would be one—by construction. More importantly, an equation in which the VSL from various studies are regressed on study and worker characteristics does not represent a structural relationship—it does not indicate how, for an individual, the VSL changes with income, or with factors that affect preferences.<sup>25</sup> Thus, the conclusion of Viscusi and Aldy (2003) that the income elasticity of the VSL is 0.5 (a finding echoed by Mrozek and Taylor (2002)) or that it is 1.0 (Miller (2000)) must be viewed with skepticism.

_Stated Preference Studies_ Hedonic wage studies are termed a revealed preference approach to estimating the VSL, because they rely on observed behavior. Compensation for fatal job risk is, however, “revealed” only by controlling for other variables, and is therefore plagued by econometric problems, some of which have been discussed above.<sup>26</sup> An alternative is to use direct questioning approaches when valuing mortality risk, which can be tailored to the age at which risk reductions occur and to the nature of the risks valued. Contingent valuation (CV) (or stated preference) studies have both advantages and disadvantages. One advantage of a contingent valuation study is that is easier to see how WTP for a risk reduction varies with age and income.<sup>27</sup> A disadvantage of CV studies is that they often make apparent respondents’ difficulties in consistently valuing small probabilities.<sup>28</sup> Because contingent valuation studies ask hypothetical questions, it is standard practice for these studies to include tests of internal and external validity of responses. External scope tests vary the size of the risk reduction valued across respondents to see whether WTP increases with the size of the risk reduction. Failure of WTP to increase with the size of the risk reduction suggests that respondents do not perceive risk changes correctly, or are valuing a generalized commodity (“good health”) rather than a quantitative risk reduction. Internal scope tests check to see whether WTP increases with the size of the risk reduction for a given respondent. Tests of external validity also include checking whether responses vary, as expected, with income.<sup>29</sup> Kochi et al. (2006) in their meta-analysis of VSL studies from high income countries draw on 18 contingent valuation studies, and 42 HW studies. When the point estimates from the studies are combined using empirical Bayes methods (i.e., weighting the VSL estimates in inverse proportion to their precision), the mean VSL from CV studies is significantly lower than for HW studies, a result noted by others. Specifically, the

> 25 Recall that income is endogenous in an hedonic labor market.  To estimate the impact of changes in nonwage income on compensating wage differentials requires estimating workers’ marginal bid functions as a function of non-wage income.  See Biddle and Zarkin (1988).

> 26 Other problems include non-classical errors in measuring fatal job risk, and the endogeneity of the risk variable (see Black et al., 2003).

> 27 Recall that, in an HW study, income is endogenous.  Estimating the impact of changes in non-wage income on compensating wage differentials requires solving the identification problem in hedonic markets (Biddle and Zarkin, 1988).

> 28 For example, WTP for a reduction in risk of death seldom increases in proportion to the size of the risk change, which suggests that respondents do not perceive risk changes as economists expect them to. 29 The results of CV studies are also sensitive to the specification of models used to analyze the data; see, for example, Alberini (2005).

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