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Policy relevant heterogeneity in the value of statistical life: New evidence from panel data quantile regressions

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Abstract

We examine differences in the value of statistical life (VSL) across potential wage levels in panel data using quantile regressions with intercept heterogeneity. Latent heterogeneity is econometrically important and affects the estimated VSL. Our findings indicate that a reasonable average cost per expected life saved cut-off for health and safety regulations is $7 million to $8 million per life saved, but the VSL varies considerably across the labor force. Our results reconcile the previous discrepancies between hedonic VSL estimates and the values implied by theories linked to the coefficient of relative risk aversion. Because the VSL varies elastically with income, regulatory agencies should regularly update the VSL used in benefit assessments, increasing the VSL proportionally with changes in income over time.

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Notes

  1. The benefit assessment procedure is consistent with that summarized by the U.S. Office of Management and Budget (2003), OMB Circular A-4, Regulatory Analysis. Although altruistic concerns may be relevant, typically the focus is on the willingness to pay by those whose risk level has been reduced by the policy.

  2. There may also be differences in the kinds of deaths involved and the associated morbidity effects, which may affect valuations as well (Viscusi 2009).

  3. The distinction arises in Section 4A of the bill S. 3564 introduced by Senator Barbara Boxer in 2008, 110th Congress, 2d Session, the “Restoring the Value of Every American in Environmental Decisions Act.”

  4. Such asymmetries in valuation are similar to a wide variety of behavioral anomalies, such as loss aversion in prospect theory and a variety of models of reference dependence.

  5. U.S. Department of Transportation, Office of the Assistant Secretary for Transportation Policy, Revised Departmental Guidance: Treatment of the Value of Preventing Fatalities and Injuries in Preparing Economic Analyses, August 2, 2005.

  6. Graham (2008) suggests that when policies have clearly different target groups, such as air travel versus bus travel, then income elasticities might be taken into account. Similarly, the Federal Aviation Administration sought to use a higher value of life than for other transportation policies because of the higher income of air travelers. See Viscusi (1993), which is based on his report to the FAA. Based on this report, the agency sought to justifying using a higher VSL in its policy analyses.

  7. More specifically, VSL must be increased at least once a year to reflect “the average annual total compensation of individuals, including income and benefits.”

  8. Should there be any downward dip in the market offer curve, no worker would ever choose such a job that is dominated by available jobs offering higher wage for lower risk.

  9. The studies, which are reviewed in Viscusi and Aldy (2003), are Viscusi (1981), Olson (1981), Dorsey and Walzer (1983), and Leigh and Folsom (1984).

  10. Ziliak and Kniesner (1998) showed that when there is non-random attrition fixed effects models should remove it along with the other time-invariant factors.

  11. Restricted access to CFOI fatality data was obtained via an agreement with the U.S. Bureau of Labor Statistics. Our variable construction procedure follows that in Viscusi (2004), which describes the properties of the 720 industry-occupation breakdown in greater detail.

  12. We used the bi-annual employment averages from the U.S. Bureau of Labor Statistics (2009), Current Population Survey, unpublished table, Table 6, Employed Persons by Detailed Industry and Occupation for 1993–2001.

  13. For policies financed by taxes, there is also an adjustment term involving the covariance of individual i’s tax rate and the inverse of VSLi. If that covariance is zero, then the appropriate unit benefit value is simply the harmonic mean VSL. When policies are funded by a lump sum tax the benefits measure equals the harmonic mean VSL. More generally, the harmonic mean will be a lower bound on the benefits measure. See Baker (2008).

  14. Let q indicate the quantile percentile VSL, then VSL = 5.578 (1.215) – 15.453 (7.373) q + 38.454 (8.181) q 2, R 2 = 0.97, where the numbers in parentheses are robust standard errors. For the semi-log version of the model, ln (VSL) = 1.142 (0.063) + 1.525 (0.374) q + 0.737 (0.383) q 2, R 2 = 0.99. Based on the linear model, the arithmetic mean VSL is $10.7 million, and the harmonic mean VSL is $7.2 million, and with the semi-log model the arithmetic mean is $10.7 million, and the harmonic mean is $7.0 million. The fitted predicted values for the semi-log specification have more attractive properties in that the VSL is always increasing as the quantile percentage rises so those estimates will be the focus of the discussion.

  15. Note that our estimates do in fact construct an income elasticity based on real family income levels, whereas what the previous literature refers to as an income elasticity is actually an elasticity with respect to worker wage levels.

  16. The linear equation used to estimate income elasticity is VSL = −5499606 (773449) + 259.3 (9.6), R 2 = 0.998.

  17. The quantile ranges are based on the quantile values at points estimated in the regressions. One would, for example, expect the elasticity value to be even greater at the 0.01 quantile.

  18. Other studies of this relationship along similar lines include Eeckhoudt and Hammitt (2001) and Evans and Smith (2010). The latter paper shows that with more complex and more realistic models the relationship between the income elasticity of VSL and the coefficient of relative risk aversion becomes less clear cut.

References

  • Aldy, J. E. & Viscusi, W. K. (2008). Adjusting the value of a statistical life for age and cohort effects. Review of Economics and Statistics, 90(3), 573–581.

    Article  Google Scholar 

  • Baker, R., Chilton, S., Jones-Lee, M., & Metcalf, H. (2008). Valuing lives equally: Defensible premise or unwarranted compromise? Journal of Risk and Uncertainty, 36(2), 125–138.

    Article  Google Scholar 

  • Black, D. A. & Kniesner, T. J. (2003). On the measurement of job risk in hedonic wage models. Journal of Risk and Uncertainty, 27(3), 205–220.

    Article  Google Scholar 

  • Chetty, R. (2006). A new method of estimating risk aversion. The American Economic Review, 96(5), 1821–1834.

    Article  Google Scholar 

  • Chetty, R. (2009). The simple economics of salience and taxation. National Bureau of Economic Research Working Paper Series, No. 15246.

    Google Scholar 

  • Dorsey, S. & Walzer, N. (1983). Workers’ compensation, job hazards, and wages. Industrial and Labor Relations Review, 36(4), 642–654.

    Article  Google Scholar 

  • Eeckhoudt, L. R. & Hammitt, J. K. (2001). Background risks and the value of a statistical life. Journal of Risk and Uncertainty, 23(3), 261–279.

    Article  Google Scholar 

  • Evans, M. F., & Smith, V. K. (2010). Measuring how risk tradeoffs adjust with income. Journal of Risk and Uncertainty, 40(1).

  • Graham, J. D. (2008). Saving lives through administrative law and economics. University of Pennsylvania Law Review, 157(2), 395–540.

    Google Scholar 

  • Harris, J. E. (1979). Pricing rules for hospitals. The Bell Journal of Economics, 10(1), 224–243.

    Article  Google Scholar 

  • Kaplow, L. (2005). The value of a statistical life and the coefficient of relative risk aversion. Journal of Risk and Uncertainty, 31(1), 23–34.

    Article  Google Scholar 

  • Kniesner, T. J. & Ziliak, J. P. (2002). Tax reform and automatic stabilization. The American Economic Review, 92(3), 590–612.

    Google Scholar 

  • Kniesner, T. J., Viscusi, W. K., Woock, C., & Ziliak, J. P. (2008). The value of a statistical life: Evidence from panel data. Syracuse, NY, Syracuse University. http://gatton.uky.edu/Faculty/ziliak/KVWZ_VSL.pdf

  • Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74–89.

    Article  Google Scholar 

  • Lamarche, C. (2006). Robust penalized quantile regression estimation for panel data. Norman, Oklahoma, University of Oklahoma. Department of Economics. http://faculty-staff.ou.edu/L/Carlos.E.Lamarche-1/rpan.html

  • Leigh, J. P. & Folsom, R. N. (1984). Estimates of the value of accident avoidance at the job depend on the concavity of the equalizing differences curve. Quarterly Review of Economics and Business, 24(1), 55–66.

    Google Scholar 

  • Manski, C. F. (2009). When consensus choice dominates individualism: Jensen’s inequality and collective decisions under uncertainty. National Bureau of Economic Research Working Paper Series, No. 15172.

    Google Scholar 

  • Mellow, W. & Sider, H. (1983). Accuracy of response in labor market surveys: evidence and implications. Journal of Labor Economics, 1(4), 331–344.

    Article  Google Scholar 

  • Olson, C. A. (1981). An analysis of wage differentials received by workers on dangerous jobs. The Journal of Human Resources, 16(2), 167–185.

    Article  Google Scholar 

  • U.S. Bureau of Labor Statistics. (2009). Employed persons by detailed industry and occupation for 1993-2001, Current Population Survey.

  • U.S. Department of Transportation, Office of the Assistant Secretary for Transportation Policy. (2005). Revised departmental guidance: Treatment of the value of preventing fatalities and injuries in preparing economic analyses. Washington, DC.

    Google Scholar 

  • U.S. Office of Management and Budget. (2003). OMB CIRCULAR A-4, Regulatory Analysis (Rep. No. A-4). Washington, DC.

  • Viscusi, W. K. (1981). Occupational safety and health regulation: Its impact and policy alternatives. In J. P. Crecine (Ed.), Research in Public Policy Analysis and Management (Vol. 2, pp. 281–299). Greenwich, CT: JAI Press.

    Google Scholar 

  • Viscusi, W. K. & Evans, W. N. (1990). Utility functions that depend on health status: estimates and economic implications. The American Economic Review, 80(3), 353–374.

    Google Scholar 

  • Viscusi, W. K. (1993). The value of risks to life and health. Journal of Economic Literature, 31, 1912–1946.

    Google Scholar 

  • Viscusi, W. K. & Aldy, J. E. (2003). The value of a statistical life: A critical review of market estimates throughout the world. Journal of Risk and Uncertainty, 27(1), 5–76.

    Article  Google Scholar 

  • Viscusi, W. K. (2004). The value of life: Estimates with risks by occupation and industry. Economic Inquiry, 42(1), 29–48.

    Article  Google Scholar 

  • Viscusi, W. K. (2009). Valuing risks of death from terrorism and natural disasters. Journal of Risk and Uncertainty, 38(3), 191–213.

    Article  Google Scholar 

  • Ziliak, J. P., & Kniesner, T. J. (1998). The importance of sample attrition in life-cycle labor supply estimation. Journal of Human Resources, 33(2), 507–530.

    Article  Google Scholar 

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Authors and Affiliations

  1. Senior Research Associate, Center for Policy Research, Syracuse University, Syracuse, NY, USA

    Thomas J. Kniesner

  2. IZA, Bonn, Germany

    Thomas J. Kniesner

  3. University Distinguished Professor of Law, Economics, and Management, Vanderbilt University, Nashville, TN, USA

    W. Kip Viscusi

  4. Carol Martin Gatton Chair in Microeconomics, Center for Poverty Research, University of Kentucky, Lexington, KY, USA

    James P. Ziliak

Authors
  1. Thomas J. Kniesner
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  2. W. Kip Viscusi
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  3. James P. Ziliak
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Correspondence to Thomas J. Kniesner.

Additional information

We wish to thank Badi Baltagi for helpful comments, Carlos Lamarche for generously sharing his programs on panel quantiles, and the U.S. Bureau of Labor Statistics for the proprietary CFOI data on workplace fatalities. The findings herein do not reflect the opinion of the BLS or any other federal agency.

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Kniesner, T.J., Viscusi, W.K. & Ziliak, J.P. Policy relevant heterogeneity in the value of statistical life: New evidence from panel data quantile regressions. J Risk Uncertain 40, 15–31 (2010). https://doi.org/10.1007/s11166-009-9084-y

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