# The Heterogeneity of the Value of Statistical Life W. Kip Viscusi University Distinguished Professor Vanderbilt University American.

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The Heterogeneity of the Value of Statistical Life W. Kip Viscusi University Distinguished Professor Vanderbilt University kip.viscusi@vanderbilt.edu American Society of Health Economists June 20, 2010

Value of Statistical Life (VSL) Academic Literature Academic Literature  Definition  Labor market studies  Variation with risk levels  Segmented labor markets  Age  Income.

VSL Outline Cont’d Policy Arena Policy Arena  Adoption of the VSL methodology  Age controversy  Income controversies The Future of VSL. The Future of VSL.

Calculating the Value of Statistical Life Suppose 1/10,000 risk to 10,000 people so 1 expected death Assume each would pay \$800 to eliminate the risk VSL = 10,000 people × \$800/person = \$8,000,000.

Dominant Approach: Wage-Risk Tradeoffs Adam Smith’s theory of compensating wage differentials Adam Smith’s theory of compensating wage differentials Controlling for other aspects of the job, how much pay for extra risk? Controlling for other aspects of the job, how much pay for extra risk? Hedonic wage model as workers pick optimal (risk, wage) combination from market offer curve.. Hedonic wage model as workers pick optimal (risk, wage) combination from market offer curve..

The Average Value of Statistical Life Median U.S. value is \$7 million (\$2000) or \$8.7 million (\$2009) based on meta analysis in Viscusi and Aldy (2003) Median U.S. value is \$7 million (\$2000) or \$8.7 million (\$2009) based on meta analysis in Viscusi and Aldy (2003) Require \$870 to face risk of 1/10,000 Require \$870 to face risk of 1/10,000 Foreign countries have VSL estimates in expected range, e.g., India is lower. Foreign countries have VSL estimates in expected range, e.g., India is lower.

Heterogeneity Based on Risk Level Workers who choose higher risk levels are on flatter part of market offer curve. Workers who choose higher risk levels are on flatter part of market offer curve.

Heterogeneity Based on Risk Level, cont’d Early studies found workers with fatality risk of 1/10,000 (Viscusi 1978, 1979) had VSL 5 times greater than study of workers facing risk of 1/1,000 Early studies found workers with fatality risk of 1/10,000 (Viscusi 1978, 1979) had VSL 5 times greater than study of workers facing risk of 1/1,000 (Thaler and Rosen 1975). Differences arise from legitimate heterogeneity in VSL tradeoffs not failure of economists to find “the value of life number.”. Differences arise from legitimate heterogeneity in VSL tradeoffs not failure of economists to find “the value of life number.”.

Segmented Labor Markets Workers may face different labor market offer curves Workers may face different labor market offer curves Settle into separate labor market equilibria (Viscusi and Hersch 2001) Settle into separate labor market equilibria (Viscusi and Hersch 2001) Test: If workers face greater risk levels but receive less total wage compensation for risk, then cannot be on same market offer curve.. Test: If workers face greater risk levels but receive less total wage compensation for risk, then cannot be on same market offer curve..

Workers facing different offer curves settle into separate equilibria.

Examples of Separate Labor Market Offer Curves Smokers and Nonsmokers Smokers and Nonsmokers (Viscusi and Hersch 2001) Black-white VSL differences Black-white VSL differences (Viscusi 2003) Mexican immigrants versus other immigrants or native Americans Mexican immigrants versus other immigrants or native Americans (Hersch and Viscusi 2010).

VSL and Immigrant Status Fatality Risk*VSL Estimates Bases on the CPS Native U.S.4.357.95 Mexican immigrants5.97Not significant Estimates Based on the NIS All immigrants4.509.35 Mexican immigrants5.70Not significant Mexican immigrants who speak English 5.703.44 * Fatality rate by industry-immigrant status-age. Risk is annual fatality rate per 100,000 workers.

Heterogeneity Based on Age VSL will vary with age because length of remaining life varies VSL will vary with age because length of remaining life varies Imperfect capital markets Imperfect capital markets Life-cycle effects. Life-cycle effects.

Age and the Labor Market Series of studies over two decades Series of studies over two decades Most recent use age-specific risk data Most recent use age-specific risk data Result is inverted-U shape pattern Result is inverted-U shape pattern Flatter if control for consumption over the life cycle or cohort effects Flatter if control for consumption over the life cycle or cohort effects VSL tracks lifetime income and consumption VSL tracks lifetime income and consumption (Kniesner, Viscusi, and Ziliak 2006).

Cohort-Adjusted and Cross-Section Value of Statistical Life, 1993-2000

What Do We Know About Age-VSL? VSL does not peak at birth VSL does not peak at birth VSL does not plummet as we age VSL does not plummet as we age VSL for workers around age 60 is higher than for workers age 20. VSL for workers around age 60 is higher than for workers age 20.

Value per Year of Life (VSLY) Not a constant, as assumed and estimated in Moore and Viscusi (1988), which developed and estimated VSLY formula and rate of discount Not a constant, as assumed and estimated in Moore and Viscusi (1988), which developed and estimated VSLY formula and rate of discount Advent of better data makes possible more refined risk measures. Viscusi-Aldy (2007) and Aldy-Viscusi (2008) use industry by age fatality rate. Advent of better data makes possible more refined risk measures. Viscusi-Aldy (2007) and Aldy-Viscusi (2008) use industry by age fatality rate. VSLY not constant and not steadily declining with age even though health may decline VSLY not constant and not steadily declining with age even though health may decline VSLY rises fairly steadily. VSLY rises fairly steadily.

Value of a Statistical Life-Year Based on Cohort-Adjusted and Cross-Section Value of Statistical Life, 1993-2000

Applications of VSL and VSLY to Private Costs of Cigarettes Viscusi and Hersch (2008) estimate VSL and VSLY specific to smoking status Viscusi and Hersch (2008) estimate VSL and VSLY specific to smoking status Calculate the private mortality costs per pack of cigarettes Calculate the private mortality costs per pack of cigarettes At 3% interest rate, cost per pack is on order of \$200 for men and \$100 for women At 3% interest rate, cost per pack is on order of \$200 for men and \$100 for women At smokers’ estimated labor market discount for years of life of 14% (Scharff and Viscusi, 2010), cost per pack drops to \$24 for men and \$6 for women. At smokers’ estimated labor market discount for years of life of 14% (Scharff and Viscusi, 2010), cost per pack drops to \$24 for men and \$6 for women.

Income Effects Proportional for present value of lost earnings Proportional for present value of lost earnings Willingness to pay increases with income Willingness to pay increases with income Estimation strategies: meta analyses across studies and quantile regression estimates within sample. Estimation strategies: meta analyses across studies and quantile regression estimates within sample.

Income Elasticity Estimates Meta analysis by Viscusi and Aldy (2003) – elasticity in 0.51 to 0.61 range for Meta analysis by Viscusi and Aldy (2003) – elasticity in 0.51 to 0.61 range for 10 different specifications. Within sample quantile estimates by Kniesner, Viscusi, and Ziliak (2010) imply mean elasticity across quantiles of 1.44. Within sample quantile estimates by Kniesner, Viscusi, and Ziliak (2010) imply mean elasticity across quantiles of 1.44. Meta analyses may suppress some income elasticity, but clearly elasticity is positive.. Meta analyses may suppress some income elasticity, but clearly elasticity is positive..

VSL in the Policy Arena Adoption of the VSL approach Adoption of the VSL approach Age variations Age variations Income variations Income variations Other controversies. Other controversies.

Valuing Lives for Policy 1982 hazard communication debate 1982 hazard communication debate Life is too sacred to value so OSHA calculated “cost of death” as present value of lost earnings Life is too sacred to value so OSHA calculated “cost of death” as present value of lost earnings OMB: Benefits did not exceed costs so rejected regulatory proposal OMB: Benefits did not exceed costs so rejected regulatory proposal OSHA appealed to V-P Bush OSHA appealed to V-P Bush I analyzed merits of proposal using proper value of statistical life (VSL) estimates – 10 times the present value of lost earnings. I analyzed merits of proposal using proper value of statistical life (VSL) estimates – 10 times the present value of lost earnings.

Using VSL Saves Lives My 1982 estimates were just over My 1982 estimates were just over \$3 million Benefits now exceeded costs, and regulation was issued Benefits now exceeded costs, and regulation was issued Historical context is that VSL was more supportive of risk regulation than making lives “priceless” Historical context is that VSL was more supportive of risk regulation than making lives “priceless” VSL now under attack for pricing lives. VSL now under attack for pricing lives.

The “Senior Discount” Controversy EPA used a senior discount of 37% in analysis of Clear Skies initiative in 2002. EPA used a senior discount of 37% in analysis of Clear Skies initiative in 2002. Political firestorm Political firestorm Seniors on sale 37% off EPA backed off approach. Proposed Senate legislation banning all demographic adjustments.. EPA backed off approach. Proposed Senate legislation banning all demographic adjustments..

International “Senior Discounts” Canada used a VSL 25% lower for those over 65 compared to those under 65. Canada used a VSL 25% lower for those over 65 compared to those under 65. In 2001, European Commission recommended VSL that declines with age.. In 2001, European Commission recommended VSL that declines with age..

Does Fairness Provide Any Insight? Is same value per statistical life equitable? Is same value per statistical life equitable?versus Is same value per statistical life year equitable? Is same value per statistical life year equitable?  Return to first principles—willingness to pay.

Should Income Levels Matter? VSL increases with income VSL increases with income Provide policies poor don’t value? Provide policies poor don’t value? Airline safety – should we regulate it more stringently than highway safety? Airline safety – should we regulate it more stringently than highway safety?  Planes versus guardrails DOT adopted Viscusi-Aldy (2003) elasticity estimate of 0.55. DOT adopted Viscusi-Aldy (2003) elasticity estimate of 0.55. Rationale is stronger if beneficiaries of safety regulation pay for higher costs of safety.. Rationale is stronger if beneficiaries of safety regulation pay for higher costs of safety..

Income at Point of Time or Over Time DOT’s proposed adjustment is very bold policy initiative to account for within population differences. DOT’s proposed adjustment is very bold policy initiative to account for within population differences. Income changes over time for future generations receive greater support. Income changes over time for future generations receive greater support. Efficient, but redistributes income from poorer current generation to richer future generation.. Efficient, but redistributes income from poorer current generation to richer future generation..

Income at Point of Time or Over Time, cont’d Reference dependence effect. Proposed Senate legislation in 2008 to require income adjustment for VSL and require that only increases in VSL be permitted.. Reference dependence effect. Proposed Senate legislation in 2008 to require income adjustment for VSL and require that only increases in VSL be permitted..

The 2008 Devaluation of Life Controversy Based on conflicting results of 2 meta analyses (Viscusi and Aldy vs. Based on conflicting results of 2 meta analyses (Viscusi and Aldy vs. Mrozek and Taylor), in 2008. EPA Air Office lowered the VSL from \$8 million to \$7 million Economic puzzle since income levels have risen. Why did studies differ? Economic puzzle since income levels have risen. Why did studies differ? Political firestorm – Bush conspiracy?. Political firestorm – Bush conspiracy?.

The 2008 Devaluation of Life Controversy, cont’d Proposed Senate legislation in Fall 2008 requiring that agencies must only raise VSL over time. Proposed Senate legislation in Fall 2008 requiring that agencies must only raise VSL over time. But EPA Air Office number still relatively high.. But EPA Air Office number still relatively high..

Other Sources of Variation in Valuing Life How people die matters How people die matters Victims of terrorism versus natural disasters differ by factor of 2 in society’s valuation of reducing their risks (Viscusi 2009) Victims of terrorism versus natural disasters differ by factor of 2 in society’s valuation of reducing their risks (Viscusi 2009) Irresponsible behavior by people who put themselves at risk reduces their societal values, e.g., railway trespassers and suicides (Covey, Robinson, Jones-Lee, and Loomes 2010).. Irresponsible behavior by people who put themselves at risk reduces their societal values, e.g., railway trespassers and suicides (Covey, Robinson, Jones-Lee, and Loomes 2010)..

Conclusion VSL has been an integral part of benefits assessment for a quarter century VSL has been an integral part of benefits assessment for a quarter century Misunderstanding of the “economic” value of life may stimulate much of the continued controversy Misunderstanding of the “economic” value of life may stimulate much of the continued controversy Opposition to VSL is often misguided Opposition to VSL is often misguided Improved fatality rate data and survey data have greatly expanded questions that researchers can address. Improved fatality rate data and survey data have greatly expanded questions that researchers can address.

Conclusion, cont’d Estimates of heterogeneity and sources of heterogeneity are becoming more refined Estimates of heterogeneity and sources of heterogeneity are becoming more refined More refined VSL estimates present new policy challenges More refined VSL estimates present new policy challenges Treating some risk reductions as “priceless” may make them “worthless”. Treating some risk reductions as “priceless” may make them “worthless”.

Selected References Aldy, Joseph E., and W. Kip Viscusi. 2007. “Age Differences in the Value of Statistical Life: Revealed Preference Evidence.” Review of Environmental Economics and Policy, 1(2): 241-260. Aldy, Joseph E., and W. Kip Viscusi. 2007. “Age Differences in the Value of Statistical Life: Revealed Preference Evidence.” Review of Environmental Economics and Policy, 1(2): 241-260. Aldy, Joseph E., and W. Kip Viscusi. 2008. “Adjusting the Value of a Statistical Life for Age and Cohort Effects.” Review of Economics and Statistics, 90(3): 573-581. Aldy, Joseph E., and W. Kip Viscusi. 2008. “Adjusting the Value of a Statistical Life for Age and Cohort Effects.” Review of Economics and Statistics, 90(3): 573-581. Hersch, Joni, and W. Kip Viscusi. 2010. “Immigrant Status and the Value of Statistical Life.” Journal of Human Resources. Hersch, Joni, and W. Kip Viscusi. 2010. “Immigrant Status and the Value of Statistical Life.” Journal of Human Resources. Kniesner, Thomas J., W. Kip Viscusi, and James P. Ziliak. 2010. “Policy Relevant Heterogeneity in the Value of Statistical Life: New Evidence from Panel Data Quantile Regressions.”Journal of Risk and Uncertainty, 40(1): 15-31. Kniesner, Thomas J., W. Kip Viscusi, and James P. Ziliak. 2010. “Policy Relevant Heterogeneity in the Value of Statistical Life: New Evidence from Panel Data Quantile Regressions.”Journal of Risk and Uncertainty, 40(1): 15-31. Scharff, Robert L., and W. Kip Viscusi. 2010. “Heterogeneous Rates of Time Preference and the Decision to Smoke.” Economic Inquiry. Scharff, Robert L., and W. Kip Viscusi. 2010. “Heterogeneous Rates of Time Preference and the Decision to Smoke.” Economic Inquiry. Viscusi, W. Kip. 1979. Employment Hazards: An Investigation of Market Performance, Harvard Economic Studies No. 148. Cambridge: Harvard University Press. Viscusi, W. Kip. 1979. Employment Hazards: An Investigation of Market Performance, Harvard Economic Studies No. 148. Cambridge: Harvard University Press.

Selected References, cont’d Viscusi, W. Kip. 2003. “Racial Differences in Labor Market Values of a Statistical Life.” Journal of Risk and Uncertainty, 27(3): 239-256. Viscusi, W. Kip. 2003. “Racial Differences in Labor Market Values of a Statistical Life.” Journal of Risk and Uncertainty, 27(3): 239-256. Viscusi, W. Kip. 2009. “The Devaluation of Life.” Regulation and Governance, 3(2): 103-127. Viscusi, W. Kip. 2009. “The Devaluation of Life.” Regulation and Governance, 3(2): 103-127. Viscusi, W. Kip. 2009. “Valuing Risks of Death from Terrorism and Natural Disasters.” Journal of Risk and Uncertainty, 38(3): 191-213. Viscusi, W. Kip. 2009. “Valuing Risks of Death from Terrorism and Natural Disasters.” Journal of Risk and Uncertainty, 38(3): 191-213. Viscusi, W. Kip, and Joseph E. Aldy. 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. Viscusi, W. Kip, and Joseph E. Aldy. 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. Viscusi, W. Kip, and Joseph E. Aldy. 2007. “Labor Market Estimates of the Senior Discount for the Value of Statistical Life.” Journal of Environmental Economics and Management, 53(3): 377-392. Viscusi, W. Kip, and Joseph E. Aldy. 2007. “Labor Market Estimates of the Senior Discount for the Value of Statistical Life.” Journal of Environmental Economics and Management, 53(3): 377-392. Viscusi, W. Kip, and Joni Hersch. 2001. “Cigarette Smokers as Job Risk Takers.” Review of Economics and Statistics, 83(2): 269-280. Viscusi, W. Kip, and Joni Hersch. 2001. “Cigarette Smokers as Job Risk Takers.” Review of Economics and Statistics, 83(2): 269-280. Viscusi, W. Kip, and Joni Hersch. 2008. “The Mortality Cost to Smokers.” Journal of Health Economics, 27(4): 943-958. Viscusi, W. Kip, and Joni Hersch. 2008. “The Mortality Cost to Smokers.” Journal of Health Economics, 27(4): 943-958.

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