Research and analysis

Annexe 4

Published 28 July 2020

RQIV: Is it possible to derive a context-free Value of a Life Year for application across different policy contexts?

1. Introduction

1.1. Background and Coverage of this research question (RQ)

It may be the case that a “contextless” Value of Life Year (VOLY) is preferable for policymaking. This may be due to its (potential) portability across domains, but might also be because it accords with the ethical principle that a risk reduction that generates an equivalent gain in life expectancy should be considered equally valuable, regardless of the policy domain and regardless of the recipient. However, there may exist instances where a compelling argument could be made to depart from this position, for instance because the preferences of the general public would suggest weighting the VOLY in certain contexts.

The primary purpose of this chapter is therefore to review the literature to establish whether there are contextual features that are so clearly important that they may justify adjusting a VOLY relative to a standard VOLY employed elsewhere^{[footnote 1]}, either within or across government departments. We do not take into account the quality of each study per se and instead examine the results with a view to identifying any consensus, or lack of consensus, with respect to the likely effect different contextual features might have on the size of a VOLY, (or Quality Adjusted Life Year (QALY) or Value of a Prevented Fatality (VPF)^{[footnote 2]}). At present, there is only limited evidence about how contextual features might influence the VOLY, and as such much of the review deals with literature that was conducted in the context of the VPF and, where appropriate, QALY and VPI.

Much of this chapter is devoted a review of contextual factors that theory suggests should matter: the age of respondent (both at the time of policy inception and timing of the risk reduction); and discounting. For each, we set out the theoretical arguments for their influence on the value of reducing risks to life and health, and then provide detailed coverage of the relevant empirical literature. Clearly age and discounting are not the only ways that context could conceivably influence the value, in terms of public Willingness-To-Pay (WTP), of a risk reduction. We therefore begin by addressing the many other possible contextual features. However, there are 2 important caveats that mean it is difficult to unambiguously identify these contextual effects.

The first caveat relates to selecting the contextual features for consideration. There are potentially limitless different contexts, with a wide range of features illustrated below and in Schedule A. Perhaps more importantly, there is little consensus on what constitutes a contextual feature. In the VPF literature, which is more established than that for the VOLY, context has often been interpreted to mean the place that the accident occurs, for example in road, rail or air accidents (Chilton et al., 2002; Covey et al., 2010; Carlsson et al., 2004). Alternatively, context has been interpreted to mean the cause of the death, for example by air pollution (Rowlatt et al., 1998; Alberini and Ščasný 2010), murder and drowning (Chilton et al., 2006) or cancer (McDonald et al., 2016, which also identifies 11 other papers relating to this particular context). Many other potential features have been suggested in addition to place and cause of fatality, and some of these are controversial: for example, the ‘probability’ is listed in Schedule A, but Chilton et al. (2006) argue that context (or more specifically the ‘dread’ invoked by different accident types) should be treated as a separate entity to the risk (i.e. the probability) of death per se. Following Sunstein’s (1997) paper Bad Deaths, ‘dread’ is often treated as a contextual feature in its own right. Rather than dwell on this point, we simply note it as a potential problem for estimating the VOLY.

The second caveat is that any findings about context might be confounded by elicitation method effects, the baseline risk that respondents face (Carlsson et al., 2010a), or the extent to which respondents understand the elicitation task (Savage 1993). Behavioural biases, such as being willing to pay more in earlier questions and less in later questions (Hammit and Liu, 2004), might also generate differences in responses that could be misattributed to context. Statistical issues such as multi- collinearity (Dekker et al., 2011; Chilton et al., 2002) and extremely wide confidence intervals around central tendency measures, may also affect the interpretation of results (Cameron et al. [2009] discuss this in the context of WTP for different type of illness, and argue that the resulting loss of information makes it too restrictive to be valuable from a policy perspective).

Despite these caveats, in this chapter we have identified a broad range of possible contextual features, mainly in the context of the VPF, that might be considered important in the decision whether to implement a standard VOLY, or else whether to adjust the VOLY to reflect the contextual features of a risk reduction. The review of academic literature is supplemented by a survey of stakeholders [not yet completed], which was undertaken to account for the fact that there may be contextual features of direct relevance or importance to policymakers that have not been addressed in the academic literature. Combining the findings of the survey and the search of the academic literature will result in a longlist of contextual features that will eventually be consolidated into a shortlist of factors that might be accounted for in any new primary research.

In what follows, we first set out in Section 2 the literature search strategy and provide an outline of the information that was extracted from the literature in respect of them. Section 3 reports on the stakeholder survey (not yet completed). Section 4 reviews the literature on the role of age and time preferences and Section 5 discusses behavioural biases and heuristics Section 6 is an overall summary.

2. General contextual effects

2.1. Literature Search Strategy

Our initial search looked to identify studies which explored how contextual factors may influence WTP for mortality risk reductions. Newcastle University LibSearch^{[footnote 3]} and Google Scholar were the 2 databases searched and the key words were as follows:

‘VSL’ OR ‘Context’ OR ‘Dread’ OR ‘risk’ OR ‘Contextual’

Combinations of the above were also used. We restricted the search to papers written in English, published after 1989. The initial search returned 3,055 results. From these, the abstracts and titles were reviewed and a shortlist was made. In addition, literature reviews within a range of academic papers were checked to ensure as complete a coverage as possible.

This strategy provided us with 28 articles, all detailing contextual factors and whether they had an impact on WTP or not. 4 additional papers found which did not quantify a VPF from elicited WTP values, but discussed contextual factors in a manner useful to this enquiry, so they were retained to give a total of 32 articles. These articles were reviewed using a data extraction tool customised to extract information on contextual effects in a systematic way across all studies in full and contained quantifiable studies.

2.2. A note on Contextless VPFs

Prior to the detailed literature review of contextual features, we draw attention to the relative lack of information in the literature regarding a ‘contextless’ VPF. This is potentially important, since it has some implications for the notion of a ‘contextless VOLY’.

Only a very few studies presented a contextless VPF, derived either indirectly or directly. Alberini and Ščasný (2010) suggested 2.07 million euros for a public provision Value of Statistical Life (VSL)^{[footnote 4]}. A particularly high derived VPF value of 30 to 110 million UK pounds was reported in Cookson (2000), although the nature of the sample (parent), the aim of the study (health valuations) and the framing (lives saved) may reduce its reliability as a “reference” contextless VPF, even though the study was carried out in the UK. Robinson et al. (2010) found that contextual questions produced different responses to the generic questions and concluded it is unlikely a generic value for “bad deaths” could be estimated. Tsuge et al. (2005) estimated VSLs for general accident risks, cancer risks and heart disease risks in Japan and concluded that there was no strong evidence to adjust the accident VSL for difference in the other types of risks, although whether a general accident risk mapped completely to a contextless VSL was an open question.

Thus, even on the basis of the VPF literature there is little evidence on which to conclude whether a contextless VOLY could be viable. Nonetheless, contextless risk- risk trade off questions (see the literature review addressing RQII) have been successfully applied in the field (Chilton et al., 2006; Nielsen et al., 2010). This suggests that preferences over mortality risks can be elicited in a scenario free from context, but there is no evidence currently available to indicate that it could be achieved in a WTP framework, where removing all context from the decision may make it difficult for respondents to report a valuation.

2.3. The Effect of Context on VPF: Evidence from the Literature

In the following, we group the contextual variables in terms of the degree to which we are confident - based on findings in the literature – that they have a significant effect on the VPF and, further, their apparent policy relevance. Where possible, we source the definition of the feature in question directly from the literature. This approach assumes that contexts that are significantly important in determining the VPF are good candidates for consideration in the VOLY context. Of course, the transferability of any context effects between the VPF and VOLY frames is ultimately an empirical question, and judgements of the appropriateness of their use as a basis for adjusting policy values is beyond the scope of this literature review.

2.3.1. Contextual effects with an identifiable impact on a VPF

Dread (“How worried/ nervous respondents are when asked about a certain risk” [Savage, 1993]). Dread has been extensively researched. There is some evidence to suggest that death by cancer is dreaded e.g. Magat et al. (1996), Alberini and Ščasný (2013), although in these studies dread effects were not separated from the effects of timing of fatalities. The finding that cancer is a dreaded fatality type was validated in the context of contemporaneous cancers by McDonald et al. (2016). Carlsson et al. (2010a) found self-reported worry (dread) was positive and significant in all 3 contexts that they tested (road accidents, fire and drowning) although the respective VSLs varied quite significantly (for example, 20 million Swedish Krona (SEK) for road accidents compared to 12.6 million SEK for drowning accidents). Alberini and Ščasný (2010) also noted that for each ‘dread point’ on their scale the VSL increased by 0.322 million Euros. Chilton et al. (2006) found strong evidence for that WTP was larger for dreaded deaths, with VPF estimates ranging from 0.36x106 for drowning to 1.98x106 for death in a public fire, with the ‘dread effect’ for each context measured relative to murder as the reference context^{[footnote 5]}. Van Houtven et al. (2008) also found evidence of a premium for cancer, but this premium was lower for those individuals who previously experienced cancer. This is interpreted as indicating adaptation, or that the reality of the experience of cancer is less bad than the dread of it. However, this result was not statistically significant.

Ostensibly then, it appears that if a cause of death is particularly dreaded, the associated VPF is larger than for a less dreaded fatality risk. However, this result may not be robust once other factors are controlled for. For example, the ‘dread premium’ noted in Chilton et al. (2006) more or less disappeared when baseline risk was controlled for. Similarly, the cancer to road accident VPF ratio observed in McDonald et al. (2016) reduced to 1:1 after a ten year latency period, or if the morbidity period preceding death was held constant across the fatality scenarios. Similarly, Robinson et al. (2010) noted that a large proportion of respondents stated that they were WTP more in the cancer case because ‘one to 2 years suffering was painful’ suggesting that morbidity effects were a significant driver of the cancer premium.

Responsibility. (“Blame” variable: “those who die bore responsibility for their fate” [Mendeloff and Kaplan, 1989]). Although heavily linked to voluntariness (see below), the literature suggests a strong relationship between responsibility and WTP. Carlsson et al. (2010a) found that respondents reported higher WTP if a road traffic accident was caused by someone else. Covey et al. (2010) found a similar relationship, showing that WTP for passenger deaths in single fatality collisions was higher than WTP for trespasser deaths. Respondents in the study by Mendeloff and Kaplan (1989) reported higher WTP to avoid death by obstacles in the road (for which they were not responsible) compared to death from pollution (which they felt responsible for to some degree). Wolff and Orr (2009) drew attention to the lower VPF implied in circumstances where a passenger does not possess a valid ticket as the train operator was no longer responsible for their safety, and hence could not be held responsible for their death.

Thus, prima facie, public preferences have been shown to imply a higher VPF for causes of death that individuals are not at least partly responsible for^{[footnote 6]}.

Age/year of birth. This feature is relevant from a theoretical as well as an empirical point of view and is discussed in detail in Section 4.2 of this chapter.

Immediacy/latency. (Whether risks and reductions “take place now or at some delayed point in time” [Tsuge et al. 2005]). This feature is relevant from a theoretical as well as an empirical point of view and is discussed in detail in Section 4.3 of this chapter.

Controllability. (“How much control people have over the risks”; [Chilton et al. 2002]). In general, the less control people perceive that they have over a type of risk, the higher the WTP for its reduction. Alberini and Ščasný (2013) argued that cancer mortality risk reductions are valued more highly partly due to their low perceived controllability. Robinson et al. (2010) found that their respondents believed railway travel should be safer than road travel due to the lower degree of control that rail passengers have over their safety compared to car drivers. Similarly, Rowlatt et al. (1998) suggested a 50% premium for an accident on the underground relative to roads, since safety on the underground is outside the individual’s control. Vassanadumrongdee and Matsuoka (2005) found a significant and positive relationship between controllability and WTP in the context of air pollution. It is important to note, however, that a number of studies found this factor to be insignificant (Tsuge et al., 2005; Carlsson et al., 2010a; Chilton et al., 2002). Clearly, controllability is closely linked to voluntariness (see below) and responsibility (see above).

Although prima facie, public preferences have been shown to imply a higher VPF for causes of death over which people have less control, the evidence is less conclusive than in the factors above.

Voluntariness. (“How much choice people have over being exposed to the risks”; [Chilton et al., 2002]). Voluntariness captures the degree to which exposure to a risk depends on a person’s voluntary behaviour. Subramanian and Cropper (2000) found that reducing the risk of death by installing air bags was valued lower than reducing risks from automobile emissions, arguably due to the voluntariness of driving compared to being exposed to emissions from cars. Wolff and Orr (2009) observed that many risks that are self-induced. They suggest that the risk of smoking-related skin/lung cancer is self-induced (individuals make the decision to smoke), and skin/lung cancer have been shown to generate the lowest WTP values due to this perceived voluntariness (a point also noted in Cameron et al., 2009). Tsuge et al. (2005) also found voluntariness to be a significant variable although Chilton et al. (2002) and Vassanadumrongdee and Matsuoka (2005) found no evidence in support of this factor.

Thus, although prima facie, public preferences have been shown to imply a higher VPF for causes of death where exposure to the risk in involuntary, the evidence is again less conclusive than for some of the factors above.

Private knowledge. (“Family or friend has faced the risk; [Mendeloff and Kaplan, 1989]). Familiarity with the cause of death can influence WTP to reduce it. For example, Vassanadumrongdee and Matsuoka (2005) found a significant and positive correlation between personal knowledge and WTP in the context of air pollution. Alberini and Ščasný (2013) showed an increase of 0.516m in the VSL from people with experience of a bad death, in line with Carlsson et al. (2010a) who found that respondents who had experience with the risk of fire had a higher WTP in this context than did those with no experience. Alberini et al. (2012) found a significantly greater VSL for those who had personally had cancer. However, they found that having friends and family who had had cancer generated a positive but insignificant effect. The positive but insignificant effect was also reported by Tsuge et al. (2005). Savage (1993) found a negative and significant variable for all modes of death when taking into account private knowledge.

Thus, prima facie there is some evidence to suggest that public preferences imply a higher VPF for causes of death for which the respondent has some experience, but the evidence is again less conclusive than for some of the other factors above.

2.3.2. Contextual effects with a possible but indeterminable impact on a VPF

Size of the probability of the risk. (“Magnitude of the risk reduction”; [Beattie et al., 1998]). There are 2 interpretations of this: the size of the risk change, and the size of the baseline risk. Baseline risk effects are discussed later under “baseline risks”, and so this discussion relates to the size of the risk change. This has been studied in 2 ways – by changing the size of the risk reduction a policy will generate (e.g. Jones- Lee), or by describing policies as helping different numbers of people (e.g. in a Person Trade-Off study). Theoretically, for small risks, WTP should increase linearly in the size of the risk change, leaving the VPF unchanged. However, scale effects, meaning the lack of a proportional increase in WTP as the risk change increases in size, have been found by many studies, including Hammit and Graham (1999), Hammit and Liu (2004),Carlsson (2004) and Carthy et al (1999).

Size and Duration of harm. (“Length of illness”; [Cameron and Deshazo, 2013; McDonald et al., 2016]). WTP might be expected to increase with a larger and longer harm. Robinson et al. (2010) note that many people prefer car driver deaths to rail passenger deaths and cite the reason as the degree of suffering involved in the latter. The relationship may be nonlinear. For example, McDonald et al. (2016) demonstrated that, when the length of illness prior to fatality from cancer increases, the cancer VPF/road VPF relativity increases at a decreasing rate (McDonald et al., 2016). Cameron and DeShazo (2013) show similar evidence, but note that morbidity valuation difference between 0.1 and 5 years is not significant. Whilst there does seem to be evidence to indicate some effect of the nature or duration of the harm, there is little insight into why this might be the case and much is left unresolved, meaning that it is difficult to conclude very much with any certainty on the importance of this factor.

Expert/public knowledge (“how much experts know about the risk”; [Chilton et al., 2002]). There has been limited investigation of this potential factor in the literature. What evidence there is appears contradictory. Evidence that people are WTP more to reduce risks perceived to be less well known by experts/scientists is provided by Vassanadumrongdee and Matsuoka (2005), although no statistically significant effect was found by Chilton et al. (2002). Tsuge et al. (2005) presented contradictory evidence suggesting that people preferred to reduce risks that were perceived to be well-understood by experts, although this became statistically insignificant when interacted with the risk reduction. Rowlatt et al. (1998) and Slovic (1987) also raised the possibility that this factor might matter but did not conduct any formal testing.

Public/private programme (“whether risk reduction programs are delivered by a public or private program”; [Alberini et al., 2012]) Alberini and Ščasný (2013) note that the WTP was significantly higher when a program is publicly funded than privately funded. Similarly, in 2012, Alberini et al. found a VPF to be 0.950 million euros higher when risk reductions for cancer come through a public programme. In their 2010 paper, Alberini and Ščasný noted that a VSL was around 2 million euros higher in general when delivered by a public programme. Conversely, Dekker et al. (2011) found people were willing to pay less for mortality risk reductions that were presented as a public good. These conflicting findings may be due to differing degrees of altruism and free riding (for public goods) in the different samples.

Baseline risk. The baseline risk of fatality is theoretically predicted to matter in determining individuals’ WTP for risk reductions (for example, Smith and Desvouges, 1987). Carlsson et al. (2004) identify a higher WTP for risk reduction with higher baseline risks. In contrast, Carlsson et al. (2010a) found higher WTPs for low baseline risk levels for 3 types of accidents. Cancer mortality risk reductions were valued more highly than other causes (Alberini and Scasny 2013), although this may be due to high dread/low controllability, lack of control of latency impacts or, as suggested by the researchers, the fact that low baseline risks may be hard to perceive. This factor is also considered in the Age section of this chapter (4.2). On the other hand, the size of probability of risk was reported as insignificant by Chilton et al., (2002). Instead of objective risk, it is often stated that the perceived risk is important for evaluating risk reductions (e.g. Beattie et al. [1998] found that respondents perceived that their own household’s fire risks were much less than road traffic risks and their WTP across the 2 contexts reflected this perception). Chilton et al. (2006) also explicitly controlled for perceived baseline risks in their estimation of the context effects in the VPF. However, Vassanadumrongdee and Matsuoka (2005) suggested that risk perceptions may have only small impact on people’s preferences.

An issue related to the risk of a specific type of fatality, but importantly different, is the background fatality risk: the probability of dying from any other cause. Eeckhoudt and Hammitt (2001) develop this argument by discussing the ‘why bother effect’ whereby people with a high background risk of death are likely to perceive reductions in specific fatality risks as less significant, reducing their WTP for these.

Overall, baseline risk appears to influence WTP, although the direction and size of this effect is not clear from the current literature.

2.3.3. Other contextual effects

Mass Casualty. (Catastrophic and/or has potential of harming many people). It has been suggested that people may be WTP more per fatality when a single accident has an impact on a large group of people, than when the same number of people would be killed in separate incidents. For example, ten radiation deaths due to a nuclear power station in one area might be considered worse than ten individual deaths due to radiation spread around the UK. Wolff and Orr, (2009) argue that a higher weighting may be placed on multiple fatalities in this case because of the “underlying maldistribution of risk”, but provide no empirical evidence about public support (or otherwise) for such an adjustment. Savage (1993) postulated that a mass casualty premium might be linked to dread, as dread is greater when the fatality is from a catastrophe, and Slovic (1987) commented on the catastrophic nature of nuclear power, but again neither study provided any empirical evidence.

In fact, in contrast to this speculation, most empirical studies find that individuals do not value a “mass casualty” risk reduction more highly than a separate casualty risk reduction. For example, Chilton et al. (2002) found no evidence of a premium for rail accident fatalities over road accident ones, and Covey et al. (2010) found direct evidence that “a multiple-fatality accident was not accorded a significantly higher value than the prevention of death in the single-fatality case”. Jones-Lee & Loomes (1995) presented early evidence against a premium for victims in mass casualty accidents.

Rowlatt et al. (1998) described the difference between a non-catastrophic dread and a catastrophic dread as a ‘scale premium’, but their report suggested:

The research resoundingly rejected the hypothesis that preference-based values of statistical life for large-scale Underground accidents or third-party accidents to resident of areas close to airports should be set at a premium relative to the values for small-scale accidents.

(Rowlatt et al., 1988 p. 25)

Cookson et al. (2000) and Robinson et al. (2010) both reported evidence related to the number of fatalities, but these were not obviously described as happening in the same incident.

Thus, prima facie, it appears that there is no evidence to support a higher VPF for causes of death which generate mass casualty.

Rule of rescue (“Different risks have different values attached to them by society”; [Wolff and Orr, 2009]).This feature relates to cases where a person is in imminent peril Wolf and Orr (2009) provide the example that certain drugs are not always funded by the NHS if official guidelines are followed, yet if a group of miners are trapped then society will do everything it can to save them, constrained only by the available facilities to help them. Although individuals in intensive care may have the same survival probabilities as the miners, excess weight may be given to the miners as they are ‘identifiable victims’. Overall, though, this factor has received little attention in the literature in general and none in the VPF literature. This may well reflect the fact that, to a degree, Cost Benefit Analysis is largely silent on how to act in such cases of imminent peril. As noted in the current Treasury Green Book, imminent peril is an example of an issue that defies explicit monetisation, but should nevertheless be noted when presenting a CBA, as a factor that decision makers need to consider. Its main role in this context is as a tool for a priori assessment of policies that may, at some stage, be called upon at times where the risks are imminent.

Variability in probability of the risk. We interpret this to mean how the probability of the harm differs across individuals or groups and/or over time, generating uncertainty about the risk. To our knowledge, no literature addresses this factor. Wolf and Orr (2009) note that some people often enjoy an element of risk, although this point relates more to the risk preference of the respondent than to the characteristic of the risk itself.

Variability of harm (riskiness). We interpret this to mean how the size of the harm differs across individuals or groups and/or over time, generating uncertainty about the harm. To our knowledge, no literature addresses this factor.

Gain in health vs Loss in health. Behavioural economics predicts that the typical individual’s willingness to pay for a gain in health will be significantly less than his/her willingness to accept compensation for a similar loss in health. Clear evidence in support of this point in the context of the VPF is provided in Carthy et al. (1999) and in Guria et al. (2005). Given the empirical evidence for these asymmetries, the choice of a gain or loss frame for elicitation procedures will be important and may be a cause for disparity between existing estimates of the value of risk changes.

Single Harm vs Multiple Harm. Dekker et al. (2011) found that WTP rises if more people within the household benefit from a private risk reduction. For more discussion on this point, please see Mass Casualty above. There is no evidence to our knowledge about whether WTP increases additively for policies that reduce risks of multiple different harms at the same time, although evidence from environmental economics on the Embedding effect (for example, Kahneman and Knetsch, 1992; Hanemann, 1994) suggests that this may not be the case.

Personal Exposure. Mendeloff and Kaplan (1989) found that people rated reducing barrier risk more highly than construction falls, suggesting a higher value for risk to oneself. Savage (1993) and Tsuge et al. (2005) found a similar pattern. However, Cookson (2000) found that many people have bequest values and prioritise reducing risks for their children over reducing risks for themselves. Alberini and Ščasný (2011) found a higher VSL for children than for adults in the Czech Republic.

Public Exposure. It might be the case that people are willing to pay more for risks that reduce public exposure to risks, as opposed to private exposure just to oneself. Alberini and Ščasný (2013) found that the VSL was around 0.402m larger for common risks, although this was only significant at the 10% level. Subramanian and Cropper (2000) found that environmental programmes had a higher WTP than non- environmental risks, although there could be other reasons for these preferences due to differences between the elicitation scenarios. For example, in the public risk reduction, preferences for aesthetics and purer water may have driven these preferences, rather than a pure “public exposure” effect. Alberini and Ščasný (2010) found VSLs to be 0.918 million euros greater when risk reductions were delivered by a public programme, although they also found evidence of double counting. That is, individuals may have added WTP for the risk reduction to other people, but if those people are also stating WTP for their own risk reduction, this would double count the benefit to those individuals. This is a strong argument for elicitation procedures to use private risk reductions (see Jones-Lee [1991] for a discussion of altruism and double counting).

Media attention. This captures the possibility that, for example, the fact that deaths in airplane crashes receive more press attention the deaths of typical cancer patients may drive up WTP to reduce such high profile risks. However, whist Chilton et al. (2002) found that WTP and media attention were positively related, this factor became insignificant once controlled for in the subsequent analysis.

Technology induced or natural hazard. With the growing reliance on technology- enabled devices, smart appliances, autonomous vehicles and Artificial Intelligence, this feature may become increasingly important in the near future. However, to date the only study to consider this factor is a conference paper by Rohrmann (2008) who suggested that judgements are more negative for technology induced hazards than for natural hazards, possibly because one can allocate blame in the case of technology induced hazards.

Regulation of health and safety in the workplace. Wolff and Orr (2009) describe this as the value that is placed on peoples’ safety in the work place relative to their safety at home or in public. Alberini and Ščasný (2010) found that the VSL increased by 0.422 million euros if the exposure to the risk occurred in the work place. This may relate to the features of Voluntariness, Responsibility and Controllability referred to previously.

Externalities. Externalities are the unintended consequences, positive or negative, of a private transaction. In the context of safety and risk reductions, reducing a risk may have extra benefits, for example by improving the attractiveness of an area due to reductions in pollution. This factor is difficult to capture in contextual sense, and most studies aim to limit the effects of externalities rather than explicitly study them, so as to isolate the value of the risk reduction under investigation. However, Subramanian and Cropper (2000) noted that a key feature of public health programs was that they serve people one at a time, whereas an environmental health program delivers a reduction in exposure to all. A very obvious additional externality is the effect illness or death has on loved ones and carers (which, is at least in principle, captured in VPF).

Gender. A number of studies have examined whether VSL varies by gender, although the overall evidence is inconclusive. Alberini and Ščasný (2013)^{[footnote 7]}, and Alberini and Ščasný (2010, 2011) found a lower VSL among women whilst Carlsson et al. (2004) found a higher VSL for women. Carlsson et al., (2010a, 2010b) and Hammit and Liu (2004) found no significant differences in WTP according to gender.

Occupation. Chilton et al. (2002) found a weak relationship (insignificant at the 5% level) between the respondents’ occupational status and their prioritisation of certain risks. Covey et al. (2010) found that those from higher social groups discriminated more between 2 types of work-related risk (a rail worker that had a lack of training vs a rail worker that broke the rules). Other than this, there was little discussion of occupation, particularly in a role as a potential contextual factor. It is possible that effects related to “virtuous” occupations may alter WTP for other people’s safety, but we are aware of no evidence on this point.

He/she a member of the population at risk. This refers to whether the respondent feels that they are a member of the population subject to a given risk (Chilton et al., 2002). There is very little evidence in the literature on this factor, although Sunstein (1997) observed that respondents were indifferent between cancer deaths and airplane deaths, even though the populations at risk varied.

Rarity. There has been some examination of this issue in the health economics literature. Rare diseases are those that are characterized by low prevalence (Copley- Merriman, 2018). Medicines for rare diseases (commonly known as orphan medicines) are typically more costly than those for common diseases and as such, a small number of studies have been conducted to elicit public preferences for giving additional weight to funding treatments for rare diseases. Typically studies have found that the public does not support giving priority for the rarity of the disease (Gu et al., 2015, Bourke et al., 2018).

Health compared to average health. Alberini and Ščasný (2013) observed that respondents were generally in good health but did not explicitly estimate the impact of this on a VSL. Cameron and Deshazo (2013) controlled for the health of respondents, presenting individuals with specific illness profiles appropriate to their gender and age. Rowlatt et al. (1998) suggested a downward adjustment of the VPF, as most people at risk of suffering acute mortality effects are older people and already impaired. Chilton et al. (2002) discuss how in valuing risk reductions respondents may wish to take into account their own personal risk level (above/below average risk) which is at least partly health dependant although perceived personal risk was negative and significant at the 10% level in only one of their models. Sunstein (1997) proposed applying a distributional weight to given risks e.g. AIDS, asthma etc. which are specific to certain groups of people. Thus, relative health states might matter in a mortality risk valuation, but whether it is best treated as a contextual or a methodological feature is an open question.

Age of person at risk compared to average age. Age as a contextual factor is given significant attention in Section 4.2 of this chapter. We interpret the present subsection as specifically referring to whether a person is older or younger than the average person at risk from this cause of fatality. Mendeloff and Kaplan (1989) found that older adults gave higher ratings to cancer/pollution risks but students gave these same risks much lower ratings, perhaps due to the difference in the students’ own age from the typical age of a person at risk from cancer and air pollution. Carlsson et al. (2010b) also showed that people tended to care most about people in their own age range, with older people placing higher weights on saving older people and respondents with children placing higher weight on saving children.

2.3.4. Summary of contextual effects

Table 1 contains an indicative summary of the relative importance of contextual factors in the context of a VSL, based upon the review of the empirical literature that aimed to explore public preferences for different contextual features of a risk reduction scenario. These are categorised by importance according to the degree of consensus in the literature and our own perceptions of their policy relevance.

Table 1: Contextual factors and the VSL

	Systematic	Mixed Evidence
Highly important factors	- Immediacy/latency - Age/year of birth - Dread Responsibility - Gain vs Loss in health	- Controllability - Voluntariness Private - Knowledge
Moderately important factors	- Size and duration of harm	- Size of the probability of the risk - Expert Public knowledge - Baseline risk Public/private programme

	Systematic and Mixed Evidence
Irrelevant factors and/or little or no evidence	- Mass causality - Variability in the probability of the risk - Variability of harm - Personal Exposure - Public exposure Media Attention - Technology induced or natural hazard - Regulation of health and safety in workplace - Externalities - Gender Occupation - Member of population at risk - Rarity - Health compared to average health - Age compared to average age - Rule of rescue

Certain contextual features have been shown to impact a VSL valuation, either increasing it relative to an average VSL or decreasing it. In many cases though the nature of the impact is indeterminate, not least because, with a couple of notable exceptions (Chilton et al., 2006; McDonald et al., 2016) the experimental design is such that it fails to unambiguosly isolate the impact of the contextual feature of interest. For example, studies that attempted to compare public and private risk reductions, or environmental and non-environmental risk reductions, may have captured preferences for “irrelevant” features such as the impact on the beauty of the local environment, the impact on local wildlife and so on, instead of purely isolating the effect of interest. More problematically, some of the important contextual features may be impossible to empirically disentangle with any degree of confidence. The review above highlighted the interdependency between controllability, voluntariness and responsibility and outlined the difficulties in separately identifying these effects. Nonetheless, the sheer volume of studies reviewed, each of which has addressed at least one of a wide range of contextual features, suggests that even if it is decided that it is preferable to use a standard VOLY in policy appraisal and evaluation, it is crucial to understand that the values in the literature depend heavily on the context under which they were elicited.

3. Report on the stakeholder survey

In addition to understanding what contextual features have been found in the literature, we also conducted an online survey with the participating government departments and agencies to exploring contextual features that might affect the VOLY^{[footnote 8]} that they would use in policy appraisal. The purpose of this survey was to determine if there were contexts that had not been identified by the existing literature reviews and provide insight into any areas for future research in any proposed empirical study.

The online survey included 15 different ‘contexts’ based on a list provided in Schedule A of the Service Requirements for the project. For each of these we were interested if they might result in the application of a non-standard (or context dependent) VOLY. In addition to this standardised list, each department or agency could provide details on any additional contextual features that they considered to be missing or if there were any that would never be considered acceptable grounds for applying a non-standard VOLY.

In response to the survey no additional contextual features were suggested. There were very few specific contextual features from the standardised list from which the departments or agencies indicated they might take account of. Age and dread factors were contextual features of interest, both of which have been extensively reviewed within RQIV.

In general, the departments and agencies highlighted the importance of the identification of a VOLY that is context free or at least is clear on the specific context in which it was derived. In some response, the role of context was presented as a normative or political decision which is separate to the values used in the appraisal process.

The results of the survey indicate that the contextual features that were reviewed in RQIV were those that were important to the stakeholders, but further empirical work with the group may be considered before the conduct of a large scale study to estimate a VOLY. Next, we turn to consider aspects of the timing of the risk reduction. Specifically, we consider age and latency effects. As mentioned in the introduction, since there is a well-defined theoretical framework for considering these features, as well as a broad empirical literature for each, we give these features much more detailed consideration than the other features previously outlined.

4. Timing and the value of risk reductions

4.1. Introduction

The standard VPF model (e.g. Jones-Lee, 1974) was developed for the case of an immediate, one-period risk reduction which would be paid for in the current period. This means that the theoretically relevant construct to be measured is the marginal rate of substitution between current wealth and immediate risk. This approach is appropriate for dealing with the prevention of accidental fatalities by means of a one- period risk reduction with immediate effect such as a temporary speed restriction.

However, many (arguably most) policies designed to reduce the risk of fatality do not have this simple temporal structure. For example, policies to reduce air pollution involve ongoing benefits (and costs, whilst policies that reduce the risk of exposure to carcinogens, involve a cost incurred now that may reduce the risk of fatality after a period of latency or delay. Even a policy with immediate one-off costs delivering immediate fatality risk reduction may have ongoing benefits. For example, installing a speed bump may reduce fatality risk today and in the future. So how should benefits and costs in the future be integrated with more immediate costs and benefits? And how can these costs and benefits be evaluated in a consistent manner that respects the preferences of the population?

The issues around time and the value of reducing fatality risk are especially pertinent when considering the choice between using the VPF or the VOLY/QALY in public sector decision-making. If we hold the VPF constant for all applications, and in particular if we do not allow the VPF to vary with age, then it is not possible to maintain that each year of life expectancy is equally valuable. The other side of this coin is that if we wish to use a constant VOLY or QALY value, then a policy that reduces the risk of instantaneous fatality for an older population such that one fatality is prevented in expectation will be valued less than reducing the same risk of instantaneous fatality for a younger population.

Since the 1980s, scholars have begun taking account of the time structure of costs and benefits when assessing the value of preventing fatality. Theoretical and empirical developments have been proposed and debated, and this review attempts to set out the main findings and unresolved questions.

We identify 5 important temporal dimensions along which a fatality risk reducing policy option can be categorised:

i. One-period vs On-going risk reduction
ii. Age when costs are incurred
iii. Age when risk reduction happens
iv. Delay until costs are incurred
v. Delay until risk reduction happens

A thorough treatment of the first point is provided elsewhere in this Scoping Study. There, it is shown how the relationship between the value of a life year delivered by a one-period risk reduction and the value of a life year delivered by an ongoing risk reduction depends upon how life expectancy and future utility are discounted. The age and delay dimensions are closely inter-related. All else being equal, an individual evaluating a risk reduction that is delayed will also be evaluating a risk reduction that happens when they are older, compared to an immediate risk reduction. The delay (and hence the age effect) may relate only to the benefits of a policy (for example, the risk reduction itself) or may relate to the costs of the policy, or both. However, this is not to say that a risk reduction for an older person is necessarily delayed, nor that a risk reduction to a younger person is necessarily immediate. The interplay between delay and age has received surprisingly little attention in the literature, not least because of the difficulties in separating empirically the effects of age and delay. However, both age and delay have independently been addressed in the context of the VPF. In this review, we outline the main theoretical and empirical arguments about age and about delay.

4.2. Age and the value of reducing fatality risks

4.2.1. Introduction

This section outlines the key literature addressing age and the value of reducing risks of fatality. First, the theoretical literature is outlined, with the conclusion that there is no clear theoretical prediction about the effect of age on the VPF. Next, the empirical literature is considered, including Revealed Preference and Stated Preference evidence. The section concludes that there is no empirical consensus about the effect of age on the VPF.

4.2.2. Theory

In general, it seems straightforward to say that the value of a risk reduction increases in the value of whatever is at stake. In the case of fatality risk reduction, the stake might be assumed to be the total remaining lifetime utility that would be enjoyed if the fatality was prevented. From this standpoint, if an older person has fewer remaining years of life to enjoy, then the VPF (marginal rate of substitution between wealth and fatality risk) ought to decline with age. However, on closer inspection this simple viewpoint does not necessarily hold theoretically – the marginal rate of substitution of wealth for risk may not decline with age.

Theoretical models that directly address the age-VSL relationship have typically been life-cycle consumption models with a budget constraint. An early, seminal contribution is by Shepard and Zeckhauser (1984). They use a lifetime consumption model in which agents choose between consumption and improving their survival probabilities. Willingness to Pay for a risk reduction is shown to depend both on future lifetime utility and on the increase in the stock of resources that can be built up if survival occurs. This combines to generate an inverted U-shape relationship between VSL and age.

Rosen (1988) also presents an intertemporal consumption model, assuming that the value of life is equivalent to the present value of consumer surplus remaining. Rosen demonstrates a negative relationship between age and the value of eliminating risk, but highlights that extending life involves adding another period’s consumption to the remaining utility function, but also reallocating consumption away from all other periods.

A second wave of theoretical papers emerged in the 2000’s that updated the earlier theoretical contributions. These papers challenged the notion that VPF must decline with age after middle age, and typically demonstrated that the effect of age on the VPF is theoretically ambiguous. Ehrlich (2000) developed a model that incorporated a new idea: that the timing of the end of life is uncertain and life expectancy is endogenous, depending on choices between consumption and probability of survival. He distinguishes between human capital and non-human assets. In a model incorporating optimal choice of life insurance and annuities where these are actuarially fair, he demonstrates that value of life ought to rise with age “as long as the accumulation of non-human assets rises sufficiently faster than the eventual decline in the value of human wealth due to the contracting life expectancy”. The increase in VPF with age reflects the increasing marginal utility that ought to be derived from risk reductions later in life. However, the value of life declines at advanced age as human wealth runs out.

Theoretical advances based on dynamic risk reduction models are also provided by Johansson (2001, 2002). In the first contribution, provocatively titled “Is there a meaningful definition of the value of a statistical life?”, Johansson (2001) asserts that the one-period VSL model fails to generalise easily to situations where the risk reduction is ongoing (Although see Jones-Lee et al. [2015] for a solution). Johansson states that a dynamic model accounting for duration and timing of risk reductions is necessary to understand the value of ongoing risk reduction. Unless consumption is age-independent, there “seems to be no way to obtain an exact estimate of the monetary value of expected remaining present value utility”. Although the issue of age is not specifically addressed by Johansson in this paper, there is reason to suppose that consumption does vary with age, perhaps in an inverted-U relationship. This would lend support for the inverted-U pattern between the VPF and age.

Johansson (2002) does specifically focus on the age-pattern of the VPF and demonstrates that the VSL-age relationship is theoretically ambiguous. Specifically, Johansson defines the VSL as the ratio between remaining expected present value utility of a person aged π years, and the marginal utility of consumption at age π. Taking the derivative with respect to current age π reveals how the VSL changes with age.

Johansson demonstrates that the sign of this derivative depends on a number of different factors: the utility discount rate, the hazard rate (which depends on age), the loss in instantaneous utility as age increases, and the marginal utility of income as a function of age. Even with a market for actuarially fair annuities, it is possible for the VSL to decrease with age, but also to be constant, or increase, or display a complex pattern like the inverted-U. With annuities, the VSL is age-independent if the utility discount rate equals the market interest rate, the hazard rate is age-independent, and non-capital income is constant across the life cycle. Clearly, these restrictive conditions are unlikely to be met in reality.

A related element not explored in detail in previous papers is the background risk of mortality. Eeckhoudt and Hammitt (2001) explain how, when background risk is high, WTP to reduce a specific risk may become very low due to what they refer to as the “why bother” effect^{[footnote 9]}. Intuitively, if there is a high chance of fatality from one cause, there is relatively less to gain by reducing a different, specified risk since there is a chance they would not be alive to enjoy the benefit of this risk reduction. This effect puts a downward pressure on WTP. The authors do not specifically focus their discussion on age, and state that in typical empirical studies background mortality risk is low such that the typical approach of ignoring background risk is likely to be reasonable. However, when considering the value of reductions in risks to the elderly, for whom background risks are typically high, the “why bother” effect may become something to bother about after all.

2 summaries of the theoretical literature relating to the VSL and age are provided in Evans and Smith (2006) and Hammitt (2007). Both conduct reviews of the theoretical literature and conclude that there is no strong theoretical reason to suppose how the VSL varies with age. As Hammitt concisely states:

The results of multiperiod models are sensitive to assumptions about the relationship between the interest rate, the rate at which future utility is discounted, the terms under which an individual can borrow against future income; and the dependence of the marginal utility of consumption on age.

(Hammitt, 2007; p. 235)

Overall, the theoretical literature is inconclusive with respect to the relationship between the VSL and age.

A final point is to consider whose perspective matters when considering the value of children relative to adults. A good summary is provided by Dockins et al. (2002), who presented theoretical justification that the relevant perspective to take account of when valuing risks to children’s lives is the perspective of the parent; however they point out that the value of reducing risks to children might differ from adults through non-age reasons including involuntariness of exposure to the risk, uncertainty about the effects of risks and so on.

Overall, the theoretical literature is inconclusive with respect to the relationship between the VSL and age.

4.2.3. Individual Revealed Preferences

Revealed preference studies capture age in terms of current period trade-offs between wealth and fatality risk.

In the earliest empirical study using a hedonic wage approach to estimating the relationship between age and the value of a life year lost, Moore and Viscusi (1988) used data from the Quality of Employment Survey. They suggested a model in which expected life years lost were simply the fatality risk multiplied by remaining discounted life expectancy in a given period. Wages were regressed against this measure of life years lost, which gives the value of a life year lost. The authors conclude that when more life years remain, the value of an additional one (i.e. marginal value of a life year) is lower. Although they do not directly estimate the relationship between age and the value of life, the study is the first empirical paper to grapple with the issues of timing, age and the value of fatality risk reduction.

No revealed preference studies specifically aimed to study the effect of age on the value of fatality risk reduction until the early 2000s, which coincides with the second wave of theoretical papers that attempted to address this question. In 2003, Aldy and Viscusi set out to specifically study the effect of age on the value of fatality risk reduction. They found evidence of an inverted U-shape that characterised the VSL-age relationship in their data. The innovation in this study was the inclusion of age- specific fatality risk estimates (not just industry-specific estimates). Their inverted U- shape relationship supported some of the theoretical predictions, and contributed to the growing consensus that recognised the existence of this relationship at the time.

However, in 2004, Smith et al. analysed the Health and Retirement Study, which includes older workers and retired people. They discovered that the oldest, and most risk averse, workers actually demanded significantly higher wages to compensate for increases in job-related fatality risks, so their results were a strong contrast to inverted- U shape. Knieser et al. (2006) presented evidence that moved the consensus further away from inverted U. They showed that, controlling for consumption over the life cycle, then the inverted-U is much less pronounced. They even provide some evidence of a premium for the elderly. This comes from reallocation of planned life- cycle consumption over time, with deferred consumption to old age.

In a review of the revealed preference evidence as part of a Symposium on age and the VSL, Aldy and Viscusi (2007) conclude that “As we age, our life expectancy shortens, but our economic resources vary as well, giving rise to a theoretical indeterminacy in the age-VSL relationship”. Their review of the Revealed Preference evidence concludes that the best designed studies that control for age-specific risk and age-specific consumption tend to observe an inverted-U shape.

More evidence in favour of the inverted-U relationship was provided by Viscusi and Aldy (2007). However, whilst older workers’ VSL estimates are lower than population average, they show that the decline is not proportional to remaining life expectancy. In fact, there appears to be a “higher offer curve” for older than younger workers, which means older workers require higher wages to work for any level of risk, but this offer curve is shown to be flatter with job risk for the older workers.

Evans and Schaur (2010) presented an innovative quantile analysis of wage-risk tradeoffs. They found evidence that the wage-risk trade-offs were typically lower for older members of their sample, but that this interacts with the wage quantiles. They conclude that the effect of age on the wage/risk trade-off is strongest for those on the lowest wages, which had not previously been recognised in the empirical literature. It may be the case that the reduced trade-off with age reflects budget constraints biting for those on lower incomes, who may be less able to reallocate their consumption over the life-cycle.

To conclude this discussion of the Revealed Preference evidence, there is little consensus between these papers, though what consensus there is tends to support an inverted-U shaped relationship between age and the VPF. However, a general concern with these revealed preference studies relates to whether the relationship between age and the value of reducing risks to life can really be understood from available data. The data tend to be restricted to individuals of working age, by necessity given the wage-risk approach. Therefore, it is difficult to estimate the VSL for those above retirement age, when in theory the age effects may differ compared to for those at working age. Also, the analyses presuppose a well-functioning labour market where individuals know and can react to the level of risk associated with the job they accept. These reasons, along with concerns about the availability of relevant data in the UK, are sufficient to rule out a policy value based on Revealed Preference evidence at this time.

4.2.4. Individual Stated Preferences

Given the doubts expressed above regarding the suitability of the Revealed Preference approach to estimating the age effect, we next turn to the Stated Preference literature. Within this, a broad range of methodologies have been employed, generating almost as broad a range of conclusions. In what follows, we outline this literature, focusing on studies that estimate the effect of age directly. By this, we mean studies that interrogate the relationship between the VSL and the age of the respondent at the time that the risk reduction is valued and/or received by them. Most of these studies are one-period in nature, so that the age at which the risk change is valued and received is the same. This is in contrast to the discounting literature discussed later in this chapter (section 4.3).

Early stated preference studies accounted for age indirectly, for example using age as a control variable in understanding the VSL, or looking at the baseline risk (which increases with age). An early, well-cited example is Jones-Lee et al. (1985) which demonstrated some limited evidence of the inverse-U relationship when all of their regression analyses are compared. Jones-Lee et al. (1993) also tested whether age and the VSL were related, with age acting as a control in their analysis. The authors found no significant relationship between the marginal rate of substitution of wealth for risk of death and age or age squared. Instead of directly looking at age, Smith and Desvouges (1987) looked at the effect of the baseline risk level in explaining the VSL. They found evidence that the marginal value of risk reduction goes the “wrong way” with changes in risk level, because it decreases as the level of baseline risk is higher. This might be evidence against the “dead anyway” effect.

In line with the theoretical and the revealed preference evidence, a second wave of interest in the age effects in the value of reducing fatality risks appeared in the Stated Preference literature in the early 2000’s. These papers directly addressed the relationship between age and value.

In a paper that appears somewhat ahead of its time, Johannesson et al. (1997) asked respondents to consider the amount that would be willing to pay for a 2/100,000 reduction from an age-specific baseline risk. The same “blip” in the hazard function was valued by everybody in the sample at their current age (i.e. with no delay) and these WTP estimates were aggregated across individuals. This sample-level age-VSL relationship was explored, with the results suggesting some support for an inverted-U shape with age, a pattern in keeping with some of the Revealed Preference literature and which could not be ruled out in theory. Use of this methodology ensured that Johannesson et al. avoided a problem, later formalised in Johansson (2002), regarding the “blip” in the hazard function: Johansson (2002) suggested that unless the risk reduction valued in empirical studies is truly a “blip” in the hazard rate then the VPF is likely to be biased.

In 2001, Persson et al. (2001) conducted a contingent valuation study by mail in Sweden. Their results, like those of Johannesson et al. (1997), showed evidence that the inverted-U relationship might hold, evidenced by a negative and significant coefficient on age and age-squared in their regression analyses. They used a simple methodology, eliciting willingness to pay for a percentage reduction in the risk of road accident fatality. The inverted U-shape appears to hold even when controlling for subjective risk and risk reduction. However, evidence from the RP literature suggests that this may be due to changing consumption patterns over the life time, which has not been controlled for in SP studies.

Krupnick et al. (2002) is one of the major papers in the literature on the age-VSL relationship. The paper reports a large online contingent valuation study of 40-75 year olds in Ontario. Their results suggested that age had no effect until age 70, and after this the VSL was estimated to be 30% lower than for the younger members of the sample. Many of the same authors were also involved in the study by Alberini et al. (2004) using essentially the same methodology, this time in US and in Canada. They, too, found that WTP for risk reductions decreases after age 70 in Canada, but they found no comparable effect in the US. These papers generated weaker evidence of the inverted-U shape, but since the youngest sample members are 40 years old, there is little scope for such an effect to be expressed. To the extent that their results suggest the VSL decreases after age 70, the inverted U may be supported, but their results are not conclusive.

Hammitt and Liu (2004) were one of the first to directly recognise that latency, rather than age per se, may partly influence the relationship. They succinctly explain that:

WTP to reduce a latent risk depends on the individual’s future WTP to reduce the future risk, i.e., his future VSL. The difference between an individual’s current and future VSL depends on 2 factors: he will be older, and the date will be later.

The empirical work conducted by Hammitt and Liu, which consisted of a contingent valuation study conducted in Taiwan, suggested that WTP declines with age at a rate of 2.3% per year. This evidence does not support the notion of an inverted-U shape, instead suggesting a decrease of VSL with age across the entire age range they surveyed. This pattern, which also fits the data from Krupnick et al. (2002) and Alberini et al. (2004), is consistent with predictions based on expected utility theory.

The most recent Stated Preference study to explore the relationship between the age of a respondent and their willingness to pay to reduce their own fatality risk was presented in Itaoaka et al. (2007). The study was a contingent valuation survey in Japan. The authors found no effect of age. The oldest sample members, those aged over 70, did express lower Willingness to Pay than their younger counterparts, but this relationship was not robust to the specification of the regression models – in some specifications the age effect turns significantly positive. The authors did, however, find evidence of discounting for future (latent) risks. We will return to this literature later in this review.

3 studies explored age in a slightly different way, by asking individuals about age and latency simultaneously through a Discrete Choice Experiment design. In 2004, DeShazo and Cameron explored 2 types of age effects, finding evidence of increasing marginal utility from reducing specific risks later in life, but also finding evidence that as individuals age, there is a downward shift in their willingness to pay for risk reductions in the future, which may be evidence of the increased background risk as age increases. This study is interesting in that it is one of few that attempts to elicit the future value of future risk reductions, but questions remain about whether accurately predicting this is possible. Cameron et al. (2009) found evidence of an age effect that differed in its direction according to the type of illness. Most recently, in 2013, Cameron and DeShazo also showed that “age shifters”, akin to the downward shift in WTP from their 2004 study, improved the fit of their models. Overall, they found that WTP increased with age, except when the risk was of immediate death.

Tsuge et al. (2005) conducted a DCE in which the delay until fatality risks would change was varied across choices. They found that over 70s had significantly lower WTP relative to younger age groups. However, the age at which the risk change happens is confounded by the latency period, and so the pure age effect cannot be estimated.

To make sense of the individual stated preference literature, Krupnick (2007) and Alberini et al. (2008) each provided a review of the literature so far. They each concluded that the results were mixed in the literature, encompassing everything from a senior discount effect, no effects at all, and even a senior premium like that found in some specifications of Itaoka et al. (2007) and others.

Overall, there are difficulties separating the influence of age at the time of the questionnaire, age at the time of fatality risk reduction, background risk and the changing utility of life years over the lifespan. For these reasons, additional evidence about the value of reducing risks to life for people of different ages seems a fruitful avenue for future research.

4.2.5. Person Trade-Off studies

An interesting subset of stated preference studies was deemed sufficiently different in perspective to deserve its own sub-section in this Chapter. This set is the Person Trade-Off Study approach. In these studies, respondents are asked to make trade- offs between saving different numbers of lives of people with different characteristics, in this case, people of different ages. This perspective is not so well grounded in standard economic theory, since the person’s MRS of wealth for fatality risk is not observed in these choices. However, they are a simple and popular method of ascertaining the potential social weights that might be applied when evaluating fatality risks that would apply to different ages, and it allows the age of the person at the time of the risk reduction to be accounted for more easily since it removes the confound between age and latency. It also allows us to consider the relative value of individuals of different ages, when those individuals are not able to express willingness to pay to reduce their own risks, such as when valuing of risks to the lives of children.

Cropper et al. (1994) presented a DCE where the respondents assumed the perspective of a social planner. They demonstrated that delay until lives are saved reduced the perceived value of a policy, and they cleverly separated this delay effect from the effect of age. Their results suggested that for the median respondent, saving one 20-year-old was perceived to be equivalent to saving 70 60-year-olds. This evidence suggests that differently aged people are not valued in proportion to their perceived remaining life expectancy, but that nonetheless younger lives receive higher social weight than older ones. In 2008, Johansson-Stenman and Martinsson took a similar approach, labelling it the “ethical preferences approach”. Like Cropper et al., they demonstrated that younger beneficiaries of the lifesaving program were “consistently given higher values” compared to older beneficiaries. They too found that the value per life year remaining was greatest for the oldest beneficiaries. This is clear evidence of the trade-off between valuing lives equally and valuing life-years equally: the respondents in these studies appeared to choose a position in between these extremes.

The most recent Person Trade-Off study was presented by Carlsson et al. (2010b). They directly addressed the question of how risks to a child’s life should be weighed against risks to the life of an older person. They found that avoiding the fatality of a single 5 to 15 year old was equivalent to avoiding the fatalities of 1.45 people ages 35 to 45 in the context of fire and traffic accident fatalities. Furthermore, the child’s fatality prevention was seen as equivalently good as preventing 3.31 fatalities in the age range 65 to 75. These results suggest that from a social planner’s perspective, protecting young lives is seen as more valuable than protecting the middle-aged or elderly.

Taken as a whole, the Person Trade-Off literature is much more coherent in its message than either the RP or the SP literature, finding unambiguously that younger beneficiaries are prioritised over older ones. However, the social planner perspective may have encouraged “virtuous responding” on the part of recipients, and given the lack of their own personal involvement the direct applicability of economic theories of fatality risk valuation are difficult to apply.

4.2.6. VOLY studies

The preceding review only covered studies for which age was a main aim. However, most studies of the VOLY include a control variable for the age of the respondent at the time of the survey, and so the indirect evidence about the effect of age on the VOLY can be summarised. We do this for the 12 directly elicited VOLY studies outlined in Chapter 1, finding mixed evidence overall.

A selection of the VOLY studies found no clear evidence of an age effect. These include Nielsen (2010); and Desaigues et al. (2011). Chanel and Luchini (2014) conclude that:

While the VOLY depends on age, it is actually respondents’ characteristics here that enable the dependence to be captured. Indeed, age acts as a proxy for preferences, health and other factors that change with age, but does not have a direct influence per se on the VOLY in our model.

Other studies found evidence of an increase in the VOLY with age. For example, Johannesson and Johansson (1996) found an increase in WTP as people aged, but since they were valuing a one-off survival increase at age 75 this may reflect the higher probability that they would live to receive the benefits. Jones-Lee et al. (2007) developed an argument, based at least in part on existing data concerning the relationship between the VSL and age, which predicts that the VOLY will be an increasing function of age. Vlachokostas et al. (2011) found an increasing relationship between age and the probability that a given individual would be willing to pay for the risk reduction.

Yet other studies found a negative relationship between age and the VOLY, or evidence of the inverse-U shape. The inverse-U, with a remarkably late peak, was observed by Desaigues et al. (2007), since willingness to pay increased up to age 74 then decreased afterwards. The Defra study (Chilton et al., 2004) found that WTP declined as age increased, as did Ara and Tekesin (2017). Alberini et al. (2006) found that older people reported higher WTP than younger people, but no age group is significantly different than its neighbour, so the age effect is not strong. Chanel and Luchini (2008) also found an age-VPF inverse U shaped relationship, but not a constant VOLY.

Hammar and Johansson-Stenman (2004) did not directly estimate the effect of age, since this was used in the calculation of discounting to include in the study. Similarly, Grisolía et al., (2018) did not report estimates of the effect of age on the VOLY.

4.2.7. Conclusion

Overall, there is no clear evidence for any particular pattern in age and the VSL. This is not, however, to say that age is irrelevant for determining the appropriate level of the value of reducing risks to life. The empirical evidence gives mixed evidence, ranging from finding no effect, other times finding evidence of a senior discount or even a senior premium. Much of this variation is likely to be due to the way that age interacts with the context of the risk itself. More variability could also be due to differences in the way age is conceptualised: as age at the time of the risk reduction, or as age at the time of the survey, or as age of other people in Person Trade-Off studies. Despite the mixed evidence overall, there does seem to be a persuasive stream of evidence to suggest that willingness to pay for risk reductions is lower in very old age, and some evidence that supports an inverted-U relationship over the lifetime. These patterns should be accounted for, in particular when assessing the reliability of VOLY estimates derived from VSL estimates, and also when assessing the VOLY for use in public policy evaluation and appraisals, even if such weights are not applied in these evaluation and appraisal decisions.

4.3. Delay, latency and discounting

4.3.1. Introduction

There are 2 broad reasons for policymakers and researchers to be interested in discounting for delay in relation to health and safety. The first reason is so that we can better understand individuals’ own behaviour and personal choices in decisions with long term consequences for them. This requires a clear understanding of individuals’ personal time preference rates. The second reason is so that individuals’ intertemporal preferences can be accounted for in public policy appraisal and evaluation. This requires estimates of individuals’ personal time preference rates in contexts where these are already embedded in policy values, including the VOLY context itself. It also requires considering society’s time preference for such impacts on unspecified victims or beneficiaries (social discounting) which can sometimes include impacts upon generations yet to exist.

With regards to the first reason, there is a substantial literature linking individuals’ time preferences to their health behaviours. An early example is Fuchs (1982). In a telephone survey of 500 adults, Fuchs measured time preference through a series of monetary choices between a sum of money “now” and a sum of money in the future. The discount rates revealed by these choices were shown to correlate negatively with health status and positively with cigarette smoking, amongst other things. Since Fuchs (1982), many scholars have been interested in the relationship between discounting and health behaviours. However, since the purpose of this Scoping Study is to discuss the Value of a Life Year, the rest of our discussion will relate exclusively to studies aiming to investigate the degree to which individuals discount future health and fatality risk outcomes; the nature of this discounting; and the possible implications for public policymaking; we will set aside the influence of time preference on personal behaviour in a general sense. Since relatively little is known about discounting for fatality risks per se, this review will also consider discounting in the context of non-fatal health outcomes.

4.3.2. Theory

For simplicity, consider choosing, for yourself or your household, between £1000 today and £1000 in one year. If you prefer the sooner £1000, you display a positive discount rate. Frederick (2006) provides a review of the classic arguments for discounting a future outcome.

Frederick (2006) first provides a summary of reasons why delaying receipt of an outcome can change the expected utility associated with receiving it:

(i.) Risk – if the £1000 is to be received after a delay, there is a greater risk that the payee or the payer will not be able to make the transaction.
(ii.) Quality/Magnitude/Duration: The objective characteristics of the outcome may worsen with time. Whilst £1000 is not subject to these effects, a bunch of flowers will wilt increasingly as days pass since they were picked. More importantly, a durable, indefinite good starting later delivers less utility in total than one starting sooner.
(iii.) Changing tastes: tastes and desires may change over time. A person may become less healthy, or wealthier, over time. If I expect to become less credit constrained in future, £1000 now is preferred to £1000 later.
(iv.) Utility from anticipation or memory: knowing an outcome will occur later may allow you to anticipate (or dread) it for longer. I may enjoy anticipating receiving the £1000, which may reduce the degree to which delaying the £1000 reduces its present value.
(v.) Opportunity cost – many goods can be invested such that they effectively grow with time. For example, a packet of seeds eaten today could instead have been planted to yield many additional seeds in future. In the monetary example, you should take £1000 today, save it at a (positive, risk-free) savings rate of i, meaning you would hold £1000(1+i) in one year^{[footnote 10]}. One year from now, you would be better off holding £1000(1+i) than £1000.

Frederick argues that these 5 factors influence the amount of future utility to be received. He distinguishes this from time preference, which means the relative weight given to future utility compared to present utility from the perspective of the person receiving the outcome.

Next, let us place these arguments in the context of factors affecting the value of changes in risk to life, as are captured in the VOLY model. For most people, delaying a risk reduction of a given magnitude will (i) reduce the likelihood that they will live to enjoy it, through increasing hazard rates with age; (ii) change the duration of the risk reduction, since the “blip” in the hazard rate will affect fewer future expected years of life (see RQII), but alter its quality in an ambiguous direction (see the Age discussion in this RQ); (iii) possibly be valued differently due to different levels of wealth at different future ages (again, see the Age discussion); (iv) alter the dread associated with fatality, as long as the individual is aware of the risk and its reduction. So regarding arguments (i) to (iv), fatality risk changes will be viewed similarly to other outcomes. However. (v) is not relevant to time preference for health and safety.

This leaves us with 2 conceptual points still to consider: the applicability of “pure” time preference for health and safety outcomes, and the appropriateness of applying a social discount rate to weight different generations differently. The following review of the empirical literature summarises compelling evidence that a majority of the population does weight future outcomes less than present ones, both in terms of future risks to their own safety or future changes in their own health; and in terms of the lives of future generations. The question then becomes whether policy appraisals and evaluations ought to respect these preferences. The arguments for and against applying a policy rate of discount that respects the preferences of the population have been summarised in detail by Krahn and Gafni (1993), amongst others.

Intergenerational time preference, sometimes called “intergenerational equity weighting”, refers to the relative weight a society places on cohorts or generations that exist at different times, from those already alive, to those who will live in the distant future. Some views reported in the literature hold that utility benefits for future generations should be given equal weight as benefits to the present generation, upholding the principle of intergenerational equity. Others advocate respecting the preferences of the present generation only.

Lipscomb (1989) suggested that:

1. Outcomes that affect an individual’s own lifetime should be discounted within the affected individual’s own lifetime, according to that individual’s own discount rate, to the present value from the perspective of that individual, and to the time of their birth, or the present (whichever is sooner).
2. These within-person Present Value estimates of the effects of a policy on an individual should then be discounted to the present according to the appropriate Social Time Preference Rate that society agrees should weight current and future generations.

Relatedly, Krahn and Gafni (1993) acknowledge the dangers of “double discounting”, highlighting that some measures of health outcomes may already include discounting at the individual level. The authors argue that discounting such measures again will undervalue these health outcomes by effectively discounting them twice. The approach suggested by Lipscomb (1989) should be implemented carefully to avoid such a pitfall.

Cropper and Portney (1990) also address the question of how to discount when policies extend beyond a single lifetime. They demonstrate that in theory, an individual’s Willingness to Pay at age 20 for a change in his conditional probability of death at age 40 (WTP_20,40) is equal to the amount he would be willing to pay at age 40 for a change in his current probability of death (WTP_40,40), discounted to age 20 at the consumption rate of interest. This theoretical contribution forms the basis for a possible empirical investigation in which the value of a change is estimated at the time it would be received, and then discounted at the consumption rate of interest elicited through monetary time preference questions. If society is appraising the value of the utility of a future 20 year old, then this WTP_20,40 may be discounted to the present using social time preference rates. However, it is not clear that it would be possible to elicit WTP_40,40 for a current 20 year old empirically, let alone for a 20 year old yet to be alive. As such, this simple empirical framework has not been operationalised in practice.

Up to now, we have discussed the reasons for discounting future benefits, and the arguments for and against applying discounting in policy evaluation. To make things more concrete, we next focus on 2 distinct concepts that characterise the measurement of time preferences, and which are negatively related to one another:

The discount factor DD(dd) – the proportion of value that an outcome retains when it is delayed by d years. 2) The discount rate rr – a parameter capturing the degree to which current consumption (or utility) is weighted more highly than future consumption (or utility).

Using notation from Chapman and Elstein (1995), and assuming a standard discounting model (variously termed “exponential”, “constant discounting” and others), then the present value V₀ of an amount of money received after a delay (V_d) is given by:

VV₀ = (VV_dd) / ((1 + rr)^dd)

The discount factor in this case is then 1 / (1+rr)^dd and the discount rate is rr. The higher the discount rate, the less value future outcomes will receive from the perspective of the present, and equivalently the smaller the discount factor will be. An important, testable hypothesis arising from the exponential discounting model is that the discount rate should be constant, and should not depend on the delay d until the outcome is received.

Empirical evidence from a wide range of domains in the context of personal discounting, contradicts this hypothesis, suggesting that the discount rate declines with delay. Frederick et al. (2002) provide a summary of this evidence, as well as outlining many other anomalies that contradict the DU model. Alternative discounting hypotheses have been proposed to account for this abundance of empirical evidence. 2 of the most important alternative models of discounting are (i) the quasi- hyperbolic (or beta-delta) model (Laibson, 1997; Phelps and Pollack, 1968), and (ii) the hyperbolic discounting model(s) (for example, Mazur, 1987; Harvey, 1986; Loewenstein and Prelec, 1992).

The quasi-hyperbolic model holds that discounting is exponential and consistent in every period except for the immediate present. In this model, the discount factor is:

δδdd = 1 / (1+rr)^dd

in the first period and:

ββδδ^dd = ββ / (1+rr)^dd

in all periods thereafter.

The hyperbolic family of models do not represent the present as a special case, but incorporate the declining discount rate into the structure of the discount factors. Different formulations have been proposed, but each one incorporates the feature that as delay until an outcome grows, the discounting applied to it becomes less severe. Other discounting models and approaches have been presented in the literature, but it is beyond the scope of this review to outline them all.

The extent to which policymakers should respect individual discounting functional forms is often an open question. Consumer sovereignty arguments suggest that the preferences of the public should be respected by the government, but since only the exponential model implies consistency in decision making over time, respecting individual discount functional forms may result in inconsistent resource allocation over time. What is uncontroversial, however, is that it is important to understand the discounting that members of the public use when generating and expressing their values for future fatality risk outcomes in surveys and experiments that are used to generate public policy values. These stated preference estimates can then be understood fully and, if appropriate, can be adjusted to account for the discount factors used in their production.

Given the central role of delay and time preferences in the policy appraisal and evaluation of health and fatality risk outcomes, it is perhaps unsurprising that a large body of literature has emerged to explore these issues. The approaches taken are diverse, and the conclusions far from precise at present. However, some common features can be gleaned from these studies. We outline the key papers and findings, organised by research method, in what follows.

4.3.3. Individual Revealed Preferences

Viscusi and Moore (1989) produced the first attempt to empirically estimate personal discount rates in the context of the value of risks to life. Specifically, they used a multi-period model to describe and analyse workers’ choice of occupational fatality risks, under the assumption that increased risk is compensated for by higher wages. The authors use estimates of the lost duration of life, and assume that each year of life is equally valuable, but that years of life are discounted so that job risk choices are made on the basis of their present value. The authors empirically estimate that the discount rate is 11% per annum on average. This contribution was a significant step forward in understanding discounting in the value of fatality risks, since it presented the first empirically tractable multi-period model incorporating the risk of fatality. However, this came at the cost of some restrictive assumptions, which were relaxed in later work involving the same authors.

Moore and Viscusi (1990) extended the ideas from their 1989 paper by suggesting 3 different approaches to model the discounting of fatality risks: a simple way with no formal underpinning (implying a 10 to 12% discount rate); a Markov model like the one they proposed in 1989, which is complex in its assumptions (implying an 11% discount rate) and a new approach using a life-cycle model of job risk, assuming all years are equally valued and that the job risk of fatality is constant over the life cycle. The discount rate for future utility is estimated to be 2% using this approach. In their model, the discount rate is applied to the utility of earned income (which in turn depends on fatality risk), in each period, which is added up over the lifetime.

More recently, Scharff and Viscusi (2011) conducted an innovative revealed preference study in which they elicited the discount rate for years of life using wage data, and then used these estimates to predict whether a member of the sample was a smoker. On average, they found that the discount rate was 13.8% for smokers, and only 8.1% for non-smokers. These discounting estimates are sensitive to the number of years of education, the worker type (blue collar or white collar), and the functional form assumed for the utility of wealth function. Nonetheless, this paper demonstrates the continuing, if rare, interest in using revealed preference data to elicit time preferences.

Overall, however, few researchers have attempted to estimate the discount rate on the basis of revealed preference data. The reasons for this are likely to include the difficulty separating the age and discounting effects empirically, the lack of detailed data on the latency of different risk types, and the lack of detailed knowledge that workers can be assumed to have about their near and distant future risks. For all these reasons, the majority of research into discounting, latency and the value of risks to life and health have been conducted using stated preference techniques. A selection of these studies is outlined in what follows.

4.3.4. Individual Stated Preferences

Fuchs (1982), Gafni & Torrance (1984) and Lipscomb (1989) are the earliest empirical studies that investigated the link between personal time preference and health outcomes. Fuchs approached this by simply measuring time preferences for monetary outcomes, and using these to predict different health related behaviours and outcomes. Fuchs demonstrated a correlation between cigarette smoking and time preference (more impatient individuals were more likely to smoke) and between health and time preference (more impatient individuals tended to report worse health). Gafni and Torrance (1984) improved upon this approach by proposing the first method for directly eliciting time preferences in the context of health. Their method involves asking people about their preferences for the temporary improvement in a chronic health condition. It should be noted that the main focus of Gafni and Torrance’s paper is actually on risk attitude, with time preference treated as a component of risk attitude.

Lipscomb (1989), on the other hand, directly addresses the issue of time preference as measured in the context of health outcomes. Holding the total amount of good and bad health constant across scenarios, but with different delays until the onset of the poor health within the profile, he elicited preferences over these profiles and concluded that there was evidence for positive discount rates in his sample. However, the main contribution of the Lipscomb (1989) paper was to propose the 2-stage discounting procedure outlined above, and he did not calculate specific discount rates nor identify functional forms. As such, up to the late 1980s, there was no stated preference based evidence about the rate at which individuals might discount future risks to their health and safety, and no evidence about the functional form that characterised their discounting. In this regard, stated preference evidence lagged behind revealed preferences (Viscusi and Moore, 1989).

The seminal paper by Chapman and Elstein (1995) investigated time preferences for health, comparing them with time preferences for money. The headline result is that discount rates for health were higher than those for money, although the authors are careful to point out that differences may arise if health outcomes are perceived to be of a different magnitude than financial outcomes. The same patterns of non-standard discounting were observed between health and financial settings, including the magnitude effect (lower discounting for larger outcomes) and the delay effect (lower discounting for distant future outcomes, consistent with the hyperbolic discounting models). The authors concluded that discounting was domain-specific, meaning it is not be appropriate to assume that health outcomes are discounted at the same rate as financial ones, even though similar patterns are observed across contexts. This conclusion was based on observing higher correlation between discount rates elicited within-context (e.g. health states with different delays) than across contexts.

A second surge of papers appeared that addressed discounting for health and risk reductions, following behind the “second wave” of age papers discussed in the previous section. In Alberini et al. (2006), the authors asked respondents to state their willingness to pay (WTP) for risk reductions that would take effect immediately and ones that would take effect at age 70. They make the distinction between age at the time of response, age at the time of risk reduction, and latency that we set out in the introduction to this Chapter. The authors elicit an average risk reduction for their Canadian sample at 3.0% to 8.6%, and discount rates for their US sample of 1.3% to 5.6%. Overall, there is strong evidence of discounting, since delaying the time that the risk reduction would take effect by 10 to 30 years “reduces WTP by more than 60%”. The authors assumed a standard exponential discounting function which allowed them to estimate the discount rate as a parameter of the regression model.

In a slightly later study of Italian residents, Alberini and Chiabai (2007) conducted a CV study with WTP for immediate and future risks of dying from cardiovascular and respiratory diseases. This mirrors the approach in Alberini et al. (2006). They compared discount rates between money versus risk, and money versus money questions. They showed that for money-risk comparisons, the discount rate was 0.3– 1.7%, while in the money-money comparisons they discount rate was 8.7%. Again, the authors did not consider nonstandard discount functions, and estimated the discount rate as a parameter of the regression model. Using a similar method, with a choice experiment in which risk reduction timing was varied across choice options, Tsuge et al. (2005) also demonstrated that respondents evaluated earlier risk reductions much more favourably than later ones, and timing is negatively related to WTP (significant at the 1% level). They estimated the discount rate to be around 20% per annum.

The Alberini et al. studies involved eliciting WTP to reduce risks of fatality over time, and this provides a way to elicit the discount rates from regression analysis. The drawback is that they rely on the accuracy of the WTP estimates. Most studies that aim to explore latency and discounting effects have instead avoided the need for WTP by employing alternative SP approaches that isolate the latency or discounting effects. An early example is that by Van Houtven et al. (2008). The authors report a choice- based stated preference study in which respondents each made a single discrete choice between 2 locations to live in, which differed in their associated risk of dying by different causes. Latency was varied, taking a value of 5, 15, or 25 years in each scenario. The main aim of this study was to identify any cancer premium, and so the latency results are tied in to that finding. Specifically, they state that “with a 5-year latency, [cancer risks] are valued roughly 3 times greater than immediate accident risks, declining to 50% greater for a 25-year latency”.

McDonald et al (2017) expanded the approach of Van Houtven et al. (2008) in that they elicited respondents’ willingness to take increases in their risk of dying by cancer. Their approach allowed the utility of the outcome to “drop out” of the empirics, since their comparisons were between the “same” fatalities at different times. The approach was to vary the risks of fatality and time of death from cancer in a Risk-Risk tradeoff. They found evidence of heterogeneity in discounting models across their sample (students in Newcastle) with a majority of participants using a sub-additive discounting model, then exponential and then hyperbolic. The median (exponential) discount rate was 10.1%. Cancer fatality risks have proved fertile grounds for studying the influence of latency and discounting on the value of reducing risks to life. For example, McDonald et al (2016) used a Risk-Risk trade-off and estimated a discount rate of 7.4%; and Viscusi, Huber and Bell (2014) conducted a stated preference approach to valuing the reduction in the risk of bladder cancer delivered through cleaner water. With a latency period of 10 years, the cancer premium is shown to be relatively low at just 21% above the value of statistical life through acute accidents. Alberini et al. (2012) used a conjoint choice experiment approach to estimate the VSL for cancer risk reductions from clearing up hazardous waste sites, and elicited a discount rate of zero, but this study is in the minority in the literature. Overall, cancer valuation studies tend to assume or discover that latent or future risk reductions are discounted relative to immediate ones.

A separate line of enquiry emerged in the health economics literature, aimed at finding ways to test discounting hypotheses without the need to estimate the utility of the health outcome. Bleichrodt and Johannesson (2001) highlighted the pitfalls of early attempts to measure discounting for health: that they required the researcher to assume a functional form for utility of life-years, and to ignore discounting within a period of health gain or loss. The authors avoided this pitfall by taking an axiomatic approach, which means testing a prediction that follows from the axioms of the discounted utility model. Specifically, they tested the stationarity axiom in individual choice. This axiom predicts that the choice between 2 outcomes should not be influenced by adding a common delay to both outcomes. Their study generates strong evidence that the stationarity is violated. Participants made pairwise choices between health profiles where ill health occurs at different times. They find strong evidence of decreasing timing aversion, and hence against stationarity – concluding that hyperbolic or quasi-hyperbolic models must be preferred over constant discounted utility models on the basis of their evidence. The use of the axiomatic approach represented a significant step forward methodologically, although their approach does rely on some restrictive assumptions about additivity in time (which is common to most discounting models) and that people have no preferences regarding the sequence with which they receive different outcomes spread out over time (this is less convincing, see Loewenstein and Prelec, 1993).

Van der Pol and Cairns (2011) took a similar approach, conducting a survey of a sample of students (n=203) in which participants were required to state the number of days of illness after some delay (up to 20 years). that they considered equivalent to a given number of days in the near future. The authors varied the delays across questions, holding constant the interval between the health outcomes allowing them to avoid the possible confound of the sub-additive discounting effect. Like Bleichrodt and Johannesson (2001) they used an axiomatic approach, removing the need to estimate discount rates directly. Their results generated compelling evidence of nonstationary time preferences, and specifically they showed that hyperbolic discounting models better fit their data than the quasi-hyperbolic model. They did, however, find much evidence of negative discounting. This may reflect their use of ill- health days, which is a loss-frame. Losses have been shown to be discounted less than gains, and sometimes negatively (for example, Frederick et al., 2002).

Continuing the axiomatic approach to testing stationarity, and so avoiding the need to estimate discount rates directly nor to specify the utility of outcomes, Bleichrodt et al. (2016) found evidence of non-standard discounting that was more pronounced for health than for money. They used an innovative “Willingness to Wait” approach, also known as the “direct method” and first proposed by Attema et al. (2010), in which the respondent has simply to specify the delays until 2 different outcomes would occur, such that they would be indifferent between the 2 sequences. Their results allowed them to reject constant and quasi-hyperbolic discounting in favour of hyperbolic discounting models, just like the results of Van der Pol and Cairns (2011). In a more recent application of Attema et al. (2010)’s approach, Attema et al (2018) conducted a comparison of discounting for time versus discounting for money. They did elicit discount rate estimates, finding median discounting for their sample in France was 2.2% for health and 6.5 % for money. Unusually, they found that the constant discounting model gave the best fit for their data.

Finally, and using another technique for their investigation, Hammitt and Tunçel (2015) explored discounting specifically in the context of the VOLY. They extended the methodology in Nielsen et al, (2010), updating it to directly account for latency. They specify that individuals can being risk seeking, risk neutral or risk averse with respect to years of life, showing theoretically that u(t) – i.e. utility of living until time t - is risk neutral only if the VSL increases at the same rate as the discount factor decreases. Risk aversion with respect to longevity implies that the present value of future VSL decreases with t, i.e., VSL decreases with age, is constant, or increases more slowly than the discount rate. They elicited the consumption discount rate for money choices, which was used in the analysis, but the relevant factor in terms of time preferences for longevity is the curvature of u(t). This insight will be useful in future discounting studies for the VOLY in terms of the Stage 1 of the 2 stage procedure outlined above. Empirically, they used delays of 10 or 20 years until onset of the risk reduction and confirmed that people were consistent in their risk neutral, risk averse or risk seeking status for longevity.

Overall, the stated preference literature leads to 2 main conclusions about personal discounting and the value of reducing future risks to one’s own life: The first conclusion is that risk reductions appear to be discounted at a positive rate (or equivalently, life years appear to be discounted, or the utility function for longevity is non-linear). The level of the discount rate tends to be estimated in the region of 10% per annum, suggesting that individuals do not discount risks, health, life years and money at the same rate – this is unsurprising given that these outcomes are non-fungible, and anyway the real monetary value of health impacts is likely to change over time with income. The second conclusion is that, in cases where it was investigated, the exponential discounting assumption has mostly been rejected, with a small number of exceptions. However, what the literature reviewed so far cannot explain is social discount rates. That is, how members of the public would trade off lives saved in the near versus the distant future, perhaps inter-generationally. The literature that addresses these questions is outlined next.

4.3.5. Person Trade-Off studies: Social time preference for utility

Both the Revealed and Stated Preference approaches outlined so far have involved individuals discounting future health or physical risk outcomes that would apply to their own selves in the future. This individual perspective is important for revealing how outcomes are, and perhaps ought to be, discounted within a person’s own lifetime (recall the discussion of Lipscomb 1989 from earlier in this chapter). However, these studies do not directly speak to the issue of the social discount rate, or the intergenerational discounting problem. A distinct series of research efforts has been undertaken in parallel to the individual focused research outlines so far. These papers, which we term “person trade off” studies, investigate how individuals would be willing to trade off numbers of illnesses prevented or lives saved over time. In many cases, the individual is assumed to take the perspective of an impartial decision maker, deciding whether and how lives now and in the future ought to be weighted differently.

Horowitz and Carson (1990) and Cropper et al. (1992) report the first empirical studies that aimed to elicit how individuals are willing to trade off saving different numbers of lives at different times. In both studies, participants were asked to choose between scenarios in which different number of lives would be saved at different times, and their choices were assumed to reveal their discount rates for saving human lives. Horowitz and Carson (1990) conducted a survey of 75 undergraduate students, whilst Cropper et al. (1992) conducted telephone surveys in the United States, surveying 3200 members of the public. In both cases, positive discount rates were revealed.

Horowitz and Carson (1990) asked participants to trade off lives saved sooner versus later in 3 different contexts, and found positive discount rates on average, although 32% of the sample were estimated to have zero or negative discount rates. The sample estimates of the discount rates were 0.045 in the context of aeroplane safety, 0.047 for workplace safety, and 0.128 for traffic safety. The participants in Cropper et al. (1992)’s studies were asked to choose between lives saved in the near or the distant future that would otherwise have been lost due to pollution. The discount rates were estimated to be between 0.03 and 0.27 per annum, depending on the delay. This range demonstrates non-standard discounting, with the discount rate declining with delay until the later fatalities would be avoided. Cropper et al. (1994) also report these data, stating that the discount rate ranges from 16.8% as implied by a willingness to equate 2.3 lives in 5 years with 1 life today; and 3.4% as implied by an equivalence of 44 lives saved in 100 years and 1 life saved today. In this version of the study, different discounting functional forms were specifically considered, with non-standard discounting prevailing. Furthermore, and like Viscusi and Moore (1989), no differences were found between discounting for lives saved versus discounting for money.

Olsen (1993) conducted another Person Trade-Off study. This survey of members of the Swedish population extended the previous literature in 2 ways: first, by looking not only at lives saved but also at cases of ill-health avoided; and second, by comparing the discount rates of members of the public to those of health care experts. In the study, individuals were asked to choose between different numbers of lives saved at different times (after either 1 vs 5 years or 1 vs 20 years delay). They were also asked to choose between different numbers of health gains after the same delay. The results suggested that the rates of discount for lives saved were lower than for health gains – suggesting people are less willing to sacrifice future lives saved than to sacrifice future gains in health. This could reflect a belief in the likely improvements in modern medicine over time. The second key result was that experts, in this case health managers and senior workers in the Department and Directorate of Health, exhibited lower discount rates on average. The discount rates were consistently shown to be lower for the 20 year horizon (9.4% for lives saved, 10.2% for health) than for the 5 year horizon (17.3% for lives saved, 22.9% for health; with corresponding expert rates of 5.8%, 7.3%, 6.6% and 11.8% respectively).

In 1997, an important new partnership appeared in the Person Trade-Off literature: that between John Cairns and Marjon van der Pol. They were the first to directly and systematically focus on what discounting models best fit the data on individuals’ choices between options that save different numbers of lives at different times. In 1997, they published 2 papers (Cairns and van der Pol 1997a, 1997b) both of which aimed to understand the functional form of discounting for lives saved. The first reported a variety of different discount rates ranging from 0.1345 to 0.4142, depending on the delay until the fatalities would be prevented, and concluded that there was strong evidence “against constant timing aversion”. The second paper went beyond this to explore which of 3 models best fit the data: the constant, proportional and hyperbolic discounting models. Their multi-level analysis accounted for individual differences and allowed the different models to be distinguished. The conclusion reached was (i) that discounting was best explained by the proportional model and (ii) that the multi-level modelling approach was a significant improvement over basic OLS analysis.

Though few Person Trade-Off studies appeared in the 2000s. Alberini et al. (2009) produced a working paper in the context of hazardous waste sites. To control for the intergenerational nature of the benefits of hazardous waste removal, they turned to the Person Trade-Off to elicit the perceived discount rate for benefits to future generations. They elicited a 12% exponential discount rate on average, but their results suggested that a hyperbolic discounting model would better fit their data, with the discount rate falling from 16% for a 10-year delay to less than 4% for a 30-year delay.

2 studies by Van der pol and Cairns do not easily fit into the category of a Person Trade-Off, nor of an individual stated preference study. These papers report Discrete Choice Experiment studies that act as a hybrid between Person Trade-Off and individual Stated Preference studies. In their 2001 study, they asked participants to trade off their own health over time to elicit discount rates (which were estimated to be between 0.055 to 0.091) and also trade off others health over time (generating discounting estimates of 0.078 to 0.147). Their results suggested that people discount their own health at a lower rate than they do others’ health, providing the first direct evidence of such a comparison. This paper is methodologically important: it is the first DCE to elicit health discount rates. In the questions, the number of days of ill health are varied (between 5 to 38), and the delay until these ill health days would occur was also varied (either 2 year, 7 year or 15 year delays). These attributes are varied in paired choices, and the modelling reveals the discount rates used. The concern with this paper is the high proportion of choices that appear to reveal a lexicographic (i.e. non-trading) preference pattern. For example, a responder may always choose the sooner ill-health, or always choose the later ill-health, or always shorter illness and so on. Further use of this methodology may be a promising avenue for eliciting the social and private discount rates simultaneously, but methodological testing will be required to ensure the validity of the findings.

Similar data were also reported in Van der Pol and Cairns (2002), as part of an investigation into the discounted utility versus hyperbolic discounting functions for social and private discounting problems. The methodology closely followed that of their 2001 paper, and this paper provided clear evidence to suggest that both social and individual discounting are non-exponential, and instead seem better fit by a hyperbolic model. Of the tested models, the Loewenstein and Prelec 2-parameter model fits best on a sample level (unsurprisingly because it allows an extra parameter to be estimated, improving the fit almost by default). However, this 2-parameter feature means that this model cannot be fit on an individual participant level. At an individual level, the Harvey model tended to give the best empirical fit for the data, again suggesting that discounting is non-standard. However, one third of the sample displayed zero or negative time preference rates and hence could not be fitted at all. (It is possible, though not clear, that the 2 Van der Pol and Cairns papers reported here discuss the same dataset).

Evidence in contradiction to the consensus described so far is provided by Frederick (2003). In that paper, he suggests that many studies of social time preference may have provided overestimates of the true discount rate. Specifically, he shows that when the complexity of the question asked is high, respondents are likely to respond according to whatever aspect of the question is most salient, be it the equity implications or the total lives saved over time. Moreover, he suggests that even when respondents do prioritise current over future generations, this may be more easily explained by expectations of technological change or concerns about the certainty of the future and current fatalities. This evidence provides a note of caution as to how strongly individuals prefer to prioritise current over future generations utility.

4.3.6. VOLY studies

As in the case of age, we have focused the discussion up to now on studies directly eliciting the discount rate or functional form for health or fatality outcomes. However, it again seems prudent to outline the discounting findings from the 12 direct VOLY studies reviewed in response to RQI.

Fewer of these studies specifically mentioned discounting than did age – those that did not empirically address discounting include Desaigues et al. (2007) who set discounting aside because it is low over the 10 year period considered; Vlastachokostas et al. (2011) who do not mention discounting; Desaigues et al. (2011) who assume it is implicit in stated preference estimates already; Alberini et al. (2004) who do not mention discounting but control extensively for age.

Other studies apply different discounting without eliciting discount rates directly. For example, Nielsen (2010) tries 0%, 3% and 6% discount rates as recommended in policy; Chilton et al (2004) employed the 1.5% discount rate recommended by the UK Treasury. Ara and Tekesin (2017) attempted to elicit individual-specific discount rates but were unable to do so, and instead they employed a range of discount rates from 0% to 10%. Hammar and Johansson-Stenman (2004) assume 0% and 5% discount rates, and test the sensitivity of their results to these assumptions. Grisolia et al. (2018) use a 3% discount rate by assumption.

Turning to the studies that do elicit a discount rate, the key scholars are Olivier Chanel & Stéphane Luchini. Chanel and Lucini (2008) estimate discount rates that vary depending on the model, but their headline discount rate is 6.4%. Chanel and Luchini (2014) use a similar technique and find discounting is 6.8% as estimated by the data from a telephone survey, but a higher rate of 18.8% was elicited in face-to-face elicitation. The only other example of discount rate elicitation amongst the 12 studies is Johannesson and Johansson (1996), who infer a discount rate according to the age of the respondents, which is possible since their promised additional year of life is to be received at age 75, regardless of the age at the time of responding. They find implied discount rates of 0.3 to 3.4% depending on the specifics of the WTP estimation.

4.3.7. Conclusion

Overall, therefore, it appears that people discount future risks to their lives and to their health. They appear to do so in a non-standard way, although evidence upon this point is relatively scarce, and many applications – particularly in the VOLY context – assume exponential discounting for analytical convenience. The discount rates elicited tend to fall around 10% per year and, where investigated, this tended to be significantly different from the rate for financial discounting. Given the crucial role of discounting in the models that describe the VOLY, and in the link between the VOLY and the VPF, it will be necessary to test and control for the discounting and latency effects in individuals’ stated preferences in any future empirical work in this area. There also appears to be a strong public preferences for prioritising risk reductions to other people if they appear sooner rather than later, as evidenced by the unanimous findings of the Person Trade-Off literature.

4.4. Summary of timing effects

We have discussed the effects of timing on the VPF and the VOLY, focusing on the 2 main channels: age and discounting. The results for discounting were relatively clear: delaying a risk reduction reduces its present value in the eyes of members of the public. The degree to which this discounting occurs, and its functional form, have both been outlined with the conclusion that the discount rate appears to be in the region of 10% for most studies (though with considerable variation between studies and between individuals) and the discounting function tends to be non-standard (except in a few rare exceptions). The age effect is less clear cut both theoretically and empirically. There is some overall evidence that as a person ages, they are willing to pay less for a reduction in their risk of fatality, but this effect is far from clearly established. Empirical studies struggle to disentangle the effects of age from effects of delay and discounting, and it is unclear to what extent the age effect is driven by changing consumption patterns over the lifetime. There is, however, no doubt that age and delay both influence the amount people are willing to pay for reductions in their risks of fatality, and that timing issues should be a top priority for future consideration.

5. Behavioural biases and heuristics

In this section we outline some key behavioural biases and heuristics to consider when interpreting stated preferences.

5.1. Preferences not conforming to Expected Utility Theory (EUT)

There is strong evidence that EUT is not a good descriptive base for describing choice and valuation (see for example Starmer, 2000). This recognition provided the basis for a growing sub-field of economics, behavioural economics, supported by experimental and data-driven empirical evidence. It is far beyond the scope of this review to outline all the ways that preferences are likely to deviate from the predictions of EUT, so we focus on those areas most pertinent to stated preference estimation of non-market values.

Preference imprecision: There is growing recognition in the economics literature that preferences may be imprecise, with implications for the consistency and stability of preference estimates in a variety of settings. For laboratory evidence, see Cubitt et al. (2015) whilst for evidence in the health context, see Pinto Prades et al. (2018), who demonstrate that people whose preferences are the most precise are least likely to commit preference reversals across different tasks. Pinto Prades et al. (2018) demonstrate that concealed iteration (based on Loomes and Pogrebna, 2016) can improve the consistency of responses.

Non-standard time preferences: The possibility that time preferences may not conform to standard exponential assumptions were explored earlier in this RQ. We outlined the literature demonstrating numerous deviations from the predictions of standard discounting theory, in favour of hyperbolic or sub-additive discounting. The possibility of nonstandard discounting is important when interpreting the values elicited in surveys.

Probability weighting: Cumulative Prospect Theory (Tversky and Kahneman, 1992) includes the insight that individuals underweight high probabilities and underweight low ones according to an inverse-S shaped probability weighting function. Recognising this may be important when interpreting the results of Standard Gamble tasks, where the usual assumption is that preferences are linear in probabilities (as predicted by expected utility). The curvature of the probability weighting function can be established empirically and, if necessary, adjusted for in post-estimation after survey data are analysed.

Loss aversion: Another core feature of Cumulative Prospect Theory is the idea that losses loom larger than gains. That is, a loss of a given magnitude reduces utility by more than an equivalently sized gain increases utility. A related phenomenon is the endowment effect, by which WTA to give up a good or service is larger than WTP to acquire that same good or service. There is substantial empirical evidence in support of the endowment effect (Knetsch 1989), and policies may differ in their gain/loss frame. There is some debate in the literature about whether loss aversion is a bias to be corrected for, or else whether it is a legitimate feature of preference that should be respected in policymaking by applying loss-weighting in policy evaluation.

5.2. Response biases in surveys

In this part, we specifically focus on evidence regarding how behavioural biases and heuristics can interact with stated preference elicitation techniques. These may arise particularly in settings where respondents are unfamiliar with the scenario so have to construct a response (for example, Fischhoff, 1991; Lichtenstein and Slovic, 2006), as outlined in the NERA report to the government (Spackman et al., 2011).

Prominence effect: Respondents in surveys may pay particular attention to aspects of the presentation of information that makes it particularly salient or noticeable. For example, response-mode bias suggests that when respondents are asked to value a lottery with a money outcome, they focus more on the money on the table than on the risk, due to what is known as the prominence effect (Tversky et al., 1988). When they are asked to report a probability equivalent they focus more on the risk in the lottery than the amount they could win. So by changing the response mode, respondents can be made to appear more or less risk averse. In a valuation study, making any aspect of the scenario salient can draw attention to it artificially.

Anchoring: The anchoring effect was first documented by Tversky and Kahneman (1974). Respondents are likely to anchor on numbers they already stated in the survey. For instance, if asked to provide a series of WTP valuations, their initial answer will tend to influence subsequent ones. This makes it very important to randomise question orders between participants to minimise the overall effect of these biases.

Middle Switching/Spatial biases: Suggested by Harrison et al. (2007) as a subset of anchoring biases, the spatial biases relate to how the information or choices are presented on a screen. Respondents tend to favour options to the left of the screen, and tend to switch in the middle of a set of options. This has given rise to the “decoy effect” in psychology (Huber & Puto, 1983), where including an irrelevant third option can change the choice between 2 existing ones. Choice sets and scenarios should be carefully designed to minimise the influence of middle switching, for instance by presenting different ranges of possible values to different participants, and by changing presentation order randomly between participants.

Rounding: In willingness to pay exercises, respondents demonstrate a tendency to report round numbers. To avoid this, payment cards can present non-round numbers to encourage accuracy in reporting, although it should be noted that encouraging spurious accuracy is not productive either (see Imprecision, above). Bateman (1996) discusses the rounding issue and notes that it is only problematic where rounding up and down are not equal and offsetting.

5.3. Conclusions

To conclude, there are numerous biases and heuristics that may influence reported willingness to pay or choices in stated preference elicitation. However, most of these can be mitigated through careful experimental design and, in some cases, corrective techniques could be explored (for instance with probability weighting). Overall, it is important to recognise the influence that behavioural biases and heuristics may have over stated preference values, particularly when these values are combined in chaining studies (e.g. Carthy et al. 1999).

6. Overall Summary

We have reviewed the literature on Context, mostly in relation to the VPF, to ascertain the contexts that have previously been found to alter the value that members of the public place on reducing their own and other people’s risks of adverse health and/or safety outcomes. The review provided an overview of the very many possible contexts that, although theoretically irrelevant for the VPF, have nonetheless been explored empirically and shown, at least in some cases, to matter to members of the public in VPF studies.

We devoted a large proportion of this chapter to a thorough discussion of 2 issues that are both theoretically and empirically relevant to the VPF and to the VOLY. These are Age (which can relate to the age at the time of paying for a risk reduction, age at the time of receiving the risk reduction, or the age of other people benefiting from the health and/or safety improvement) and latency, or discounting. We demonstrated that age is theoretically and empirically important, and yet that neither theory nor empirical analysis so far has been able to unambiguously determine the age effect. There is some overall evidence that as a person ages, they are willing to pay less for a reduction in their risk of fatality, but this effect is far from clearly established. The results for discounting were relatively more clear: delaying a risk reduction reduces its present value in the eyes of members of the public. The degree to which this discounting occurs, and its functional form, have both been outlined with the conclusion that the discount rate appears to be in the region of 10% for most studies (though with considerable variation between studies and between individuals) and the discounting function tends to be non-standard (except in a few rare exceptions). Empirical studies struggle to disentangle the effects of age from effects of delay and discounting, and it is unclear to what extent the age effect is driven by changing consumption patterns over the lifetime. There is, however, no doubt that age and delay both influence the amount people are willing to pay for reductions in their risks of fatality, and that timing issues should be a top priority for future consideration.

We ended with a discussion of behavioural biases and heuristics that may influence stated preference estimates of the value of risks to life and health as estimated in surveys.

7. References

Alberini, A. and Chiabai, A., (2007). Discount rates in risk versus money and money versus money tradeoffs. Risk Analysis: An International Journal, 27(2), 483-498.

Alberini, A., Cropper, M., Krupnick, A. and Simon, N.B. (2004). Does the value of a statistical life vary with age and health status? Evidence from the US and Canada. Journal of Environmental Economics and Management, 48(1), 769-792.

Alberini, A., Cropper, M., Krupnick, A. and Simon, N.B. (2006). Willingness to pay for mortality risk reductions: Does latency matter? Journal of Risk and Uncertainty, 32(3), 231-245.

Alberini, A., Hunt, A. and Markandya, A. (2006). Willingness to pay to reduce mortality risks: evidence from a 3-country contingent valuation study. Environmental and Resource Economics, 33(2), 251-264.

Alberini, A. and Ščasný, M. (2010). Does the cause of death matter? The effect of dread, controllability, exposure and latency on the VSL. FEEM Working Paper No. 139.2010.

Alberini, A. and Ščasný, M. (2011). Context and the VSL: evidence from a stated preference study in Italy and the Czech Republic. Environmental and resource economics, 49(4), 511-538.

Alberini, A., Ščasný, M., Guignet, D. and Tonin, S. (2012). Cancer values of prevented fatalities (VPFs), one size does not fit all: the benefits of contaminated site cleanups in Italy. Journal of the Air & Waste Management Association, 62(7), 783-798.

Alberini, A. and Ščasný, M. (2013). Exploring heterogeneity in the value of a statistical life: cause of death v. risk perceptions. Ecological Economics, 94, 143-155.

Alberini, A., Tonin, S. and Hunt, A. (2008). Literature review about VSL over time: estimating the mortality benefits of environmental policies. Report of the EXIOPOL project, 1-34.

Alberini, A., Tonin, S. and Turvani, M. (2009). Rates of time preferences for saving lives in the hazardous waste site context. FEEM working paper.

Aldy, J.E. and Viscusi, W.K. (2003). Age variations in workers’ value of statistical life (No. w10199). National Bureau of Economic Research.

Aldy, J.E. and Viscusi, W.K. (2007). Age differences in the value of statistical life: revealed preference evidence. Review of Environmental Economics and Policy, 1(2), 241-260.

Ara, S. and Tekeşin, C. (2017). The Monetary valuation of lifetime health improvement and life expectancy gains in turkey. International Journal of Environmental Research and Public Health, 14(10), 1151.

Attema, A.E., Bleichrodt, H., L’Haridon, O., Peretti-Watel, P. and Seror, V. (2018). Discounting health and money: new evidence using a more robust method. Journal of Risk and Uncertainty, 56(2), 117-140.

Attema, A.E., Bleichrodt, H., Rohde, K.I. and Wakker, P.P. (2010). Time-tradeoff sequences for analyzing discounting and time inconsistency. Management Science, 56(11), 2015-2030.

Bateman, I. J. (1996). Household willingness to pay and farmers’ willingness to accept compensation for establishing a recreational woodland. Journal of Environmental Planning and Management, 39(1), 21-44.

Beattie, J., Covey, J., Dolan, P., Hopkins, L., Jones-Lee, M., Loomes, G., Pidgeon, N., Robinson, A. and Spencer, A., (1998). On the contingent valuation of safety and the safety of contingent valuation: part 1-caveat investigator. Journal of Risk and Uncertainty, 17(1), 5-26.

Bleichrodt, H., Gao, Y. and Rohde, K.I., (2016). A measurement of decreasing impatience for health and money. Journal of Risk and Uncertainty, 52(3), 213-231.

Bleichrodt, H. and Johannesson, M. (2001). Time preference for health: A test of stationarity versus decreasing timing aversion. Journal of Mathematical Psychology, 45(2), 265-282.

Bourke, S.M., Plumpton, C.O. and Hughes, D.A. (2018). Societal preferences for funding orphan drugs in the United Kingdom: an application of person trade-off and discrete choice experiment methods. Value in Health, 21(5), 538-546.

Cairns, J. and Van der Pol, M. (1997a). Constant and decreasing timing aversion for saving lives. Social Science and Medicine, 45(11), 1653-1659.

Cairns, J.A. and van Der Pol, M.M. (1997b). Saving future lives. A comparison of 3 discounting models. Health Economics, 6(4), 341-350.

Cameron, T.A. and DeShazo, J.R. (2013). Demand for health risk reductions. Journal of Environmental Economics and Management, 65(1), 87-109.

Cameron, T.A., DeShazo, J.R. and Johnson, E.H. (2009). Willingness to pay for health risk reductions: differences by type of illness. Department of Economics, University of Oregon.

Carlsson, F., Daruvala, D. and Jaldell, H. (2010a). Value of statistical life and cause of accident: a choice experiment. Risk Analysis: An International Journal, 30(6), 975- 986.

Carlsson, F., Daruvala, D. and Jaldell, H., (2010b). Preferences for lives, injuries, and age: a stated preference survey. Accident Analysis & Prevention, 42(6), 1814-1821.

Carlsson, F., Johansson-Stenman, O. and Martinsson, P. (2004). Is transport safety more valuable in the air? Journal of Risk and Uncertainty, 28(2), 147-163.

Carthy,T., Chilton, S., Covey, J., Hopkins, L., Jones-Lee, M., Loomes, G., Pidgeon, N. and Spencer, A. (1999). On the contingent valuation of safety and the safety of contingent valuation: part 2 – the CV/SG “chained” approach. Journal of Risk and Uncertainty, 17(3), 187-213.

Chanel, O. and Luchini, S. (2008). Monetary values for air pollution risk of death: A contingent valuation survey. HAL open access report.

Chanel, O. and Luchini, S., (2014). Monetary values for risk of death from air pollution exposure: a context-dependent scenario with a control for intra-familial altruism. Journal of Environmental Economics and Policy, 3(1), 67-91.

Chapman, G.B. and Elstein, A.S. (1995). Valuing the future: temporal discounting of health and money. Medical Decision Making, 15(4), 373-386.

Chilton, S., Covey, J., Hopkins, L., Jones-Lee, M., Loomes, G., Pidgeon, N. and Spencer, A. (2002). Public perceptions of risk and preference-based values of safety. Journal of Risk and Uncertainty, 25(3), 211-232.

Chilton, S., Covey, J., Jones-Lee, M., Loomes, G. and Metcalf, H. (2004). Valuation of health benefits associated with reductions in air pollution. Defra Publication PB, London.

Chilton, S., Jones-Lee, M., Kiraly, F., Metcalf, H. and Pang, W. (2006). Dread risks. Journal of Risk and Uncertainty, 33(3), 165-182.

Cookson, R. (2000). Incorporating psycho-social considerations into health valuation: an experimental study. Journal of Health Economics, 19(3), 369-401.

Copley-Merriman, K., (2018). Rare diseases: addressing the challenges in diagnosis, drug approval, and patient access. Value in Health, 21(5), 491-492.

Covey, J., Robinson, A., Jones-Lee, M. and Loomes, G. (2010). Responsibility, scale and the valuation of rail safety. Journal of Risk and Uncertainty, 40(1), 85-108.

Cropper, M.L., Aydede, S.K. and Portney, P.R. (1992). Rates of time preference for saving lives. The American Economic Review, 82(2), 469-472.

Cropper, M.L., Aydede, S.K. and Portney, P.R., (1994). Preferences for life saving programs: how the public discounts time and age. Journal of Risk and Uncertainty, 8(3), 243-265.

Cropper, M.L. and Portney, P.R., (1990). Discounting and the evaluation of lifesaving programs. Journal of Risk and Uncertainty, 3(4), 369-379.

Cubitt, R. P., Navarro-Martinez, D., and Starmer, C. (2015). On preference imprecision. Journal of Risk and Uncertainty, 50(1), 1-34.

Dekker, T., Brouwer, R., Hofkes, M. and Moeltner, K., (2011). The effect of risk context on the value of a statistical life: a Bayesian meta-model. Environmental and Resource Economics, 49(4), 597-624.

Desaigues, B., Ami, D., Bartczak, A., Braun-Kohlová, M., Chilton, S., Czajkowski, M., Farreras, V., Hunt, A., Hutchison, M., Jeanrenaud, C. and Kaderjak, P. (2011). Economic valuation of air pollution mortality: A 9-country contingent valuation survey of value of a life year (VOLY). Ecological indicators, 11(3), 902-910.

Desaigues, B., Rabl, A., Ami, D., My, K.B., Masson, S., Salomon, M.A. and Santoni, L. (2007). Monetary value of a life expectancy gain due to reduced air pollution: Lessons from a contingent valuation in France. Revue D’économie Politique, 117(5), pp.675-698.

DeShazo, J.R. and Cameron, T.A. (2004). Mortality and morbidity risk reduction: an empirical life-cycle model of demand with 2 types of age effects, Working Paper, Department of Public Policy, UCLA.

Dockins, C., Jenkins, R.R., Owens, N., Simon, N.B. and Wiggins, L.B. (2002). Valuation of childhood risk reduction: The importance of age, risk preferences, and perspective. Risk Analysis, 22(2), 335-346.

Eeckhoudt, L. R., and Hammitt, J. K. (2001). Background risks and the value of a statistical life. Journal of risk and uncertainty, 23(3), 261-279.

Ehrlich, I. (2000). Uncertain lifetime, life protection, and the value of life saving. Journal of Health Economics, 19(3), 341-367.

Evans, M.F. and Schaur, G. (2010). A quantile estimation approach to identify income and age variation in the value of a statistical life. Journal of Environmental Economics and Management, 59(3), 260-270.

Evans, M. F. and Smith, V. K. (2006). Do we really understand the age–VSL relationship? Resource and Energy Economics, 28(3), 242-261.

Fischhoff, B. (1991). Value elicitation: Is there anything in there? American Psychologist, 46(8), 835.

Frederick, S. (2003). Measuring intergenerational time preference: Are future lives valued less? Journal of Risk and Uncertainty, 26(1), 39-53.

Frederick, S. (2006). Valuing future life and future lives: A framework for understanding discounting. Journal of Economic Psychology, 27(5), 667-680.

Frederick, S., Loewenstein, G. and O’donoghue, T. (2002). Time discounting and time preference: A critical review. Journal of Economic Literature, 40(2), 351-401.

Fuchs, V.R., (1982). National Bureau of Economic Research, Fuchs, V.R., 1982. Time preference and health: an exploratory study. Economic Aspects of Health, 93-120. University of Chicago Press, Chicago.

Gafni, A. and Torrance, G.W. (1984). Risk attitude and time preference in health. Management Science, 30(4), 440-451.

Grisolía, J.M., Longo, A., Hutchinson, G. and Kee, F. (2018). Comparing mortality risk reduction, life expectancy gains, and probability of achieving full life span, as alternatives for presenting CVD mortality risk reduction: A discrete choice study of framing risk and health behaviour change. Social Science & Medicine. 211, 164-174.

Gu, Y., Lancsar, E., Ghijben, P., Butler, J.R. and Donaldson, C. (2015). Attributes and weights in health care priority setting: a systematic review of what counts and to what extent. Social Science & Medicine, 146, 41-52.

Guria, J., Leung, J., Jones-Lee, M. and Loomes, G. (2005). The willingness to accept value of statistical life relative to the willingness to pay value: evidence and policy implications. Environmental & Resource Economics, 32, 113-127.

Hammar, H. and Johansson‐Stenman, O. (2004). The value of risk‐free cigarettes–do smokers underestimate the risk? Health economics, 13(1), 59-71.

Hammitt, J. K. (2007). Valuing changes in mortality risk: lives saved versus life years saved. Review of Environmental Economics and Policy, 1(2), 228-240.

Hammitt, J.K. and Graham, J.D. (1999). Willingness to pay for health protection: inadequate sensitivity to probability? Journal of risk and uncertainty, 18(1), 33-62.

Hammitt, J.K. and Liu, J.T. (2004). Effects of disease type and latency on the value of mortality risk. Journal of Risk and Uncertainty, 28(1), 73-95.

Hammitt, J.K. and Tunçel, T. (2015). Preferences for life-expectancy gains: Sooner or later? Journal of Risk and Uncertainty, 51(1), 79-101.

Hanemann, W.M. (1994). Valuing the environment through contingent valuation. Journal of Economic Perspectives, 8(4), 19-43.

Harrison, G. W., Lau, M. I., and Rutström, E. E. (2007). Estimating risk attitudes in Denmark: A field experiment. Scandinavian Journal of Economics, 109(2), 341-368.

Harvey, C.M., (1986). Value functions for infinite-period planning. Management Science, 32(9), 1123-1139.

Horowitz, J.K. and Carson, R.T. (1990). Discounting statistical lives. Journal of Risk and Uncertainty, 3(4), 403-413.

Huber, J., and Puto, C. (1983). Market boundaries and product choice: Illustrating attraction and substitution effects. Journal of Consumer Research, 10(1), 31-44.

Itaoka, K., Krupnick, A., Akai, M., Alberini, A., Cropper, M. and Simon, N. (2007). Age, health, and the willingness to pay for mortality risk reductions: a contingent valuation survey of Shizuoka, Japan, residents. Environmental Economics and Policy Studies, 8(3), 211-237.

Johannesson, M. and Johansson, P.O. (1996). To be, or not to be, that is the question: an empirical study of the WTP for an increased life expectancy at an advanced age. Journal of Risk and Uncertainty, 13(2), 163-174.

Johannesson, M., Johansson, P.O. and Löfgren, K.G. (1997). On the value of changes in life expectancy: blips versus parametric changes. Journal of Risk and Uncertainty, 15(3), 221-239.

Johansson, P. O. (2001). Is there a meaningful definition of the value of a statistical life? Journal of Health Economics, 20(1), 131-139.

Johansson, P. O., (2002). On the definition and age-dependency of the value of a statistical life. Journal of Risk and Uncertainty, 25(3), 251-263.

Johansson-Stenman, O. and Martinsson, P. (2008). Are some lives more valuable? An ethical preferences approach. Journal of Health Economics, 27(3), 739-752.

Jones-Lee, M. (1974). The value of changes in the probability of death or injury. Journal of Political Economy, 82, 835–849.

Jones-Lee, M.W. (1991). Altruism and the value of other people’s safety. Journal of Risk and Uncertainty, 4(2), 213-219.

Jones-Lee, M., Chilton, S., Metcalf, H. and Nielsen, J. S., (2015). Valuing gains in life expectancy: clarifying some ambiguities. Journal of Risk and Uncertainty, 51(1), 1-21.

Jones-Lee, M.W., Hammerton, M. and Philips, P.R. (1985). The value of safety: results of a national sample survey. The Economic Journal, 95(377), 49-72.

Jones-Lee, M., Loomes, G., O’Reilly, D. and Philips, P. (1993). The value of preventing non-fatal road injuries: findings of a willingness-to-pay national sample survey. TRL Contractor Report, (CR 330).

Jones-Lee, M.W. and Loomes, G. (1995). Scale and context effects in the valuation of transport safety. Journal of Risk and Uncertainty, 11(3), 183-203.

Jones-Lee, M., Loomes, G. and Spackman, M. (2007). Human costs of a nuclear accident: Final rRport. Health and Safety Executive. NERA Economic Consulting, London.

Kahneman, D. and Knetsch, J.L. (1992). Valuing public goods: the purchase of moral satisfaction. Journal of Environmental Economics and Management, 22(1), 57-70.

Keeler, E.B. and Cretin, S. (1983). Discounting of life-saving and other nonmonetary effects. Management science, 29(3), 300-306.

Knetsch, J. L. (1989). The endowment effect and evidence of nonreversible indifference curves. American Economic Review, 79(5), 1277-1284.

Kniesner, T.J., Viscusi, W.K. and Ziliak, J.P. (2006). Life-cycle consumption and the age-adjusted value of life. The BE Journal of Economic Analysis & Policy, 5(1),1-36.

Koopmans, T.C. (1969). Objectives, constraints, and outcomes in optimal growth models. In Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner, 110-132. Springer, Berlin, Heidelberg.

Krahn, M. and Gafni, A. (1993). Discounting in the economic evaluation of health care interventions. Medical Care, 31(5) 403-418.

Krupnick, A. (2007). Mortality-risk valuation and age: stated preference evidence. Review of Environmental Economics and Policy, 1(2), 261-282.

Krupnick, A., Alberini, A., Cropper, M., Simon, N., O’brien, B., Goeree, R. and Heintzelman, M. (2002). Age, health and the willingness to pay for mortality risk reductions: a contingent valuation survey of Ontario residents. Journal of Risk and Uncertainty, 24(2), 161-186.

Laibson, D. (1997). Golden eggs and hyperbolic discounting. The Quarterly Journal of Economics, 112(2), 443-478.

Lichtenstein, S., and Slovic, P. (Eds.). (2006). The construction of preference. Cambridge University Press, MA.

Lipscomb, J. (1989). Time preference for health in cost-effectiveness analysis. Medical Care, S233-S253.

Loewenstein, G. and Prelec, D. (1992). Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics, 107(2), 573-597.

Loewenstein, G.F. and Prelec, D. (1993). Preferences for sequences of outcomes. Psychological review, 100(1), 91.

Loomes, G and Pogrebna, G. (2016). Do Preference Reversals Disappear When We Allow for Probabilistic Choice? Management Science 63(1),166-184.

Magat, W.A., Viscusi, W.K. and Huber, J. (1996). A reference lottery metric for valuing health. Management Science, 42(8), 1118-1130.

Mazur, J.E. (1987). An adjusting procedure for studying delayed reinforcement. In Commons, ML. Mazur, JE. Nevin, JA, (eds.) Quantitative analyses of behaviour. 5, 55-73.

McDonald, R.L., Chilton, S.M., Jones-Lee, M.W. and Metcalf, H.R. (2016). Dread and latency impacts on a VSL for cancer risk reductions. Journal of Risk and Uncertainty, 52(2), 137-161.

McDonald, R.L., Chilton, S.M., Jones-Lee, M.W. and Metcalf, H.R.T. (2017). Evidence of variable discount rates and non-standard discounting in mortality risk valuation. Journal of Environmental Economics and Management, 82, 152-167.

Mendeloff, J.M. and Kaplan, R.M. (1989). Are large differences in “lifesaving” costs justified? A psychometric study of the relative value placed on preventing deaths. Risk Analysis, 9(3), 349-363.

Moore, M.J. and Viscusi, W.K., (1988). The quantity‐adjusted value of life. Economic Inquiry, 26(3), 369-388.

Moore, M.J. and Viscusi, W.Ksta. (1990). Discounting environmental health risks: new evidence and policy implications. Journal of Environmental Economics and Management, 18(2), S51-S62.

Nielsen, J.S. (2010). Approaching the value of a life year: empirical evidence from a Danish contingent valuation survey. Nationaløkonomisk Tidsskrift, 148(1), 67-85.

Nielsen, J.S., Chilton, S., Jones-Lee, M. and Metcalf, H. (2010). How would you like your gain in life expectancy to be provided? An experimental approach. Journal of Risk and Uncertainty, 41(3), 195-218.

Olsen, J.A. (1993). Time preferences for health gains: an empirical investigation. Health Economics, 2(3), 257-265.

Persson, U., Norinder, A., Hjalte, K. and Gralén, K., (2001). The value of a statistical life in transport: findings from a new contingent valuation study in Sweden. Journal of Risk and Uncertainty, 23(2), 121-134.

Phelps, E.S. and Pollak, R.A. (1968). On second-best national saving and game- equilibrium growth. The Review of Economic Studies, 35(2), 185-199.

Pinto‐Prades, J. L., Sánchez‐Martínez, F. I., Abellán‐Perpiñán, J. M., & Martínez‐ Pérez, J. E. (2018). Reducing preference reversals: The role of preference imprecision and non-transparent methods. Health economics, 27(8), 1230-1246.

Ramsey, F.P. (1928). A mathematical theory of saving. The Economic Journal, 38(152), 543-559.

Robinson, A., Covey, J., Spencer, A. and Loomes, G. (2010). Are some deaths worse than others? The effect of ‘labelling’ on people’s perceptions. Journal of Economic Psychology, 31(3), 444-455.

Rohrmann, B. (2008). Risk perception, risk attitude, risk communication, risk management: A conceptual appraisal. In Conferencia presentada en la Sociedad Internacional de Gerenciamiento de Emergencias.

Rosen, S. (1988). The value of changes in life expectancy. Journal of Risk and Uncertainty, 1(3), 285-304.

Rowlatt, P., Spackman, M., Jones, S., Jones-Lee, M. and Loomes, G. (1998). Valuation of deaths from air pollution. Report prepared by National Economic Research Associates for the Department of Environment, Transport, and the Regions and the Department of Trade and Industry, London.

Savage, L., (1993). An empirical investigation into the effect of psychological perceptions on the willingness-to-pay to reduce risk. Journal of Risk and Uncertainty, 6(1), 75-90.

Scharff, R.L. and Viscusi, W.K. (2011). Heterogeneous rates of time preference and the decision to smoke. Economic Inquiry, 49(4), 959-972.

Shepard, D. S. and Zeckhauser, R. J. (1984). Survival versus consumption. Management Science, 30(4), 423-439.

Slovic, P. (1987). Perception of risk. Science, 236(4799), 280-285.

Smith, V.K. and Desvousges, W.H. (1987). An empirical analysis of the economic value of risk changes. Journal of Political Economy, 95(1), 89-114.

Smith, V.K., Evans, M.F., Kim, H. and Taylor Jr, D.H. (2004). Do the near-elderly value mortality risks differently? Review of Economics and Statistics, 86(1), 423-429.

Spackman, M., Evans, A., Jones-Lee, M., Loomes, G., Holder, S., Webb, H. and Sugden, R. (2011). Updating the VPF and VPIs: Phase 1: Final Report Department for Transport. NERA. London.

Starmer (2000). Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Rislk. Journal of Economic Literature XXXVIII, 332-382

Subramanian, U. and Cropper, M. (2000). Public choices between life-saving programs: The tradeoff between qualitative factors and lives saved. Journal of Risk and Uncertainty, 21(1), 117-149.

Sunstein, C. (1997). Bad deaths. Journal of Risk and Uncertainty, 14(3), 259-282.

Tsuge, T., Kishimoto, A. and Takeuchi, K. (2005). A choice experiment approach to the valuation of mortality. Journal of Risk and Uncertainty, 31(1), 73-95.

Tversky, A., and Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131.

Tversky, A., and Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297-323.

Tversky, A., Sattath, S., and Slovic, P. (1988). Contingent weighting in judgment and choice. Psychological review, 95(3), 371.

Van der Pol, M. and Cairns, J. (2001). Estimating time preferences for health using discrete choice experiments. Social Science & Medicine, 52(9), 1459-1470.

Van der Pol, M. and Cairns, J. (2002). A comparison of the discounted utility model and hyperbolic discounting models in the case of social and private intertemporal preferences for health. Journal of Economic Behavior & Organization, 49(1), 79-96.

Van der Pol, M. and Cairns, J. (2011). Descriptive validity of alternative intertemporal models for health outcomes: an axiomatic test. Health Economics, 20(7), 770-782.

Van Houtven, G., Sullivan, M.B. and Dockins, C. (2008). Cancer premiums and latency effects: A risk tradeoff approach for valuing reductions in fatal cancer risks. Journal of Risk and Uncertainty, 36(2), 179-199.

Vassanadumrongdee, S. and Matsuoka, S. (2005). Risk perceptions and value of a statistical life for air pollution and traffic accidents: evidence from Bangkok, Thailand. Journal of Risk and Uncertainty, 30(3), 261-287.

Viscusi, W.K. and Aldy, J.E. (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.K., Huber, J. and Bell, J. (2014). Assessing whether there is a cancer premium for the value of a statistical life. Health economics, 23(4), 384-396.

Viscusi, W.K. and Moore, M.J. (1989). Rates of time preference and valuations of the duration of life. Journal of public economics, 38(3), 297-317.

Vlachokostas, C., Achillas, C., Slini, T., Moussiopoulos, N., Banias, G. and Dimitrakis, I. (2011). Willingness to pay for reducing the risk of premature mortality attributed to air pollution: a contingent valuation study for Greece. Atmospheric Pollution Research, 2(3), 275-282.

Weinstein, M.C. and Stason, W.B. (1977). Foundations of cost-effectiveness analysis for health and medical practices. New England Journal of Medicine, 296(13), 716-721.

Wolff, J. and Orr, S. (2009). Cross-sector weighting and valuing of qalys and vpfs a report for the inter-departmental group for the valuation of life and health. online at http://www.ucl.ac.uk/cpjh/docs/IGVLH.pdf.

Appendix 1: Data Extraction Tool

A data extraction tool was devised and applied to each paper to ensure quality and consistency in the reporting of each contextual feature identified within study. The contextual features analysed included those identified in the literature search and the contextual factors described in Schedule A.

Contextual Feature

The Risk (Purely Random; Controllability; Deliberate harm by others; Carries potential responsibility for risk to others e.g. Infection; WTA vs WTP; Size of the Probability of the Risk; Variability of the Probability of Risk)

The Harm (Size and Duration; Mainly affecting life expectancy; Variability; Gain in health vs Loss in health; Single harm vs Multiple Harm).

Dread Factors (Voluntariness; Responsibility; Personal Exposure; Public Exposure; Media Attention; Immediacy/latency; Number per year; Technology Induced or Natural Hazard)

Knowledge (Private; Expert-Knowledge/Public Knowledge)

Other (Regulation of health and safety in the workplace; Rule of Rescue; Externalities (not involving increased risk; Public or Private Programme)

The Person at Risk (Age/year of Birth; gender; Occupation; Income; Quality of Life and/or life Expectancy]; Income; Member of a Population at Risk; Basline risk)

Other People (Rarity; Mass Casualties; Own Health compared to Average Health; Age compared to average age; wealth compared to average wealth)

1. We choose not to consider the issue of deflating a VOLY, since the political ramifications of recommending such a procedure render it highly unlikely to happen in practice. ↩

2. Where authors in the literature have used the term VSL (or Value of Statistical Life) we have tended to follow suit. Elsewhere, we use the term VPF in accordance with UK government convention. ↩

3. LibSearch includes the following databases (among others): Compendex, EBSCO, JSTOR, Medline, Ovid, ProQuest, Scopus, and Web of Science. ↩

4. Although we use the term VPF in general, in this subsection we follow the convention of VSL, as in the source studies. ↩

5. However, these effects were largely negated when baseline risk was factored in. ↩

6. We emphasise that these summary statements are intended to give a clear impression of the consensus (or lack thereof) of the findings in the literature and are not intended as recommendations for policy change. ↩

7. Although they note that women also had a lower income. ↩

8. This could also be WTP-QALY. ↩

9. The “why bother” is opposite to the “dead-anyway” effect whereby a high level of a specific risk may increase WTP to reduce that risk, since the opportunity cost of paying to reduce the risk is low in expectation. Since this is not necessarily related to age, we do not consider the dead-anyway effect further in this section. ↩

10. If you are a net borrower, you should use the £1000 to pay off £1000 of your debt today, avoiding paying £1000 * i in interest on this debt. The logic still dictates that £1000 now is better than £1000 in one year. ↩