Valuation Of Mortality Risks Research Articles

Value per Statistical Life at the Sub-National Level as a Tool for Assessing Public Health and Environmental Problems.

This article aims to estimate the Value per Statistical Life (VSL) and Value per Statistical Life Year (VSLY) at the sub-national level, which can be used to calculate the economic impact of health and environmental problems. We estimate the value of life for Mexico and its 32 states, grouped into 5 regions for 2021. We used the OECD's guidelines on "Mortality Risk Valuation in Environment, Health and Transport Policies," which applies the measure of Willingness to Pay (WTP) and Cost-Benefit Analysis (CBA). Mexico's overall VSL of $2 000 000 USD in 2021 showcases the value placed on human life. The variation in VSL across the 32 states, with Chiapas having the lowest VSL of $400 000 USD and Mexico City boasting the highest VSL of $3 300 000 USD highlights the different levels of regional development and people's willingness to pay to reduce the risk of mortality. Our estimates of VSL and VSLY have the potential to contribute to the evaluation of public policies in the fields of health and the environment. Monetizing human life through these estimates can offer valuable insights to policymakers at both the national and sub-national levels. By quantifying the economic value placed on human life, this paper helps decision-makers prioritize investments, assess the cost-effectiveness of interventions, and allocate resources to maximize societal well-being.

The global COVID-19 mortality cost report card: 2020, 2021, and 2022.

The United States is the country with the greatest number of COVID-19 deaths in 2020, 2021, and 2022. Both the U.S. and the world exhibited an increase in the number of COVID-related deaths in 2021 and a decrease in 2022. The U.S. share of COVID-related deaths declined in 2021 but rose in 2022, leading to a cumulative total U.S. mortality share of 17%. The extent to which the U.S. is an outlier is even greater based on the monetized mortality costs. Using the value of a statistical life to monetize the mortality impact increases the performance gap between the U.S. and the rest of the world because of the high mortality risk valuation in the U.S. The worldwide COVID-19 mortality cost was $29.4 trillion as of January 1, 2023, with a U.S. share of $12.7 trillion, or 43% of the global total. Throughout the COVID pandemic, the U.S. mortality cost share has been in the narrow range of 43% to 45%. Given the high U.S. value of a statistical life, these monetized mortality cost values are more than double the U.S. share of COVID-related deaths. The U.S. mortality cost share is greater if the value of a statistical life declines more than proportionally with income for low-income countries.

Premature Deaths, Statistical Lives, and Years of Life Lost: Identification, Quantification, and Valuation of Mortality Risks.

Mortality effects of exposure to air pollution and other environmental hazards are often described by the estimated number of “premature” or “attributable” deaths and the economic value of a reduction in exposure as the product of an estimate of “statistical lives saved” and a “value per statistical life.” These terms can be misleading because the number of deaths advanced by exposure cannot be determined from mortality data alone, whether from epidemiology or randomized trials (it is not statistically identified). The fraction of deaths “attributed” to exposure is conventionally derived as the hazard fraction (R – 1)/R, where R is the relative risk of mortality between high and low exposure levels. The fraction of deaths advanced by exposure (the “etiologic” fraction) can be substantially larger or smaller: it can be as large as one and as small as 1/e (≈0.37) times the hazard fraction (if the association is causal and zero otherwise). Recent literature reveals misunderstanding about these concepts. Total life years lost in a population due to exposure can be estimated but cannot be disaggregated by age or cause of death. Economic valuation of a change in exposure‐related mortality risk to a population is not affected by inability to know the fraction of deaths that are etiologic. When individuals facing larger or smaller changes in mortality risk cannot be identified, the mean change in population hazard is sufficient for valuation; otherwise, the economic value can depend on the distribution of risk reductions.

Effect of Income Heterogeneity on Valuation of Mortality Risk in Taiwan: An Application of Unconditional Quantile Regression Method.

According to theory and existing empirical results, heterogeneity in personal characteristics, with income variation being one of them, affects the marginal willingness to pay (WTP) for reducing fatal risk. In this study, the effect of income heterogeneity on the value of statistical life (VSL) in Taiwan through unconditional quantile regression analysis using the data collected by the “Manpower Utilization Survey” is investigated. The results of this empirical study show that the hedonic wage function that was constructed using empirical data from Taiwan was in line with the general form of non-linear function rather than the semi-log function that has been often used in previous studies, which should have great impact on the estimation of the VSL. The empirical results also show that the estimated VSL of Taiwanese labor varied with the difference in wages, which needs to be taken into account when discussing the public policies using VSL.

Mortality-risk valuation, age and cause of death: out-of-hospital cardiac arrest

Economic evaluation of policies regarding out-of-hospital cardiac arrest (OHCA) is important. The value of a statistical life (VSL) for OHCA victims is the most important component in a cost-benefit analysis of interventions that have the possibility to reduce mortality from this cause. This value is not known. We use responses to a national Swedish mail survey, based on the stated-preference technique to directly elicit individuals’ hypothetical willingness to pay for a reduced risk of dying from OHCA. A lower-bound estimate of VSL for OHCA would be in range of SEK 30 to 50 million. The value is found to be higher than for comparable VSL estimates from the transport sector, even though individuals who suffer OHCAs are generally older and less healthy than people who die in road traffic accidents. The results indicate that it is not an overestimation to use the ‘baseline’ VSL value from the transport sector (SEK 24 million) in cost-benefit analysis of OHCA policy decisions and that the cause of death is important when examining willingness to pay for death risk reductions. We do not support a general declining VSL due to the age of the victims, i.e. a ‘senior death discount’, for this cause of death.Published: Online January 2017. In print December 2017.

Age effects in mortality risk valuation.

We provide more evidence on the functional relationship between willingness-to-pay for risk reductions and age (the senior discount). We overcome many of the limitations of previous literature that has dealt with this issue, namely, the influence of the assumptions used in statistical models on the final results. Given our large sample size (n=6024) we can use models that are very demanding on data. We use parametric (linear, quadratic, dummies), semi-nonparametric, and non-parametric models. We also compare the marginal and the total approach and show that they provide similar results. We also overcome one of the limitations of the total approach, that is, we include the effects of socioeconomic characteristics that are correlated with age (education and income). Our main result is that all these different approaches produce very similar results, namely, they show an inverted-U relation between the value of a statistical life (VSL) and age. Those results can hardly be attributed to problems of collinearity, omitted variables or statistical assumptions. We find a clear senior discount effect. This effect seems concentrated on those who have lower education and income levels. We also find that the value of a statistical life year (VSLY) increases with age.

Evidence of variable discount rates and non-standard discounting in mortality risk valuation

Time discounting is central to the valuation of future health and mortality risks in public sector allocative decision-making, particularly for environmental policies with delayed health impacts. Using a Risk-Risk trade-off survey, we elicit discount rates for fatality risks and establish discounting functional forms on both a sample and an individual level. We find wide variation in implicit discount rates for fatality risk between individuals, as well as between-individual heterogeneity in discounting functional forms. In aggregate, the sample is best characterised by subadditive discounting. Our work has implications for the academic investigation of intertemporal choice involving mortality risks, and potentially for the evaluation of policy options with delayed mortality risk outcomes. A thought experiment cautions against the standard practice of assuming that exponential discounting characterises society's time preferences.

From insurance risk to credit portfolio management: a new approach to pricing CDOs

We present a new approach for pricing collateralized debt obligations (CDOs) which takes into account the issue of the market incompleteness. In particular, we develop a suitable extension of the actuarial framework proposed by Bayraktar et al. [Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities. J. Econ. Dyn. Control, 2009, 33, 676–691], Milevsky et al. [Financial valuation of mortality risk via the instantaneous Sharpe-ratio: Applications to pricing pure endowments. Working Paper, 2007. Available at: http://arxiv.org/abs/0705.1302], Young [Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio: Theorems and proofs. Technical Report, 2007. Available at: http://arxiv.org/abs/0705.1297] and Young [Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio. Insurance: Math. Econ., 2008, 42, 691–703], which is based on the so-called instantaneous Sharpe ratio. Such a procedure allows us to incorporate the attitude of investors towards risk in a direct and rational way and, in addition, is also suitable for dealing with the often illiquid CDO market. Numerical experiments are presented which reveal that the market incompleteness can have a strong effect on the pricing of CDOs, and allows us to explain the high bid-ask spreads that are frequently observed in the markets.

Pricing Lives for Corporate and Governmental Risk Decisions

The value of a statistical life (VSL) is the most influential single parameter used in calculating the benefits of governmental regulations. While there are some interagency differences, there is a commonality in the conceptual approach, the central role of mortality risk valuation in benefit assessment, and the general range of valuations used. Corporate risk decisions are based on a less rigorous risk analysis procedure. As typified by the General Motors ignition switch recall problems and the company’s lax corporate safety culture, there is often little systematic corporate balancing of cost and risk. This suppression of safety concerns may be attributable to the adverse experiences automobile companies had after conducting risk analyses that valued fatalities based on damages awards for wrongful death, and in response juries levied blockbuster punitive damages awards. Instead, companies should adopt the VSL in its product risk decisions. Companies should also be provided with a safe harbor reference point for responsible risk decisions. Regulatory agencies should use the VSL in setting regulatory sanctions.

Exploring heterogeneity in the value of a statistical life: Cause of death v. risk perceptions

Most current environmental policy analyses use Value of a Statistical Life (VSL) figures inferred from workplace safety and traffic accident contexts to compute the benefits of environmental programs that avoid premature deaths. There is considerable debate about the appropriateness of this practice, in part because the effect of cause of death may be partly confounded with latency, initial risks, and competing risks. Preference for reducing risks can be also affected by individual-assessed risk attributes that are rarely controlled in valuation studies. This paper explores reasons for differences in preferences for mortality risk reductions (if any), and establishes the magnitude of the effects of such risk attributes as compared to other sources of VSL heterogeneity. In our conjoint choice experiments, cause of death, the size of the risk reduction, and latency, the “price” of the risk reduction and the mode of delivery of the risk reduction are explicit attributes of the alternatives to be examined by the respondent. Our statistical models also control for actual and perceived exposure to risks, initial risks, risk attributes such as dread, and sensitivity to and controllability of specific risks. We find that there is significant heterogeneity in the valuation of mortality risks and thus in the VSL. The VSL increases with dread, exposure to risk, and the respondents' assessments of the baseline risks. It is higher when the risk reduction is delivered by a public program, and increases with the effectiveness rating assigned by the respondent to the mode of the risk reduction. Even when we control explicitly for all of these factors, the cause of death per se accounts for a large portion of the VSL. All else the same, the fact that the cause of the death is “cancer” results in a VSL that is about one million euro above the amount predicted by dread, exposure and other risk perception variables. The VSL in the road safety context is about one million euro less than what is predicted by dread, exposure, or beliefs compared to VSL for the respiratory risk context. The effect of cause of death is thus as large as the effect of other sources of VSL heterogeneity. Our respondents do not seem to discount future risks.

Valuing Mortality Risk Reductions from Environmental, Transport, and Health Policies: A Global Meta‐Analysis of Stated Preference Studies

We conduct, to our knowledge, the first global meta-analysis (MA) of stated preference (SP) surveys of mortality risk valuation. The surveys ask adults their willingness to pay (WTP) for small reductions in mortality risks, deriving estimates of the sample mean value of statistical life (VSL) for environmental, health, and transport policies. We explain the variation in VSL estimates by differences in the characteristics of the SP methodologies applied, the population affected, and the characteristics of the mortality risks valued, including the magnitude of the risk change. The mean (median) VSL in our full data set of VSL sample means was found to be around $7.4 million (2.4 million) (2005 U.S. dollars). The most important variables explaining the variation in VSL are gross domestic product (GDP) per capita and the magnitude of the risk change valued. According to theory, however, VSL should be independent of the risk change. We discuss and test a range of quality screening criteria in order to investigate the effect of limiting the MA to high-quality studies. When limiting the MA to studies that find statistically significant differences in WTP using external or internal scope tests (without requiring strict proportionality), we find that mean VSL from studies that pass both tests tend to be less sensitive to the magnitude of the risk change. Mean VSL also tends to decrease when stricter screening criteria are applied. For many of our screened models, we find a VSL income elasticity of 0.7-0.9, which is reduced to 0.3-0.4 for some subsets of the data that satisfy scope tests or use the same high-quality survey.

Stochastic Mortality: Experience-Based Modeling and Application Issues Consistent with Solvency 2

This paper is motivated by the need to have appropriate tools for the valuation of mortality risks when carrying out an internal assessment of the insurance business, such as a portfolio valuation or a solvency investigation based on internal models. The case of life annuities is in particular addressed, due to the importance of mortality on the cost of living benefits for the elderly. Our aim is to describe a stochastic mortality model calibrated on the best-estimate life table available to the insurer and to the mortality experienced in the insurer's portfolio. As we address life annuities, uncertainty of future mortality improvements, i.e. the aggregate mortality risk, needs in particular to be accounted for. Following Olivieri and Pitacco (2009), we extend some classical results about the modeling of the number of deaths joint to the modeling of parameter uncertainty. We explore the features of two alternative approaches: a Beta-Binomial and a Poisson-Gamma setting; we then focus on the latter only. Thanks to a Bayesian inferential procedure, the parameters, initially assigned referring to the best-estimate life table, are updated according to the mortality experienced in the portfolio. Extending a traditional tool-kit, the framework we define is in particular suitable for practical work. Due to calibration, clearly the scope of the model is within internal assessments. To provide an example of application of the model, we perform a capital assessment. Solvency rules which could be adopted as an alternative to a standard, regulatory requirement are tested. The Solvency 2 requirement for longevity risk is referred to for the design of an internal rule which could get validation for replacing the standard one.

Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities

We develop a theory for valuing non-diversifiable mortality risk in an incomplete market by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saá-Requejo [2000. Beyond arbitrage: good deal asset price bounds in incomplete markets. Journal of Political Economy 108, 79–119] and of Björk and Slinko [2006. Towards a general theory of good deal bounds. Review of Finance 10, 221–260] applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure, and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.

Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities

We develop a theory for valuing non-diversifiable mortality risk in an incomplete market by assuming that the company issuing a mortality contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saa-Requejo (2000) and of Bjork and Slinko (2006) applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure, and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.

Mortality-risk Valuation and Age: Stated Preference Evidence

Controversy over the value of statistical life (VSL) centers on whether a single value should be applied to all age groups, as currently done by US government agencies, or whether lower values should be used for the elderly, recognizing that their life expectancies are shorter than those of younger people. Surveys of different age groups' willingness to pay (WTP) for mortality-risk reductions can potentially help resolve this issue.This paper reports on an analysis of this survey literature. Of some 36 studies reviewed, the literature is split on whether older people have a lower WTP for mortality-risk reductions. Even among the studies that find such a discount, its size varies widely. A simple statistical analysis of this literature reveals that larger samples and samples with a higher fraction of older people are significantly associated with finding this effect, suggesting that conducting a larger, more thorough study may help resolve this issue. The paper also raises the possibility that the WTP estimated when all factors related to age are allowed to vary may be more useful to policy than the WTP estimated when all such factors are held constant. A clear finding is that there is no evidence to support use of a uniform value of statistical life year.

IOM: The Economics of Better Environmental Health

Over the past two decades, epidemiological studies have strengthened the link between air pollution and specific respiratory ailments, yielding better valuations for the pollution-related costs of illness and thus pinpointing the benefits of environmental regulations. Much work remains to be done, however, in linking air pollution to other important health outcomes, such as cancer, infant mortality, and even doctor visits. Nagging questions also remain about how best to translate health effects into economic values. These were some of the questions addressed at the 14 November 2006 Roundtable on Environmental Health Sciences, Research, and Medicine. a project of the National Academies’ Institute of Medicine cosponsored by the NIEHS along with several other public and private entities. Economists and public health analysts outlined developing methodologies to identify and quantify the health benefits of reduced air pollution and to pinpoint costs to industry of complying with air quality regulations. “Overall, estimating risk from air pollution is becoming more precise as the pathway from air pollution to health is better characterized,” said C. Arden Pope, a Brigham Young University economist, at the roundtable. Monitoring large groups of people for long periods has enabled researchers to better control for confounding factors such as age, sex, and cigarette smoking, said Pope. More interdisciplinary work is needed to expand the scope of health benefits that can result from reduced pollution as well as further pinpoint measurable compliance costs of regulation.

Hedging life insurance with pure endowments

We extend the work of Milevsky et al., [Milevsky, M.A., Promislow, S.D., Young, V.R., 2005. Financial valuation of mortality risk via the instantaneous Sharpe ratio (preprint)] and Young, [Young, V.R., 2006. Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio (preprint)] by pricing life insurance and pure endowments together. We assume that the company issuing the life insurance and pure endowment contracts requires compensation for their mortality risk in the form of a pre-specified instantaneous Sharpe ratio. We show that the price P m , n for m life insurances and n pure endowments is less than the sum of the price P m , 0 for m life insurances and the price P 0 , n for n pure endowments. Thereby, pure endowment contracts serve as a hedge against the (stochastic) mortality risk inherent in life insurance, and vice versa.