Value of Statistical Life Year

Value of Statistical Life Year in Cost-Benefit Analysis

The value of a statistical life year, usually shortened to VSLY, puts a money figure on a small gain in life expectancy, so that the mortality benefits of a health or safety policy can be counted in years of life rather than in deaths averted. It sits beside the value of statistical life (VSL), which values a small change in the risk of death without regard to how many years the people affected have left. The difference matters whenever a programme mainly protects children or older people, because the two measures can rank the same pair of options in opposite order. It is normally calculated from a VSL with an assumption about remaining life expectancy and often a discount rate, and those assumptions carry much of the result.

Life years and deaths as units of benefit

A policy that lowers the chance of dying this year does not make anyone immortal. It postpones death, and the gain can be described either as a fall in expected deaths or as a rise in expected years lived. The Guidelines for Regulatory Impact Analysis issued by the US Department of Health and Human Services (HHS) in 2016 describe the VSL as the rate at which an individual substitutes money for reductions in current mortality risk, and the VSLY as the rate at which the same person substitutes money for gains in life expectancy.

Both are willingness to pay measures. A review of mortality valuation for global benefit-cost analysis by Robinson, Hammitt and O'Keeffe describes the VSLY as the rate at which an individual is willing to trade small changes in his or her own life expectancy for spending on other goods and services. Under the VSLY approach in the HHS guidelines, a reduction in mortality risk is valued by working out the gain in life expectancy and multiplying it by a VSLY, with future life years generally discounted first. The same guidelines note that few primary studies estimate the VSLY itself, and that it is usually derived from a VSL estimate using simple assumptions.

These values belong to cost-benefit analysis, where health effects must be expressed in money before they can be set against costs, and they are one product of monetary valuation.

Converting a VSL into a constant VSLY

The simplest conversion spreads the VSL evenly over the years that the average person in the underlying studies still expects to live. It treats every remaining year as worth the same amount and ignores when the years arrive.

$$\text{VSLY}_{u} = \frac{\text{VSL}}{L}$$

where $\text{VSLY}_{u}$ is the undiscounted value per statistical life year, $\text{VSL}$ is the value of statistical life for the population studied, and $L$ is the remaining life expectancy, in years, at the average age of that population.

The second conversion treats the VSL as the present value of an even stream of yearly values, in the same way that a loan is turned into equal repayments. Aldy and Viscusi used this annuity form when they built age-specific VSLY estimates from age-specific VSLs, with a 3% discount rate in the main results and a 7% rate as a check.

$$\text{VSLY}_{d} = \frac{r \times \text{VSL}}{1 - (1 + r)^{-L}}$$

where $\text{VSLY}_{d}$ is the discounted value per statistical life year, $r$ is the annual discount rate, $L$ is remaining life expectancy in years, and the quantity $(1 - (1 + r)^{-L})/r$ is the present value of one life year received at the end of each of the $L$ years. The same annuity factor underlies the time value of money.

Once a VSLY exists, the benefit of a policy for one person is the VSLY multiplied by that person's expected gain in life years.

$$B = \text{VSLY} \times \Delta Y$$

where $B$ is the money value of the mortality risk reduction for one person and $\Delta Y$ is the gain in expected life years, discounted at rate $r$ when $\text{VSLY}_{d}$ is used and undiscounted when $\text{VSLY}_{u}$ is used. Robinson and colleagues note that for people of the average age in the source studies this gives the same answer as applying the VSL, and that it gives larger values for younger people and smaller values for older people.

Discounting the life years or not

The HHS guidelines and Robinson and colleagues take different positions on discounting. The HHS guidelines say future life years are generally discounted first and refer the analyst to the department's general rules on discounting. For sensitivity analysis in low and middle income countries, Robinson and colleagues recommend dividing the VSL by undiscounted life expectancy at the average adult age and multiplying by the undiscounted change in life expectancy. They give two reasons. People may discount their own future years at a lower rate than money, and discounting the years flattens the link between age and value, which pulls the result back towards a single VSL for all ages. Whichever rule is chosen, the same treatment of years has to be used when the VSLY is derived and when it is applied.

What a constant VSLY assumes about age

A single VSLY for everyone is a modelling convenience, and its theoretical basis is narrow. Aldy and Viscusi explain that when consumption is constant over the life cycle the VSL should fall with age and can be annuitised into an age-invariant VSLY. Whether consumption is constant depends on perfect capital and insurance markets, and in practice consumption rises and then falls over the life cycle. Earlier labour market studies built that constancy in. One estimated implicit discount rates of about 10% and a VSLY of about USD 300,000.

Aldy and Viscusi instead estimated hedonic wage equations with fatal risk measured separately by age, using US survey data for 1993 to 2000, and reported their values in year 2000 dollars. In the cross-section results the VSLY peaked at USD 375,000 at age 45 and fell to about USD 150,000 for workers in their early 60s. After adjusting for birth cohort, the peak was USD 401,000 at age 54 with a gentler decline to about USD 350,000 by age 62, and the average VSLY was USD 296,000 in the cross-section and USD 302,000 with the cohort adjustment. They concluded that the conventional assumption of a constant VSLY is not borne out, and noted that the finding also bears on QALY methods that assume a constant value per year apart from health status.

The wider literature is no tidier. Robinson and colleagues summarise research from high income countries suggesting that values for children may be around twice the adult average, that values for working age adults may follow an inverse U shape peaking in middle age, and that values at older ages may stay level or fall, while warning that results are inconsistent across studies. They describe a constant VSLY as a rough proxy for the effects of age and life expectancy that is not well supported by theory or the available empirical research.

Worked example with two mortality programmes

All numbers here are illustrative and are not taken from any guidance document. An agency uses a VSL of GBP 2,000,000, and the average adult in the studies behind that figure has 40 years of life remaining. Programme A prevents 10 deaths among older people who each have 10 years left. Programme B prevents 4 deaths among young adults who each have 55 years left. For simplicity the remaining years are treated as certain, whereas a full analysis would use a life table, and health quality is ignored.

The undiscounted VSLY is GBP 2,000,000 / 40 = GBP 50,000. For the discounted version at an illustrative 3% rate, the annuity factor for 40 years is 23.115, so the VSLY is GBP 2,000,000 / 23.115 = GBP 86,524. The annuity factors for 10 and 55 years at 3% are 8.530 and 26.774.

Each row can be recomputed by hand. With one VSL per death, A is worth 10 × 2,000,000 = 20,000,000 and B is worth 4 × 2,000,000 = 8,000,000. With the undiscounted VSLY, A is worth 10 × 10 × 50,000 = 5,000,000 and B is worth 4 × 55 × 50,000 = 11,000,000. With the discounted VSLY, A is worth 10 × 8.530 × 86,524 = 7,380,497 and B is worth 4 × 26.774 × 86,524 = 9,266,374.

The VSL ranks Programme A first because it averts more deaths. Both VSLY rules rank Programme B first because it saves more life years, 220 against 100. Discounting narrows B's advantage from 2.2 times to about 1.26 times, the flattening that Robinson and colleagues describe, because the distant years that make up most of B's gain count for less. As a check on consistency, a person of average age gains 40 undiscounted years worth 40 × 50,000 = 2,000,000, or 23.115 discounted years worth 23.115 × 86,524 = 2,000,002, which recovers the VSL apart from rounding. A ranking that changes with the valuation rule is a result worth reporting.

How appraisal guidance uses the VSLY

In the HHS guidelines the VSL remains the primary approach, and the VSLY appears mainly as a check. The HHS guidelines say that where a regulation largely affects the very young or the very old, analysts should at minimum add a sensitivity analysis based on the expected value of future QALYs, and they note that many analyses have used a VSLY for the same purpose. For the value of a QALY, the guidelines describe the common shortcut of applying a VSLY found by dividing the VSL by the discounted expected life years remaining, and prefer dividing by expected QALYs instead. Because health tends to decline with age, future QALYs are fewer than future life years, so the value per QALY comes out larger than the VSLY.

The Green Book (2026) from HM Treasury says that a proposal which might change life expectancy should be valued with a generic price known as the value of a statistical life year (SLY) or the value of a life year (VOLY). It describes this as the social value of a small change in the probability of losing or gaining a year of life expectancy, useful when options involve different changes to life expectancy. Effects on quality of life are valued through QALYs, at GBP 70,000 per QALY in 2020 to 2021 prices, and risks to life through the value of a prevented fatality published in the Department for Transport TAG data book. The Green Book adds that these values come from representative population samples and are not meant for emergency or rescue contexts.

Converting life year values into QALY values has been studied directly. Hirth and colleagues converted 42 value of life estimates into implied values per QALY using the life expectancy of each study population, age-specific QALY weights and a 3% real discount rate. Median values in 1997 US dollars ranged between USD 24,777 for estimates based on the human capital approach and USD 428,286 for job risk revealed preference estimates. Mason, Jones-Lee and Donaldson set out two ways of deriving a willingness to pay value of a QALY from the UK value of a prevented fatality, one conventional and one new.

Where the VSLY stops and cost-effectiveness analysis begins

In cost-effectiveness analysis, life years gained and QALYs stay in natural units and the cost per unit is compared with a willingness-to-pay threshold. The VSLY instead turns those years into money, so the result is a net benefit that can be compared across sectors such as transport, environment and health. A VSLY derived from individual risk trade-offs and a threshold chosen for a health budget answer different questions, and one should not be substituted for the other without saying so. Applying a VSLY estimated in one country to another country is a problem of benefit transfer.

Where VSLY figures mislead

The commonest misreading treats the VSLY as the worth of a year of a named person's life. It is a rate of exchange for small changes in risk spread across many people. The Green Book makes the same point about the value of a prevented fatality, and the HHS guidelines say that the VSL is not the value of saving an individual's life with certainty. The VSLY inherits both cautions.

A second error mixes conventions. A VSLY derived with discounted life expectancy and then multiplied by undiscounted life year gains, or the reverse, will not reproduce the VSL for a person of average age, and the error grows with the length of the gain.

A third problem is the age profile itself. A constant VSLY makes value proportional to remaining years, which favours deaths averted among the young, and the empirical work by Aldy and Viscusi does not support that proportionality. The choice between a VSL per death and a VSLY per year therefore carries an ethical judgement about how deaths at different ages should count, as well as an empirical claim about what people are willing to pay.

Finally, a VSLY counts years without regard to the health in which they are lived. The HHS guidelines note that a VSLY implicitly averages over future health, while a value per QALY takes into account the expected decline in health with age. Where a policy changes quality of life as well as length of life, a VSLY alone leaves part of the effect unvalued.

Sources

• Aldy JE, Viscusi WK. Adjusting the value of a statistical life for age and cohort effects. Review of Economics and Statistics. 2008;90(3):573-581. https://doi.org/10.1162/rest.90.3.573
• Robinson LA, Hammitt JK, O'Keeffe L. Valuing mortality risk reductions in global benefit-cost analysis. Journal of Benefit-Cost Analysis. 2019;10(Suppl 1):15-50. https://doi.org/10.1017/bca.2018.26
• US Department of Health and Human Services, Office of the Assistant Secretary for Planning and Evaluation. Guidelines for Regulatory Impact Analysis. 2016. https://aspe.hhs.gov/sites/default/files/private/pdf/242926/HHS_RIAGuidance.pdf
• HM Treasury. The Green Book (2026). Updated 28 October 2026. https://www.gov.uk/government/publications/the-green-book--2/the-green-book-2026
• Hirth RA, Chernew ME, Miller E, Fendrick AM, Weissert WG. Willingness to pay for a quality-adjusted life year: in search of a standard. Medical Decision Making. 2000;20(3):332-342. https://doi.org/10.1177/0272989X0002000310
• Mason H, Jones-Lee M, Donaldson C. Modelling the monetary value of a QALY: a new approach based on UK data. Health Economics. 2009;18(8):933-950. https://doi.org/10.1002/hec.1416