Hedonic wages and the value of a statistical life

A hedonic wage function is the relationship between wages and a job characteristic, such as the risk of a fatal injury, traced out by the equilibrium matches of workers and firms. At each job its slope equals both the matched worker’s price for bearing risk and the matched firm’s cost of reducing it. For fatal risk that slope is the value of a statistical life (VSL), which governments use to value the lives that safety rules save.

The intuition

With many levels of risk instead of two jobs, every firm chooses a wage-risk package and every worker picks the package she likes best. Workers who hate risk end up in safe, lower-paid jobs at firms that can make work safe cheaply; workers who mind risk little end up in risky, higher-paid jobs at firms for which safety is expensive. The data show only the resulting matches. The line through them is not anyone’s indifference curve or any firm’s cost curve: it is a market outcome.

Firms: isoprofit curves

An isoprofit curve is the set of wage-risk combinations that give a firm the same profit. Three properties:

1. It slopes upward. Making a job safer costs money, so a firm that cuts risk must also cut the wage to keep profit constant.
2. It is concave. Safety has diminishing returns. Removing the first hazards is cheap; removing the last ones is very expensive, so near zero risk the wage must fall a lot for each further cut in risk.
3. Higher curves mean lower profit. At any risk level, a higher curve pays a higher wage. In long-run competitive equilibrium each firm is on its zero-profit curve.

Firms differ in how cheaply they produce safety, so they have different isoprofit curves.

Risk level on the zero-profit curve, ρ

2.0

Wage on the zero-profit curve

$19.20

Slope: wage given up per point of risk removed

$3.20

Open in Graph Lab

Figure 1. Isoprofit curves of one firm at profits of $0, $2 and $4 per worker-hour. Lower curves give higher profit, and along the zero-profit curve the wage given up per point of risk removed rises from $0.20 at 9.5 percent risk to $3.80 at 0.5 percent.

Matching workers to firms

Workers have upward-sloping wage-risk indifference curves that differ in steepness (see compensating differentials). Each worker chooses the job that puts her on the highest indifference curve; each firm offers the package that keeps it at zero profit. A match occurs where a worker’s indifference curve is tangent to a firm’s isoprofit curve.

Slope at A's job (wage per point of risk)

$3.40

Slope at B's job

$2.50

Slope at C's job

$1.60

Open in Graph Lab

Figure 2. The risk-averse worker A matches with firm X, which produces safety cheaply, and the risk-tolerant worker C with firm Z. The hedonic wage function joins the tangency points, and its slope falls from $3.40 per point of risk at A's job to $1.60 at C's.

The hedonic wage function has three properties worth stating on an exam:

• It slopes upward: riskier jobs pay more.
• At each match its slope equals the worker’s marginal rate of substitution between wage and risk and the firm’s marginal cost of safety. The slope is the market price of risk at that point.
• It need not be linear, and it describes the market, not a person. It does not say how much any one worker would need to accept a very different job.

Key idea

The market marries workers who dislike risk with firms that make safety cheaply. The observed wage-risk line is a locus of tangencies between indifference curves and isoprofit curves.

Estimating it: the value of a statistical life

A hedonic wage regression estimates

$$w_i = \alpha \rho_i + \text{other variables},$$

where $w_i$ is worker $i$‘s annual earnings, $\rho_i$ is the annual probability of a fatal injury in her job (usually her industry’s or occupation’s fatality rate), and the other variables hold constant schooling, experience, union status, region and other traits that affect pay. The coefficient $\alpha$ is the extra pay per unit of fatality probability, which is the value of a statistical life. For two jobs X and Y that differ only in risk, the same idea gives

$$\text{VSL} = \frac{w_Y - w_X}{\rho_Y - \rho_X}.$$

The name comes from adding up. If a job with 1 extra death per 10,000 workers a year pays $900 more, then 10,000 workers together receive $9 million in exchange for one expected death. No identified life is valued: the VSL is the rate at which workers trade money for small changes in risk.

Estimates vary widely, for three reasons:

1. Unobserved worker and job traits. Riskier jobs attract workers with less aversion to risk and may require skills that the data do not measure. The wage gap then mixes the risk premium with pay for those skills and tastes.
2. Different baseline risks. A rise in annual risk from 1 in 10,000 to 2 in 10,000 and a rise from 50 in 10,000 to 51 in 10,000 are the same change in probability, but the workers who accept the higher baseline are far more tolerant of risk and demand less for the extra unit.
3. Mismeasured risk. Industry fatality rates are noisy measures of an individual’s own risk, and long-term disease risks are barely measured.

Safety regulation

Canada has fourteen sets of occupational health and safety laws, one federal, ten provincial and three territorial.¹ In the United States the federal regulator is the Occupational Safety and Health Administration (OSHA). A standard that caps risk at $\bar\rho$ has opposite effects depending on whether workers understand the risks they face.

Informed workers. A worker who understands her risk chooses point P, where her indifference curve $U^*$ is tangent to her employer’s zero-profit isoprofit curve. At a capped risk $\bar\rho$ below P, her indifference curve lies above the isoprofit curve, because the two only touch at P. No wage keeps both sides as well off as before: a wage on $U^*$ means losses for the firm, a wage on the isoprofit curve puts the worker on a lower indifference curve, and anything between leaves both worse off. With zero profits in the long run, the wage falls to the isoprofit curve at Q and the worker bears the loss. She was already paid for the risk.

Misinformed workers. If workers think their risk is lower than it is, they accept jobs with too much risk for the pay. Judged by the true risk, those jobs sit on a low indifference curve. A standard moves the job along the isoprofit curve to a safer, lower-paid point Q, which can be on a higher true indifference curve.

Share of the true risk workers perceive

100%

Maximum risk allowed by the standard, ρ̄ (percent)

3.00

Risk chosen without the standard

5.0%

Risk workers believe they face there

5.0%

Change in true well-being from the standard (wage per hour)

−$1.20

Open in Graph Lab

Figure 3. With accurate beliefs the worker chooses 5 percent risk at P, and a standard capping risk at 3 percent lowers her true well-being by the equivalent of $1.20 an hour. If she perceives only half the true risk she chooses 7.8 percent, and a standard at 5 percent raises her true well-being by $2.31 an hour; a standard below about 2.2 percent leaves her worse off than no standard.

The case for regulation therefore rests on workers misperceiving risk, on the regulator knowing the true risk, and on the standard not being set too strictly.

Worked example

Job X pays $58,000 a year with an annual fatality risk of 2 in 100,000. Job Y is identical except that it pays $58,900 with a risk of 12 in 100,000.

1. Convert risks to probabilities. $\rho_X = 0.00002$ and $\rho_Y = 0.00012$, so $\rho_Y - \rho_X = 0.0001$.

2. Compute the VSL. $\text{VSL} = 900 / 0.0001 = 9{,}000{,}000$, so $9 million.

3. Check by adding up. Among 10,000 workers, job Y means one extra expected death a year, and those workers together receive $900 \times 10{,}000$, or $9 million, in extra pay.

4. Value a regulation. A rule lowers fatality risk by 1 in 100,000 a year for 2 million workers, avoiding $2{,}000{,}000 \times 0.00001 = 20$ expected deaths a year. At a VSL of $9 million the benefit is $180 million a year. If the rule costs less than that, it passes a cost-benefit test.

Exercise: the first labour market estimate

Thaler and Rosen found that jobs with an extra death risk of 0.001 a year paid about $176 a year more in the late 1960s.² The implied VSL is $176 / 0.001 = 176{,}000$ dollars in the dollars of that time. Among 1,000 such workers there is one extra expected death a year, and they collectively receive $176,000.

Evidence

Estimates. Thaler and Rosen’s estimates, from 1967 survey data and insurance records of extra deaths by occupation, clustered around $200,000 in the dollars of the time.² A 2003 review put the median VSL for prime-aged US workers at about $7 million in 2000 US dollars, with confidence intervals whose upper bounds could exceed the lower bounds by a factor of two or more. On the same basis most Canadian labour market estimates fell between $3 million and $6 million; one Montreal study that asked about 200 workers for their own perceptions of risk found $18 million to $20 million.³

Values used in policy. The US Department of Transportation uses a VSL of $14.2 million for analyses with a 2025 base year.⁴ The US Department of Health and Human Services uses a central value of $14.1 million for 2026, with a range of $6.6 million to $21.5 million.⁵ In Canada, the Treasury Board Secretariat sets the VSL at $6.4 million in 2007 dollars, which a 2024 federal regulatory analysis converted to $9.3 million in 2024 dollars.⁶

Workplace deaths. Canadian workers’ compensation boards accepted 1,046 fatality claims in 2024. Exposure to harmful substances or environments accounted for 650 of them, cancers and other tumours for 440, and 566 of the people who died were over 64.⁷ Risks that show up decades later are the kind workers are least likely to perceive when they take a job, which strengthens the case for regulating them. In the United States there were 5,070 fatal work injuries in 2024, a rate of 3.3 per 100,000 full-time equivalent workers.⁸

Do inspections work? California’s safety regulator chose workplaces for inspection at random. Compared with 409 matched workplaces that were eligible but not chosen, 409 randomly inspected ones saw injury rates fall 9.4 percent and injury costs fall 26 percent, with no detectable loss of employment, sales, credit ratings or survival.⁹ The study measured injuries and firm outcomes, not wages or well-being, so it cannot by itself tell the informed and misinformed cases apart.

Common mistakes

Traps on exams

• Dividing by the risk count. Risk of 10 in 100,000 is a probability of 0.0001. Dividing a $900 gap by 10 instead of 0.0001 gives $90 instead of $9 million.
• Calling the hedonic wage function an indifference curve. It joins tangencies of many workers and firms; each worker’s indifference curve touches it at one point only.
• Reading isoprofit curves like indifference curves. Higher isoprofit curves mean lower profit.
• Assuming safety rules always help workers. With informed workers and competitive markets, a binding standard makes them worse off. The case for regulation rests on misperceived risk.

On the exam

For the hedonic diagram, draw two or three upward-sloping concave isoprofit curves (firms X, Y, Z) and convex indifference curves (workers A, B, C) tangent to them, then join the tangency points and label the result. For regulation, draw the tangency at P, the vertical standard at $\bar\rho$, the new point Q on the isoprofit curve and the lower indifference curve through it.

Check yourself

1.

True or false, with the wage on the vertical axis and risk on the horizontal axis, higher isoprofit curves give the firm lower profits.

1True2False

Check answer

2.

Job X pays $61,000 a year and has an annual fatality risk of 4 in 100,000. Job Y is identical except that it pays $61,720 a year and has a fatality risk of 12 in 100,000. If the pay gap is a compensating differential, what value of a statistical life does it imply, in millions of dollars?

Your answer (million dollars)

Check answer

3.

Workers believe their risk of injury is half of what it really is. A safety standard caps risk near the level they would choose if they were informed. What happens to their true well-being?

1It rises, even though their wage falls2It falls, because their wage falls3It is unchanged, because the standard only affects firms4It rises, because their wage rises to compensate for the standard

Check answer

Practise more questions on this topic

Sources

1. Canadian Centre for Occupational Health and Safety, Health and safety legislation in Canada: introduction. ↩

2. Thaler, R. and Rosen, S. (1976). The value of saving a life: Evidence from the labor market. In N. E. Terleckyj (ed.), Household Production and Consumption, chapter 5. NBER. NBER chapter page. ↩ ↩²

3. Viscusi, W. K. and 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 to 76. NBER working paper 9487. ↩

4. US Department of Transportation, Revised departmental guidance on valuation of a statistical life in economic analysis (effective March 20, 2026). ↩

5. US Department of Health and Human Services, Office of the Assistant Secretary for Planning and Evaluation (2026). HHS standard values for regulatory analysis, 2026. Values in constant 2025 dollars. ↩

6. Canada Gazette, Part I, Vol. 158, No. 52 (December 28, 2024), Regulations Amending Certain Regulations Made Under the Food and Drugs Act (Shortages and Discontinuation of Sale of Drugs and Medical Devices), regulatory impact analysis statement. ↩

7. Association of Workers’ Compensation Boards of Canada, National Work Injury, Disease and Fatality Statistics, fatalities data for 2024. ↩

8. US Bureau of Labor Statistics (2026), National census of fatal occupational injuries in 2024, news release, February 19, 2026. ↩

9. Levine, D. I., Toffel, M. W. and Johnson, M. S. (2012). Randomized government safety inspections reduce worker injuries with no detectable job loss. Science, 336(6083), 907 to 911. ↩