 T2 T2 T2 T2 T2 T2 T2
 Car-users deaths/year in route TF-5 5 5 5 5 5 5 5 5 5
 Severe car-users injuries/year in route TF-5 32 32 32 32 32 32 32 32 32
 Pedestrian victims/year in route TF-5 3 3 3 3 3 3 3 3 3
Alternate route
 Travel cost C-50 % C C + 50 % C + 50 % C C-50 % C-50 % C C + 50 %
 Travel time under severe congestion T1-25 % T1-25 % T1 + 50 % T1-25 % T1 T1 + 50 % T1 + 50 % T1 T1
 Travel time for low/moderate congestion T2-25 % T2 + 25 % T2 T2 + 25 % T2 T2-25 % T2 + 25 % T2 T2-25 %
 Car-users deaths/year in route TF-5 7 5 5 5 3 3 7 3 7
 Severe car-users injuries/year in route TF-5 32 22 22 42 42 42 32 22 32
 Pedestrian victims/year in route TF-5 F-5 3 2 2 4 2 4 3 4 3

Appendix 2: Calculation of kilometres driven

Vehicle counts
Number of vehicles Km travelled
Km Going up Going down Total Going up Going down Total
0 27,290 830 28,120 39,297.6 1195.2 40,492.8
1.44 52,867 49,584 102,451 37,536 35,205 72,740
2.15 63,766 56,004 119,770 303,526 266,579 570,105
6.91 63,302 52,245 115,547 141,163 116,506 257,670
9.14 51,826 63,574 115,400 171,026 209,794 380,820
12.44 43,089 42,478 85,567 389,955 384,426 774,381
21.49 34,330 33,315 67,645 386,556 375,127 761,683
32.75 31,722 33,843 65,565 205,559 219,303 424,861
39.23 13,428 13,769 27,197 2686 2754 5439
39.43 14,030 14,224 28,254 100,595 101,986 202,581
46.6 24,488 1076 25,564 66,852 2937 69,790
49.33 12,721 12,293 25,014 42,107 40,690 82,796
52.64 7357 13,416 20,773 2281 4159 6440
52.95 6693 7028 13,721 18,406 19,327 37,733
  1. In each row, a marker along the TF-5 indicates where the vehicle estimated entry or exit station is located
  2. Source Cabildo Insular de Tenerife

The above table displays information about registered vehicles expressed as a daily annual average traffic. Under the assumption that the entries and exits of vehicles on the TF5 coincide with sites with vehicle estimates, the calculation of vehicle-km would be exact and equal to 3,687,532. Considering an average distance of 17.8 km per trip and assuming that traffic is 30 % of a regular day during weekends, we obtain that the total annual traffic would be 11,894,887 trips, under the assumption that the number of vehicles that complete the trip until the next station is inversely proportional to the distance between both stations.

These figures could seem contradictory since the total trips are less than those reported at some stations. However, these stations are located in urban areas where many vehicles use the TF5 for very short routes. If these drivers follow a path that does not belong to the TF5, adding their WTP would imply unrealistic increases in the calculation of the value of statistical life.

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González, R.M., Román, C., Amador, F.J. et al. Estimating the value of risk reductions for car drivers when pedestrians are involved: a case study in Spain. Transportation 45, 499–521 (2018). https://doi.org/10.1007/s11116-016-9736-0

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Keywords

  • Value of risk reduction
  • Stated choice experiment
  • Efficient design
  • Willingness to pay
  • Road accidents
  • Pedestrian victims