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The European Journal of Health Economics

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01.08.2011 | Original Paper

Age effects in monetary valuation of reduced mortality risks: the relevance of age-specific hazard rates

verfasst von: Andrea M. Leiter

Erschienen in: The European Journal of Health Economics | Ausgabe 4/2011

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Abstract

This paper highlights the relevance of age-specific hazard rates in explaining the age variation in “value of statistical life” (VSL) figures. The analysis—which refers to a stated preference framework—contributes to the ongoing discussion of whether benefits resulting from reduced mortality risk should be valued differently depending on the age of the beneficiaries. By focussing on a life-threatening environmental phenomenon I show that the consideration of the individual’s age-specific hazard rate is important. If a particular risk affects all individuals regardless of their age so that their hazard rate is age-independent, VSL is rather constant for people at different age; if hazard rate varies with age, VSL estimates are sensitive to age. The results provide an explanation for the mixed outcomes in empirical studies and illustrate in which cases an adjustment to age may or may not be justified. Efficient provision of live-saving measures requires that such differences to be taken into account.

For example, see Alberini et al. (2004, 2006), Johannesson et al. (1997), Jones-Lee et al. (1985), Liu et al. (2007).

See Hammitt (2007), Aldy and Viscusi (2007), and Krupnick (2007) for a comprehensive discussion of the background and overview of the relevant literature.

Viscusi and Aldy (2007) provide a discussion of how an individuals’ hazard rate influence VSL estimates in a revealed preference framework.

Snow avalanches are a common phenomenon in winter and affect skiers but also residents. This is due to the topographical characteristics of residential areas in Tyrol. Tyrol is situated in the middle of the Alps. One-third of its 12,600 km² area is not habitable (glaciers, rocks, mountain pastures). Residential areas are often located in rather steep terrain or are at least surrounded by mountains. Although public and private institutions (communities, ski resorts) take various precautions (e.g. construction and maintenance of tunnels and barriers, premature blasting of dangerous accumulations of snow) to protect individuals on roads, in residential areas and in ski resorts an element of risk remains. The 10-year average of avalanche-related fatalities amounts to 16 deaths per year.

Unfortunately 43.5% did not answer the question relating to their income, which complicates the estimation of the income effect. In order to avoid losing these observations, a single imputation method (Davey et al. (2001), Little and Rubin (1987), Whitehead (1994)) was applied and missing income is replaced by the mean income of employed persons in the individual’s residence. In addition, a dummy variable is generated which equals 1 in cases where a replacement has been made to control for potential influences of the imputation.

Health categories were provided in the form of functionality examples (healthy: no diseases or only occasional short-lived diseases such as flu; moderate illness: chronic diseases such as hay fever and allergies; severe illness/severe disability: severe chronic illness or severe physical impairment, in need of long-term care).

992 respondents in autumn and 672 in winter were asked to value the prevention of an increase from 1/42,500 to 2/42,500 (=group 1). 333 individuals (=group 2) in the winter sample based their decisions on a hypothetical prevention of a three times higher increase from 1/42,500 to 4/42,500 (=quadruplication of baseline risk).

To define the range of the bid vector, information from a previous pre-test sample was used.

Though only yes/no answer possibilities were offered, a “do not know” response was accepted. To ensure conservative estimates, the “do not know” responses were interpreted as negative responses and are included in the analysis. See Carson et al. (1998) for a related discussion.

A sensitivity analysis shows that the results and implications regarding age effects still hold if this group were included.

Supportive arguments for this procedure are given in Hackl and Pruckner (2005) and Olsen et al. (2004).

The hazard function denotes the probability of dying after age s conditional on attaining age s.

The central findings in this paper are based on the comparison of two sub samples that consist of individuals of all ages (but differ in their hazard rate). Hence, potential changes in consumption patterns should occur in both samples and the size may be similar for both groups. In the following derivations, the potential age-dependency of consumption is ignored (i.e. consumption is considered as constant over time so that ERPVU is proportional to the discounted remaining life expectancy) and the focus is on the influence of age-specific hazard rates for VSL estimates.

Previous sensitivity analyses have shown that models assuming a Weibull or log-normal distribution of the error term leads to similar findings concerning the sensitive factors on WTP. Additionally, also a logistic and normal distribution was used, simultaneously allowing for a positive probability of zero responses (analogous to Tobit models). The results in these models also correspond quite well with the findings for the Weibull and log-normal distribution. However, regarding the log likelihood values, the Weibull model is superior to the other distribution assumptions.

The error term in the Weibull follows the Type I extreme value distribution where the scale parameter varies across individuals: ψ_i = exp(X _iβ).

CBA are associated with potential pareto improvements. A change is favoured if nobody is getting worse but at least one individual can improve his/her status or, respectively, if the winner of an action could compensate the loser. The mean takes into account such considerations (Carson 2000).

Conducting separate regressions for each age class would postulate an adequate sample size for each group, which is not given by the Tyrolean data set.

Clearly, an individual’s health status and their fitness also determine the probability of survival once caught in an avalanche. As this holds for skiers and non-skiers alike, this does not explain the different hazard rates across the two groups.

However, statistics also show that avalanches can also affect residential areas, as was seen in the winter of 1998/1999 when 31 people died due to a single avalanche event (Amt der Tiroler Landesregierung, Lawinenwarndienst Tirol 2003).

Considering only the corresponding numbers for the survey period (winter 2004/2005), the youngest (oldest) face the lowest (highest) risk.

As risk perception is a complex measure that might be influenced by factors that cannot be controlled for, this variable might be correlated with the error term. However, when risk perception is regressed on a set of variables and the error term is included as additional explanatory variable in the original equation, the error coefficient does not reveal a significant influence on WTP. This approach is analogous to that of Smith and Blundell (1986) and Rivers and Vuong (1988), who discussed the exogeneity test in a Tobit and probit framework.

The variables healthy and jobrisk were introduced to test for the “background risk hypothesis” (Eeckhoudt and Hammitt 2001). These authors found that if the marginal utility of bequest is positive and high competitive risks (background risks) occur, WTP for reducing a specific mortality risk is smaller due to lower benefits from risk reduction when respondents still face a high residual risk level. Assuming that healthy people (workers in risky jobs) face lower (higher) remaining risks the corresponding coefficients estimated do not support their hypothesis.

Kahneman et al. (1993) show that WTP is higher for the correction of man-made harm than for damages from natural causes because the former seems to be considered more upsetting by the individual. However, Walker et al. (1999) find lower WTP to undo problems caused by humans compared to naturally occurring events, which relates to the individuals’ own responsibility to reduce their risk exposure.

Out of 1,481 respondents, 254 cited the larger risk reduction. Hence, the average respondent refers the WTP statement to the smaller risk change. Calculating separate WTP values for the larger risk reduction would lead to imprecise estimates due to the low number of observations, particularly in the upper age classes.

There are further considerable deviations in absolute WTP values (e.g. between age-class 35–44 and 55–62 or 55–62 and 63+) but they are statistically insignificant due to large standard errors and the small sample size in the penultimate age class.

These findings are also in line with the findings in Viscusi and Aldy (2007), who discuss the relevance of age-specific hazard rates for VSL estimates in a revealed preference setting.

Haab and McConnell (2002) provide a detailed explanation and examples how to calculate Turnbull mean values in a CV framework.

See Haab and McConnell (2002), pp. 80–83, for a discussion.

WTP is significantly lower for the 35–44 year-olds compared to the 18–24 group. Significantly higher WTP values are observable for non-skiers aged 45–54 and 54–64 compared to people at age 35–44.

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Titel: Age effects in monetary valuation of reduced mortality risks: the relevance of age-specific hazard rates
verfasst von: Andrea M. Leiter
Publikationsdatum: 01.08.2011
Verlag: Springer-Verlag
Erschienen in: The European Journal of Health Economics / Ausgabe 4/2011
Print ISSN: 1618-7598
Elektronische ISSN: 1618-7601
DOI: https://doi.org/10.1007/s10198-010-0240-8

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