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Age, autos, and the value of a statistical life

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Abstract

The value of a statistical life (VSL) is used to assign a dollar value to the benefits of health and safety regulations. Many of those regulations disproportionately benefit older people, but most estimates of the VSL come from hedonic wage regressions with few older workers and no retirees. Using automobile purchase decisions, I estimate a VSL for individuals from the age of 18 up to the age of 85. Combining information on vehicle holdings and use, household attributes, used vehicle prices, crash test results, and yearly fatal accidents for each make, model, and vintage automobile, I calculate a separate willingness to pay for reduced mortality for different age groups. I find a significant inverted-U shape to the age-VSL function that ranges from $1.5 to $19.2 million (in 2009 dollars). The shape and magnitude of the vehicle-based age-VSL relationship corroborate labor market estimates and extend the age range of revealed preference evidence on the relationship between age and the VSL.

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Notes

  1. For example, the EPA uses a VSL estimate derived from a meta-analysis of 26 studies, including 21 hedonic wage studies (US Environmental Protection Agency 2010).

  2. See, for example, Viscusi (2009, 2011). See also Evans and Smith (2006) and Scotton and Taylor (2011) for a discussion of several House and Senate bills limiting adjustments to the VSL.

  3. The EPA currently recommends a constant VSL of $9.7 million in 2013 dollars (US Environmental Protection Agency 2016). The Department of Transportation advises a VSL of $9.6 million in 2015 dollars (US Department of Transportation 2016).

  4. See Viscusi and Aldy (2003), Aldy and Viscusi (2007), Evans and Smith (2006), and Krupnick (2007) for additional review of the literature surrounding age and VSL.

  5. A handful of non-labor market studies have also obtained mixed results, such as in Portney (1981) (housing prices and local air pollution), who finds a substantially negative age-VSL relationship; Andersson (2008) (hedonic vehicle prices), who finds no age effect; Mount et al. (2004) (hedonic vehicle prices), who find different VSLs for families with seniors, adults, and children; and Rohlfs et al. (2015) (hedonic vehicle prices and air bags) who find no effect.

  6. Other studies have focused on revealed preferences without relying on labor market data, but do not address the age-VSL relationship. Examples include Ashenfelter and Greenstone (2004) (mandated speed limits); Atkinson and Halvorsen (1990) and Dreyfus and Viscusi (1995) (hedonic vehicle prices); Blomquist et al. (1996) (seatbelt, helmet, and child seat use); Schnier et al. (2009) (commercial fishing decisions), and León and Miguel (2013) (estuary crossings in Sierra Leone). Winston and Mannering (1984) do not measure a VSL explicitly, but employ a vehicle choice model to examine the costs and benefits of various automobile safety regulations.

  7. See for example Arrow et al. (1993), Portney (1994), Diamond and Hausman (1994), and Hausman (2012) for a discussion of the advantages and disadvantages of contingent valuation.

  8. This study also provides VSL estimates that are directly relevant to transportation risk. Even though many workplace fatalities are vehicle-related, there may be differences between wage-risk tradeoffs made by workers and price-risk tradeoffs made by automobile purchasers. Focusing on occupational risk, Viscusi and Gentry (2015) estimate hedonic wage regressions that include transport-specific and non-transport-specific risks and find a transport VSL similar to the non-transport VSL.

  9. The range of VSL estimates is based on a summary of recent age-VSL studies shown in Table 1. Separate from age-VSL studies, Viscusi and Aldy (2003) conduct a meta-analysis of VSL estimates and find labor market values ranging from $0.6 to $25.9 million with a median VSL of $8.3 million; Kniesner et al. (2010) use quantile regressions and panel data on workers’ wages and find VSL estimates ranging from $4.2 to $26.7 million; and Viscusi and Masterman (2017) conduct a meta-analysis of 68 VSL studies and find a base value of $8.7 million based on papers that use the US Census of Fatal Occupational Injuries. All figures have been adjusted to 2009 dollars.

  10. A linear utility function implies that consumers are risk-neutral over all vehicle attributes, including safety. In this context, I assume that consumers face a constant marginal disutility from fatality risk.

  11. See, for example, Train (2009) for further discussion.

  12. In their multinomial choice model, Winston and Mannering (1984) also express cost as a share of income. Hedonic vehicle price models such as Atkinson and Halvorsen (1990) and Dreyfus and Viscusi (1995) instead regress vehicle price directly on fatality risk and do not include household income. See also Viscusi and Aldy (2003) for a discussion of hedonic wage estimates of the VSL.

  13. A similar assumption is made in other automobile-based valuations. For example, Dreyfus and Viscusi (1995) assume that “each vehicle’s market price reflects the opportunity cost of owning that specific vehicle.” Mannering and Winston (1985) assume that “households evaluate their vehicle holding and determine vehicle utilization every 6 months. In reality, this evaluation is undertaken in a continuous manner.”

  14. If transaction costs are not trivial, consumers may anticipate their future preferences when making automobile purchase decisions. In this case, the VSL I measure for each age group would under-emphasize differences across age groups.

  15. The majority of VSL studies rely on statistical risk to proxy for risk perceptions (Viscusi and Aldy 2003). In the road safety context, statistical deaths is also commonly used to proxy for vehicle fatality risk, as in Atkinson and Halvorsen (1990) (fatal accidents per vehicles sold) and Dreyfus and Viscusi (1995) (fatalities per vehicle on the road). In this paper I use information on mileage to convert fatalities per vehicle to fatalities per year.

  16. Figure A.1 in the appendix shows the number of deaths per mile for the 10 safest and riskiest automobiles in my estimation sample.

  17. I could add additional variables such as gender and education to reduce unobserved heterogeneity when calculating fatalities per mile. This would yield a separate VSL estimate for each of those groups. The underlying assumption would be that individuals perceive the number of deaths per mile in each make, model, and vintage automobile that are suffered exclusively by people of their same age-gender-education cohort. The number of fatal accidents per group decreases substantially with additional covariates, making it impractical to group individuals into narrowly defined cohorts.

  18. Separately identifying perceptions of riskiness from valuations of risk is a common challenge for revealed preference VSL studies and is not limited to age-based studies or to the road-safety context. Across myriad settings, even when individuals are aware of aggregate risk levels there is evidence of “optimism bias,” wherein individuals acknowledge risk to others but don’t believe they will be affected themselves (Viscusi 2002).

  19. See Train (1993, 2009) for a discussion of alternative-specific constants and IIA.

  20. Depending on the specific variables included in the regression, the choice sets for each individual range in size from 670 to 1061 alternatives. For 2009 (January through April) the choice sets range from 120 to 200 alternatives.

  21. See Train (2009) for a detailed discussion of various multinomial choice estimation techniques. Train and Winston (2007) don’t examine safety, but implement a vehicle choice model using a mixed logit that is not subject to IIA. They focus on a custom sample of new vehicle purchases in 2000, acknowledging that widening the scope would “result in an enormous choice set that could not be reduced because our model does not invoke the IIA assumption.”

  22. The results of this analysis are robust to using five or 15 alternatives.

  23. As an aside, it is possible that IIA may not introduce a significant bias when the focus is on estimating parameters of the underling utility model rather than generating substitution patterns, as is the case here. There is some evidence that the multinomial logit (subject to IIA) performs as well or better than a multinomial probit or mixed logit (not subject to IIA) in terms of parameter estimation (Kropko 2010; Dahlberg and Eklöf 2003).

  24. The NHTS is conducted by the US Department of Transportation. Along with its predecessor survey, the NHTS has been conducted roughly every five to 8 years since 1969. Previous studies have utilized the Residential Transportation Energy Consumption Survey (e.g. Dreyfus and Viscusi 1995), a household survey conducted by the Department of Energy between 1985 and 1994, the National Household Transportation Panel, a 2-year follow-up to the National Interim Energy Consumption Survey conducted by the Energy Information Administration in 1978 (e.g. Winston and Mannering 1984; Mannering and Winston 1985), or aggregate non-household data (e.g. Atkinson and Halvorsen 1990).

  25. Because I don’t have information on specifically who purchased the vehicle, I assume that the primary driver purchased the vehicle. This is similar to Dreyfus and Viscusi (1995), who assume that cars are purchased by the household head.

  26. I exclude 330 vehicles with mileage greater than 60,349 miles per year and 205 vehicles that had used values greater than $43,107.

  27. I focus on recent purchases, limiting the sample to vehicles acquired between 2007 and 2009. Results are not significantly different if instead I adjust each household’s income based on the average growth of real income from the US Census.

  28. The FARS was formerly referred to as the Fatal Accident Reporting System and is the standard source for information on automobile fatalities (Atkinson and Halvorsen 1990; Dreyfus and Viscusi 1995). Other sources of automobile safety information, such as the Highway Loss Data Institute, rely on FARS for fatality data (Insurance Institute for Highway Safety 2017).

  29. The vehicle identification number (VIN) is standardized by the National Highway Traffic Safety Administration. The first 10 digits contain make, model, characteristics, and model year information. Other sources of vehicle price information include the Automobile Red Book used car valuations (Winston and Mannering 1984; Dreyfus and Viscusi 1995), the average sticker price and dealer cost (Atkinson and Halvorsen 1990), or the manufacturer’s suggested retail price (Train and Winston 2007).

  30. See http://www.nada.com/b2b/Support/Glossary.aspx.

  31. The various discount rates lead to slight and insignificant shifts in scale for the age-VSL function.

  32. I calculate a per-mile fuel cost based on direct estimates of annual fuel expenditure in the NHTS divided by total VMT, averaged across vehicles of the same make, model, and model year. Other vehicle safety papers have estimated fuel cost as average annual VMT, divided by the vehicle’s mpg rating, multiplied by the average price per gallon of gasoline (Atkinson and Halvorsen 1990; Dreyfus and Viscusi 1995).

  33. Fatality risk is not included as a vehicle characteristic in these studies.

  34. This approach is an adaptation of Dubin and McFadden (1984), who estimate the joint decision of home appliances and electricity consumption.

  35. Listed coefficients are significant at the 1% level, except passenger volume, which is significant at the 5% level. Standard errors are calculated based on 1000 bootstrap repetitions. Because of the non-linear nature of the VSL (a ratio), outliers are trimmed from the bootstrap calculation.

  36. The following brands are considered luxury: Acura, Audi, BMW, Cadillac, Infiniti, Jaguar, Land Rover, Lexus, Mercedes-Benz, and Porsche.

  37. The risk coefficient for the 18–24 age group (−5.42) is significant at the 5% level; the cost coefficients for the 45–54 and 55–64 age groups (−2.34 and − 1.45, respectively) are not statistically significant. The remaining risk and cost coefficients are significant at the 1% level.

  38. I estimate a negative coefficient on engine displacement in column 2, but the coefficient itself is not statistically significant, nor is the change from column 1. Vehicle width (0.33) and weight (−0.23) are significant in column 2, but not in column 1, whereas passenger volume is no longer significant in column 2. I also add an interaction term between pickup trucks and the number of cylinders and find a significantly positive effect (0.11).

  39. Table A.1 in the appendix shows pairwise differences in the VSL estimates across groups (based on column 2 of Table 4) and supports a statistically significant inverted-U.

  40. NHTSA conducts regular vehicle crash tests and publishes the results. In the 2011 model year roughly 60% of the light vehicle fleet was tested (National Highway Traffic Safety Administration 2012). Vehicles are retested after changes to an existing model’s structure or safety features, and safety ratings for model years without substantive changes generally carry over (Hershman 2001).

  41. Other studies often focus on the effects of relative vehicle weight on safety, controlling for unobserved differences using various techniques; see for example Anderson and Auffhammer (2013), Gayer (2004), and Sheehan-Connor (2012).

  42. I assume that once a vehicle is tested, all subsequent model years carry the same ratings until the model is tested again.

  43. Using a negative binomial distribution rather than a Poisson distribution yields similar results.

  44. Regressions in Table 3 assume constant marginal utility for non-risk, non-cost covariates across age groups (these variables are not interacted with age-group indicators). For robustness, I repeat the regression in column 3 of Table 3 separately for each age group, allowing all coefficients to vary by age. The VSL results are not statistically distinguishable from column 3 of Table 4, although the peak occurs slightly earlier at $21.3 million for the 45–54 age group. The VSL estimates based on separate regressions for each age group are shown in Figure A.2 in the appendix.

  45. See footnote 3. The VSL of $9.7 million (in 2013 dollars) from the EPA and $9.6 million (in 2015 dollars) from the DOT are adjusted to 2009 dollars using the Consumer Price Index for All Urban Consumers (CPI-U). These results are also similar to hedonic vehicle price studies such as Atkinson and Halvorsen (1990), who estimate a VSL of $6.6 million, and Dreyfus and Viscusi (1995), who estimate a VSL of $5.6 million, adjusted to 2009 dollars using the CPI-U.

  46. Dreyfus and Viscusi (1995) do not focus on age, but they do include non-fatal injury rates in addition to fatal accident risk in their hedonic vehicle price regressions.

  47. See Viscusi and Aldy (2003) for a survey of the labor market VSL literature, a discussion of omitting non-pecuniary job characteristics, and attempts to solve the associated bias. Kniesner et al. (2012) address the endogeneity of on-the-job fatality risk using panel data and find a VSL ranging from $7 million to $12 million.

  48. In addition to Viscusi and Aldy (2003), see also Chay and Greenstone (2005) for a discussion of hedonic methods and a thorough implementation in the context of air quality.

  49. For example, Atkinson and Halvorsen (1990) and Dreyfus and Viscusi (1995) conduct hedonic regressions of vehicle prices on fatality risk and do not control for omitted factors related to riskiness and price. Winston and Mannering (1984) examine safety using a multinomial choice model similar to this paper and likewise are unable to control for unobserved factors related to vehicle prices. Outside the VSL context, the vehicle choice literature has made further strides towards controlling for endogenous prices. For example, Train and Winston (2007) examine the market share of US auto manufacturers using a mixed logit estimator and instrument for vehicle prices using non-price attributes of other vehicles.

  50. The Survey of Consumer Finances is a cross-sectional survey of US families’ balance sheets, pensions, incomes, and demographics. The survey is conducted by the Federal Reserve Board and data are available at: http://www.federalreserve.gov/econresdata/scf/scfindex.htm.

  51. The NHTS extended questionnaire indicates “we want to include income from sources such as wages and salaries, income from a business or a farm, Social Security, pensions, dividends, interest, rent, and any other income received” (US Department of Transportation 2009).

  52. Nursing homes appear to be the main source of increased expenditure between ages 70 and 90 (Nardi et al. 2016). Individuals in nursing homes are not included in the NHTS and are not part of this study.

  53. Results based on the sample excluding seniors are shown in Appendix Table A.2. VSL estimates range from $2.5 million and $1.58 million for the youngest two cohorts to $20.97 million for the 45–54 age cohort. These estimates are not statistically different from the corresponding estimates based on the full sample found in column 3 of Table 4.

  54. The resulting VSL estimates are shown on the solid line of Figure A.3 in the appendix, overlaid against the estimates from column 3 of Table 4 (dotted line). The number of observations used in this regression is 12,257.

  55. The VSL estimates are shown on the solid line of Figure A.4 in the appendix, overlaid against the estimates from column 3 of Table 4 (dotted line). Having children could also increase parents’ valuation of their own safety, which should be included in VSL estimates. Aldy and Viscusi (2003) check for robustness in their labor market study by controlling for children via interaction terms and find no difference in the VSL of workers with or without children.

  56. Even without differences across age groups, credit constraints can contribute to age variation in the VSL. Shepard and Zeckhauser (1984) explore a life-cycle consumption-allocation model and find that a no-borrowing restriction leads to a much more pronounced inverted-U shaped WTP relative to perfect markets (though both scenarios still produce an inverted-U shape).

  57. See Table 6.

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Acknowledgements

The author would like to thank Arik Levinson, Matt Harding, Garance Genicot, Rick Lotspeich, Billy Jack, Mary Evans, Kip Viscusi, participants of Camp Resources and SITE Segment 6 workshops, and participants of the Georgetown Economics Department Seminar for helpful suggestions; Angelica Marra for research assistance; and Steve Stafford at the National Automobile Dealers Association for providing batch data from the NADA Used Car Guide.

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  1. Department of Economics, Gettysburg College, 300 N. Washington St., Gettysburg, PA, 17325, USA

    James O’Brien

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Correspondence to James O’Brien.

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O’Brien, J. Age, autos, and the value of a statistical life. J Risk Uncertain 57, 51–79 (2018). https://doi.org/10.1007/s11166-018-9285-3

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