Mortality Risk Valuation in Policy Assessment

2. Theory and methods of mortality risk valuation

Abstract

There are many metrics for mortality risk and the economic benefits of reducing mortality risk can be estimated in different ways. This chapter provides a theoretical overview of the Value of Statistical Life (VSL), a key concept in cost-benefit analysis derived from the willingness-to-pay (WTP) approach. It discusses existing methods to elicit VSL estimates, in particular Stated Preferences (SP) and Revealed Preferences (RP) methods. The chapter also presents alternatives concepts to VSL, such as the Value of a Statistical Year (VOLY) and health-adjusted life years. Finally, the chapter presents approaches to transferring VSL estimates across policy contexts that differ by year and location.

2.1. The value of statistical life concept

The Value of Statistical Life (VSL) remains a key concept in cost-benefit analysis. Individuals constantly make decisions that embody trade-offs between costs and benefits. For example, a home buyer may observe a trade-off between neighbourhood environmental amenities and the price of a house. In the same vein, regulatory authorities may juxtapose the health benefits of shutting down a pollution-intensive plant against the social cost of higher unemployment in a small town. In this example, economic theory suggests that shutting down the plant would result in a welfare improvement only if the economic benefit of health improvements resulting from the closure exceeds the social cost of unemployment. Consequently, when a policy change involves changes in mortality risk, it can be useful to provide an economic value of such changes that can be compared against other costs and benefits of the proposed policy change.

VSL is commonly computed through the willingness to pay (WTP) approach. There is significant evidence showing that individuals exhibit a positive WTP to reduce their personal mortality risk1 (Kniesner et al., 2012[1]). Formally, the WTP can be defined as the maximum amount that can be subtracted from an individual’s income or wealth in exchange for a given improvement in mortality risk without leaving the individual worse off. Such a valuation may also be treated as the willingness to accept (WTA) a higher mortality risk in exchange for compensation, such as accepting a more hazardous job in exchange for a higher salary. VSL can thus be defined as the rate at which individuals are willing to trade off wealth or income for a reduction in their risk of dying. It is important to note that VSL is based on the value of marginal variations in mortality risk, rather than the value of risk attached to a specific death. This chapter discusses in detail the VSL concept, the methods by which it is estimated, and provides examples of these concepts. This chapter also discusses alternative metrics to VSL and how VSL can be applied to policy analysis where primary studies are not available through the use of benefit transfer methodologies.

Two primary approaches exist for eliciting an individual’s WTP for changes in mortality risk, namely Stated Preference (SP) and Revealed Preference (RP) methods. SP methods rely on surveys, asking respondents to state their preferences for specific changes in mortality risks in a hypothetical scenario or situation. Such surveys may ask them directly for their WTP for a given but hypothetical mortality risk reduction or ask them to choose between mortality risk reduction scenarios with different costs attached to them. In contrast, RP methods observe actual behaviour relative to risk in labour and consumer markets, with a focus on observing trade-offs between mortality risk and income and between willingness to WTP for a product and its expected impact on an individual’s risk of dying.

To derive a VSL estimate for a population, the average WTP of a population can be estimated through a survey for a given marginal improvement of a specific mortality risk, $∆R$. The WTP for this risk change can then be aggregated until $∆R$ reaches 1, which corresponds to the value of a statistical life. Formally, VSL can therefore be defined as:

Equation ‎2.1

$VSL=\frac{{WTP|}_{∆R}}{∆R}$

To illustrate, consider a risk scenario for a population where the average WTP for a fatality risk reduction of 1 in 100 000 (or 0.00001) is USD 50. The VSL can then be calculated as USD 50 ÷ 0.00001 = USD 5 million. The VSL can equivalently be thought of as the average individual WTP for a given marginal fatality risk reduction aggregated over a population until the fatality risk reaches 1, in this case 100 000 individuals, i.e. USD 50 per individual × 100 000 = USD 5 million.

2.2. Stated preference (SP) methods

Stated Preference (SP) studies explicitly ask individuals how much they would be willing to pay (or willing to accept in compensation) for a small reduction (increase) in mortality risk. The two main SP methods are the Contingent Valuation (CV) method and Discrete Choice Experiments (CE). The main difference between these two approaches is that CV methods explicitly ask respondents for their WTP for either a private good that reduces their mortality risk or for a public programme that reduces population-wide mortality risk. CV approaches cover different elicitation methods such as open-ended maximum WTP questions, single-bounded dichotomous choices, double bounded dichotomous choices, or payment cards listing amounts to choose from. Under the CE approach, respondents are asked to make a series of choices between risks with different characteristics (including different probabilities) and monetary costs. The design of SP methods should follow best practise guidelines, such as those laid out in Johnston et al. (2017[2]).

SP have three main advantages. First, they are able to elicit WTP from broad segments of the population. Second, the size of mortality risk changes are explicitly stated, unlike RP studies where the mortality risk may be less clear to the individuals making choices on trade-offs. Third, SP analyses can value the causes of death that are specific to certain types of risks (e.g. environmental hazards). However, the main limitation of SP methods is that the stated choices are hypothetical insofar as the amounts respondents indicate they are willing to pay may differ from what they may actually be willing to pay in reality.2

2.2.1. Contingent valuation methods

In Contingent Valuation (CV) surveys, a mortality risk reduction policy scenario is carefully constructed and presented to focus groups and survey respondents. The policy setting in these scenarios can be generic or refer to a specific intervention that reduces the respondents’ probability of dying prematurely (e.g. traffic safety measures, air pollution policies or new health treatments). There are different ways of illustrating the mortality risk reduction, ranging from simply conveying the odds (e.g. 1 in 10 000 is the reduction in the probability of dying prematurely) to using grid cell diagrams or placing the mortality risk reduction in a geographical context. For example, respondents could be told to imagine that they live in a city of 10 000 inhabitants, and that a regulatory measure would reduce the number of premature deaths per year by one person. They are then asked for the maximum amount they would be willing to pay to achieve this (through an open-ended question or by showing them a payment card with different amounts from which they can choose the highest amount they would pay with certainty). In a dichotomous choice CV, respondents may be asked whether they would vote for or against a policy with an assigned cost, aimed at reducing their individual risk of dying prematurely by 1 in 10 000. Different sub-samples of the population are asked to pay different amounts. WTP estimates are subsequently derived from the percentage of respondents supporting the policy at different costs. Box ‎2.1 provides an example of a CV survey for deriving VSL.

Box ‎2.1. Contingent valuation for health effects in Kuwait

Alolayan et al. (2017[3]) uses CV methods to estimate VSL for Kuwaiti citizens. The valuation scenarios were related to cancer and heart attacks, and respondents were presented with a mortality risk reduction of 1 in 10 000 and 3 in 10 000, respectively. Consistency tests were performed which required that an individual reported strictly positive WTPs for mortality-risk reductions and that the responses to dichotomous choice CV questions for alternative risk reductions were consistent with the theoretical requirement that WTP should be less than, but close to proportional to the change in risk reduction. The authors estimated the VSLs to between USD 18 and 32 million, which is 2 to 3 times larger than values used in the United States. This finding was attributed mainly to the difference in net income levels between the United States and Kuwait. The authors suggested that the valuation results could be applicable to analysis of policy interventions in other countries in the region with similar income levels and societal contexts.

Source: Alolayan et al. (2017[3])

2.2.2. Discrete choice experiment methods

Discrete Choice Experiments (CE) are an indirect SP method that aims to derive an individual’s valuation of the characteristics that define a given reduction in mortality risk. In addition to the mortality risk reduction itself, these characteristics may include the latency period, type of risk, the cause of death and the time in life (now or later) at which the risk impact would be expected. In practice, respondents are shown choice cards with a reference alternative (often including the status quo as a zero cost option) alongside one or more policy alternatives with different characteristics, including their cost. Respondents are then asked to choose their preferred alternative from a series of choice cards in which the values for each attribute, including the costs, vary across alternatives. Using data from these repeated choices, WTP for the different attributes and mortality risk reduction can be derived. Box ‎2.2 provides an example of a CE survey and the choice cards used.

Box ‎2.2. Discrete choice experiment for mortality and morbidity valuation in China

Huang, Andersson and Zhang (2018[4]) conducted a discrete choice experiment (CE) in Beijing, China to estimate the VSL and the value of a statistical illness¹ to be used for policy analysis in China. Figure ‎2.1 is an example of a choice card used to elicit individuals’ WTP for mortality and morbidity risk reductions. The levels of the attributes, in addition to the cost attribute, for Programs A and B varied across choice cards, and respondents were asked to answer several of these choice cards. The analysis also examined how different payment regimes influenced WTP and whether WTP was age-dependent. VSL and the value of a statistical illness estimates were robust across different econometric model specifications and aligned with previous Chinese studies. There was no evidence of any VSL-age relationship, and the payment scheme had no significant effect on VSL (but had some effects on value of a statistical illness).

Figure ‎2.1. Discrete choice experiment choice card example

Note: Table translated from Chinese by Huang, Andersson and Zhang (2018[4]); Figures adapted from Huang, Andersson and Zhang (2018[4]).

1. The value of a statistical illness (or a statistical case of a particular illness) is a morbidity equivalent of the VSL. Analogous to Equation ‎2.1, the value of a statistical illness can be defined as the WTP to reduce the probability of contracting a specific illness divided by the change in probability of contracting the illness resulting from the policy intervention.

Source: Huang, Andersson and Zhang (2018[4])

2.3. Revealed preference methods

Two main RP methods are used to derive VSL, namely the hedonic wage (HW) method, which analyses individuals’ choice of jobs with different mortality risk, and the consumer market (CM) approach, which analyses individuals’ consumption of consumer products that can reduce their mortality risk (also known as the averting cost approach). Both approaches are based on an analysis of individuals’ actual behaviour in the labour and consumer product markets. in this way, the choices individuals make reveal their preferences for reducing their mortality risk.

2.3.1. Hedonic wage methods

The HW method (or wage-risk method) studies workers’ actual behaviour in the labour market. All else equal, it is expected that an individual engaged in a job with an above-average mortality risk would require a higher wage to compensate for this risk. Hence, the value that they attach to the risk can be estimated by observing the wage premiums associated with higher risk jobs. While attractive in that it offers insights into actual behaviours, the HW method has some limitations that should be considered. First, it provides estimates of VSL only for working age population segments. Second, HW studies value mainly current risk of accidental death, whereas environmental hazards, (e.g. asbestos or PCBs), are likely to cause death (via cancer or chronic respiratory illness) only after a latency period. Third, HW analyses may not be able to distinguish between actual and perceived risks, as well as other factors that shape wage variation. Box ‎2.3 provides an example of a representative HW study.

Box ‎2.3. Using hedonic wage methodologies to estimate risk-based wage differentials in Australia

Hedonic wage (HW) regressions have served as the main econometric tool to estimate the size and significance of compensating wage differentials (CWDs) payments for work-associated disamenities. Studies that find evidence of CWDs can compute value of statistical life (VSL) and value of statistical injury estimates as they can be directly inferred from HW regressions. This HW study looked at whether for Australian workers using data from the Household, Income and Labour Dynamics in Australia Survey, and risk data from Safe Work Australia. The following model was estimated to determine the existence of CWDs for job risk:

${\mathit{w}}_{\mathit{i}\mathit{t}}=\mathit{ }{\mathit{\beta }}_1{\mathit{R}\mathit{i}\mathit{s}\mathit{k}}_{\mathit{i}\mathit{t}}+{\mathit{\beta }}_2{\mathit{R}\mathit{i}\mathit{s}\mathit{k}²}_{\mathit{i}\mathit{t}}+{\mathit{\beta }}_3\left({\mathit{R}\mathit{i}\mathit{s}\mathit{k}}_{\mathit{i}\mathit{t}}\mathit{*}\mathit{ }{\mathit{U}}_{\mathit{i}\mathit{t}}\right)+{\mathit{\beta }}_4\left({\mathit{R}\mathit{i}\mathit{s}{\mathit{k}}^2}_{\mathit{i}\mathit{t}}\mathit{*}\mathit{ }{\mathit{U}}_{\mathit{i}\mathit{t}}\right)+{\mathit{X}\mathit{\text{'}}}_{\mathit{i}\mathit{t}}{\mathit{\beta }}_5+{\mathit{\alpha }}_{\mathit{i}}+{\mathit{\mu }}_{\mathit{i}\mathit{t}}$

where ${\mathit{w}}_{\mathit{i}\mathit{t}}$ is the log of the respondent’s hourly wage. ${\mathit{R}\mathit{i}\mathit{s}\mathit{k}}_{\mathit{i}\mathit{t}}$ is the job fatality or injury risk, which varies by the worker’s industry (industry risk), occupation (occupation risk) or industry-occupation (composite risk), depending on the model under consideration. Interaction terms between risk, risk squared, and the dummy variable for worker union membership, $\mathit{U}\mathit{i}\mathit{t}$, are included to capture union influence in the size of CWDs for workplace risk. ${\mathit{X}}_{\mathit{i}\mathit{t}}$ is a vector of worker and workplace characteristics that includes work experience, work experience squared, occupation tenure, job tenure, six dummies for workplace size, a dummy for public sector, two dummies for employment contract type, a dummy for worker union status, four dummies for education, a dummy for marital status, two dummies for country of birth, two dummies for dependent children, eight dummies for waves, and twelve dummies for location. The location dummy controls are useful in capturing any differences in worker compensation benefits between states and territories. The wave dummies, which control for time effects, are expected to alleviate the impact of Safe Work Australia’s exclusion of commuter deaths from the fatality reports from 2012 onwards. The unobservable individual-specific heterogeneity, represented by ${\mathit{\alpha }}_{\mathit{i}}$_, is treated as a part of the random error (pooled estimation) or individual-specific intercepts (fixed-effects estimation). The term ${\mathit{\mu }}_{\mathit{i}\mathit{t}}$ is the idiosyncratic error term.

The study found evidence of CWDs for the risk of workplace fatalities that are smaller in magnitude compared to the estimates previously reported in the 1990s for Australia. Using panel data and a risk variable that varies by both the worker’s industry and occupation of employment, Australian workers facing the mean level of fatality risk were found to receive a CWD of between 0.13% and 0.44% for a unit increase in risk, depending on the model specification. These estimates correspond to a VSL of AUD 9.7 million and AUD 34.9 million.1

1. These correspond to USD₂₀₂₀ 6.9 million and USD₂₀₂₀ 24 million, respectively.

Source: Reynolds, Nahm and MacMillan (2022[5]).

2.3.2. Consumer market methods

Another RP approach to valuing mortality and morbidity risk is the consumer market (CM) approach, also known as the averting cost or self-protection approach. This method observes and analyses the expenditures that people make to reduce the probability or severity of an adverse outcome. Practical examples range from purchasing safer cars, safety helmets and fire alarms, to buying a residence in a safer and cleaner part of a city. The underlying assumption is that a rational consumer will buy these averting goods until the individual’s marginal improvement in risk is equal to the price. One advantage of this RP method is that it is also based on actual behaviour. Moreover, it can cover a much larger part of the population than HW approaches since it is not tied to labour markets. Box ‎2.4 provides an example of a CM study to illustrate the approach.

Box ‎2.4. Valuing mortality risk through the housing markets

Bishop et al. (2024[6]) conduct a consumer market study to provide evidence on the rate at which spatial variation in all-cause mortality risk is capitalised into US housing prices. Using a hedonic framework, the study determined an annual implicit cost of a 0.1 percentage-point reduction in mortality risk among older Americans and found this cost to be less than USD 3 453 for a 67-year-old and diminishes with age to less than USD 629 for an 87-year-old. These estimates, while similar to estimates from the market for health care, are far below comparable estimates from markets for labour and automobiles, suggesting that the housing market could provide a lower cost alternative for reducing mortality risk. This conclusion was found to be robust to a wide range of econometric model specifications, including accounting for associated expenditures on property taxes and the physical and financial costs of moving.

Source: Bishop et al. (2024[6])

2.4. Alternatives to VSL

While this report focuses on VSL, alternative metrics to measure and compare health effects exist, including those that combine mortality and morbidity effects into a joint metric. This chapter briefly explains the most common alternative metrics.

2.4.1. The value of a statistical life year (VOLY)

The nature and time horizon of risk to life and health can differ. For example, some risks pose an immediate danger to life (e.g. road accidents) while others have lifetime impacts (e.g. air pollution). Furthermore, the implications of some risks may be uncertain or occur in the future (e.g. climate change). Consequently, it may sometimes be more appropriate to value some risks insofar as they impact the length of a life. To this end, a standard adaptation of the VSL concept is the value of a statistical life-year (VOLY or VSLY) which was first introduced by Moore and Viscusi (1988[7]). For simplicity it is often assumed that a VOLY is constant over an individual’s remaining lifetime, i.e. that each remaining life-year is valued equally. With this approach, the relationship between VSL and VOLY can be described as follows:

Equation ‎2.2

$VSL={\sum }_t^{T}VOLY\bullet {\left(1+\delta \right)}^{-t}$

In this equation, $t$ represents time in years and $T$ is the number of expected remaining life years, counting from the current average age of the population that is being studied ($t=0$). The social discount rate is denoted $\delta$ and is applied to discount future life year. VOLY can be estimated directly through stated preference (SP) methods as well as from VSL estimates by applying a discount rate and using population demographic data. Studies that elicit VOLY directly exist but are relatively few (Chilton et al., 2004[8]; Desaigues et al., 2011[9]). VOLY studies were not included in the meta-data for this report since converting them to VSLs would require additional assumptions (see also Chilton et al. (2020[10]), for a review of approaches to estimate VOLY).

It is important to highlight that VOLY estimates can produce conflicting recommendations relative to the VSL, particularly if the policy disproportionately affects the very young or the very old. For example, using a constant VOLY for all age groups implies that saving young lives offers greater benefits than saving older lives due to their higher expected number of remaining life years. Even if older people were to value each remaining life year more than young adults (which both theory and empirical studies indicate, e.g. (Hammitt, 2023[11]; Robinson, Sullivan and Shogren, 2021[12]), it may still result in a higher valuation of younger lives due to the differences in expected remaining life years. Consequently, there may be differences in estimated policy benefits when using life years saved multiplied by a (constant) VOLY versus using the number of avoided premature deaths together with the VSL. Hammitt (2023[11]) concludes that the common practice of valuing a transient or persistent risk reduction using a constant VSL, VOLY or Value of a Quality Adjusted Life Year (QALY) yields large differences in aggregated benefits which depend on the age at which the risk reduction begins, its duration, evolution, and whether the future lives, life years, or quality-adjusted life years are discounted.

2.4.2. Health-adjusted life years: The case of QALY and DALY

In addition to the VSL and VOLY, other metrics seek to capture the combined effects of mortality and morbidity. One example where such approaches could be useful is in estimating the benefits of a policy aimed at reducing the occurrence of a disease that leads to both pain and suffering and premature death. The most common metrics in this context are Quality-Adjusted Life-Years (QALYs) and Disability-Adjusted Life-Years (DALYs). For a QALY, a life-year in perfect health is represented by a value of 1. The life-year can then be adjusted downwards to account for disability and loss of quality of life at different ages in a population, including full life-years lost due to premature death. To use QALYs for policy analysis, the sum of QALYs for different policy alternatives can be compared, where a larger number of QALYs would normally be preferred for a given cost. DALYs also vary from 0 to 1, but for an individual over his/her lifetime. In contrast to QALYs, DALYs measure the life-years lost due to disability and premature death and can be defined as the sum of life-years lost to premature death and life-years lost due to disability and/or pain and suffering. A weighting factor is usually applied to a year lived with disabilities to signify its severity relative to a life-year lost. DALYs can be summed over affected populations by policy alternatives and are often used in cost-effectiveness analysis, where for a given cost, the policy with the lowest DALY score is generally preferred. QALYs and DALYs can be converted to monetary terms but are more often used without monetisation for comparing the relative impacts of policies (UNEP, 2013[13]; IHME, 2024[14]).

2.5. Benefit transfer methods

There are many situations where it may not be feasible to conduct a primary valuation VSL study to estimate the economic value of mortality effects for a new policy, for example due to time or budget constraints. Therefore, many CBAs rely on transferring values from existing VSL studies to different study contexts within a country, transferring values from one country to another, as well as transferring VSL estimates over time. Considering the long practice of using benefit transfer methods, the guidance and best practices in this area are relatively well established (Johnston et al., 2021[15]). In this section, two main groups of benefit transfer approaches are discussed, namely unit value transfer approaches and benefit function approaches.3

2.5.1. Unit value transfer approaches

Simple (naïve) unit value transfer

The simple (naïve) unit value transfer approach is the most basic benefit transfer technique, in which benefit estimates are directly transferred from a study context to the policy context. This approach infers that the monetary value of a mortality risk reduction is the same in the study context as that of the policy context. This is a strong assumption which may not always be true. Two main drivers of potential differences in VSL across these contexts can be observed. First, affected individuals in the policy context might be different from those in the study contexts, for example in terms of their income, education, age, religion, ethnicity or other socio-economic characteristics that inform mortality risk valuations. Second, even if individuals’ preferences for mortality risk reductions in the policy and study contexts were similar, the mortality risk characteristics (e.g. degree of suffering, dread, latency, voluntariness, etc.) and the magnitude of the risk change considered across these contexts may differ. Robinson et al. (2021[12]) discuss evidence related to several of these issues, including the magnitude of risk changes necessary to affect VSL estimates.

Unit value transfer with income adjustments

The simple unit value transfer approach should not be used for transferring values between areas with different income levels and costs of living. Instead, a unit transfer with income adjustments may be more appropriate. It has been shown in many studies that income is one of the key drivers of VSL differences between regions and countries (see Chapter 5 for a discussion). A common approach for an income-adjusted unit transfer is shown in Equation ‎2.3:

Equation ‎2.3

${VSL}_p={VSL}_s{\left(\frac{Y_p}{Y_s}\right)}^{\beta }$

where ${VSL}_p$ is the desired VSL to apply in the policy context, ${VSL}_s$ is the original VSL estimate from the study context, $Y_s$ and $Y_p$ are the income levels in the study and policy context, respectively, and $\beta$ is the income elasticity of VSL with respect to WTP for reducing the mortality risk.

Mortality risk reductions are considered to be a “normal” good with a positive income elasticity and many studies have attempted to estimate this elasticity, which is not necessarily constant. Note that, if the income elasticity $\beta$ is equal to 1, then Equation ‎2.1 can be simplified to multiplying VSL at the study site by the ratio of income at the policy site to income at the study site. Chapter 5 provides details on estimations of the income elasticity of VSL based on the meta-data collected for this report.

Household income levels are not always available as a basis for income-based benefit transfers, as is indeed the case for the current report. When there is lack of data on the income, an alternative is to use Gross Domestic Product (GDP) per capita as an approximation for income in international benefit transfers4. An added complication in international benefit transfers is that applying official exchange rates to convert VSL estimates to the currency of the policy context may not reflect the true purchasing power of currencies given that official exchange rates reflect political and macroeconomic risk factors. It is therefore common practice to use Purchasing Power Parity (PPP) adjusted exchange rate for such conversions. Nevertheless, even if PPP-adjusted GDP figures and exchange rates can be used to adjust for differences in income and cost-of-living in different countries, other important differences may remain, such as differences in individual preferences, baseline levels of risks, magnitude of risk changes, risk contexts, or cultural and institutional differences between countries.

Unit value transfer for separate age groups

It is also common to adjust VSL values for age. However, translating age-adjusted analysis into practical policy has proven challenging for two main reasons. First, while there are theoretical grounds for employing age-differentiated VSLs in cost-benefit analysis (Hammitt, 2023[11]; Viscusi and Aldy, 2007[16]), the evidence on the relationship between age and VSL is at best mixed5. Second, the use of age-differentiated VSLs in policy analysis is in general unpopular, despite the recognition in policy circles that health benefits may accrue disproportionately across age groups. Notably, the ethical debates surrounding age-related adjustments are known to trigger social and political backlash6. Consequently, apart from using them for sensitivity analyses, applying age adjustments of any kind to central VSL estimates is not a common policy practice and is also not recommended in this report (see the discussion in Chapter 5).

2.5.2. Benefit function approaches

Benefit transfer function

Considering the challenges discussed above, it is unsurprising that transferring a more nuanced benefit function is theoretically more appealing than simply transferring unit values, as functions can account for more information in the transfer. Note that the benefit function could come from one study or from several studies combined (in e.g. a meta-analysis benefit function). Equation ‎2.4 shows a simple benefit function, which can be used for transferring benefits from a single primary valuation study:

Equation ‎2.4

${WTP}_{ij}=b_0+b_1{\mathit{G}}_j+b_2{\mathit{H}}_i+e$

Where ${WTP}_{ij}$ is the willingness to pay of household $i$ for mortality risk reduction $j$. ${\mathit{G}}_j$ contains a set of mortality risk reduction characteristics (including the size of the mortality risk reduction), ${\mathit{H}}_i$ is a set of characteristics pertaining to household $i$ (e.g. household size or composition). Finally, $b_0$, $b_1$, and $b_2$ are parameters and $e$ is the random error term.

To implement the approach above, the analyst could obtain estimates of the constant $b_0$ and the slope parameters $b_1$ and $b_2$ from existing studies in the literature. The second stage proceeds with data collection at the policy site covering the two sets of independent variables $\mathit{G}$ and $\mathit{H}$, which are then inserted into the equation to calculate the WTP in the policy context of interest. VSL is then computed by dividing the WTP by the mortality risk reduction.

Meta-analytic benefit transfer

A challenge in applying the benefit function approach is that the data needed for the independent variables in the benefit function are not necessarily available in published papers or in publicly available documentation, as there are no standard reporting requirements for VSL studies. Furthermore, the same type of data upon which the original benefit function was built is also necessary for applying the function to the context where the benefits are to be transferred. In practice, this information is often not available. Therefore, rather than simply transferring the benefit function from a single primary valuation study, results from several mortality risk valuation studies can be combined in a meta-analysis to estimate a common benefit function.

The meta-analysis approach has often been used to synthesise research findings, improve the quality of literature reviews of valuation studies and derive VSL unit values. Using this approach, several original studies are analysed as a group, with results from each survey treated as a single observation in a regression analysis. If multiple estimates from each survey are used, various meta-regression specifications can be used to account for such ‘panel effects’. Furthermore, it is possible to evaluate the influence of a wider range of characteristics of the mortality risk, the features of the samples used in each analysis (including characteristics of the affected population, such as age and income) and the modelling assumptions employed.

However, as noted above, the detailed characteristics of the mortality risk change and the underlying population are often unreported in primary studies. This is especially the case for studies published in academic journals given that their focus is often on methodological tests of valuation methods rather than on reporting monetary estimates. Hence, such studies may lack the type of data required for a meta-regression analysis, leading to challenges in obtaining such data.

Nevertheless, the resulting meta-regression functions explaining variations in VSL can be combined with collected data on the independent variables that describe the policy context to construct an adjusted VSL estimate. The regression from a meta-analysis looks similar to the benefit transfer function in Equation ‎2.4 above, but a set of variables capturing the differences across valuation methods must be added. The importance of accounting for heterogeneity in valuation methods cannot be overemphasised, as meta-analyses typically find that differences in valuation methodologies explain a significant part of the variation in mean WTP (or direct VSL) estimates across sampled studies. Chapter 4 provides a detailed discussion of the meta-analytic approach used in this report.

The valuation of mortality risks among individuals, and hence the derived VSL from RP and SP studies, can depend on a number of factors pertaining to the risk considered in the valuation, such as the cause of death (respiratory illness, cancer, road traffic accident), the beneficiary of the risk reduction (adults or children)7 and the mode of provision for the risk reduction (public programme vs. private good). Additional factors relate to when the risk reduction sets in (i.e. latency vs. immediate), whether people have some degree of perceived control and whether there is perceived dread. Beyond these factors, demographic characteristics such as health status, gender, religion, country and income could also influence how individuals value the risk change. Chapter 5 explores the role of key mortality risk factors in the meta-analysis by including selected factors as explanatory variables in the meta-regression and conducting a literature review of related existing evidence in order to consider the resulting implications for potential adjustments to base VSL estimates.

2.5.3. Adjusting the VSL over time

Often, CBAs need to consider mortality effects that are expected to occur over time and therefore need to estimate the VSL for the future benefits of a policy, which means that the VSL for a future date must first be estimated from today’s values based on growth in real income over time, and then be discounted to the present value of those future benefits using a social discount rate. The present value of a statistical life saved at a future point in time can therefore be written as a modification of Equation ‎2.4 above:

Equation ‎2.5

${{VSL}_t|}_{t0}={VSL}_{t0}{\left(\frac{Y_t}{Y_{t0}}\right)}^{\beta }{(1+\delta )}^{-(t-t0)}$

Where $t$ is the time of the future VSL, $t0$ is the present time to which the future VSL is discounted, ${VSL}_{t0}$ is the VSL at time $t0,$ $Y_t$ is the real income at time $t$, $Y_{t0}$ is the real income at $t0$ and $\delta$ is the social discount rate. The role of the income elasticity $\beta$ is discussed further in Section 5.2 of Chapter 5.

References

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Notes

← 1.  As well as fatalities among their broader population, indicating altruism (Long, 2022[23]; Robinson and Hammitt, 2011[21]).

← 2.  Note that both RP and SP studies assume that the individual making the choices that trade off risks for costs/income has a complete understanding of the risks and that their valuation of these risks is stable over time.

← 3.  Smith, Van Houtven and Pattanayak (2002[19]) suggest a less frequently used preference calibration transfer method. This method assumes a specific form for preferences and uses available benefit information to identify and calibrate preference parameters to match the existing benefit estimates.

← 4.  For a discussion of the differences between GDP per capita and the income measures used in most VSL studies, see for example Robinson et al. (2019[20]).

← 5.  Empirical evidence indicates that the age-VSL relationship may take different forms or shapes (e.g. inverted U-shape) (Aldy Seamus J Smyth et al., 2014[26]; O’Brien, 2018[22]; Viscusi and Aldy, 2003[17]).

← 6.  For example, the 2003 cost-benefit analysis by the US EPA (USEPA, 2003[18]) which applied a 37% social discount to the VSL of individuals over 70 years old, was heavily criticized, leading the US Congress to prohibit the use of age adjustments in the cost-benefit analyses conducted by Federal agencies (O’Brien, 2018[22]). More recently, similar ethical debates have arisen regarding the COVID-19 pandemic (Carrieri, Peccatori and Boniolo, 2020[25]; Ehni and Wahl, 2023[24]).

← 7.  More generally this pertains to whether the beneficiary of the risk reductions is a private (adult) individual or someone in addition to or instead of that individual (sometimes termed “public” risk), which may introduce complications regarding how to deal with altruistic preferences.