- <sup>_r_</sup> _i_<sup>:</sup> fatal job risk, worker _i_

- <sup>_q_</sup> _i_<sup>:</sup> nonfatal job risk, worker _i_

- _WCi_ :  worker's compensation

- <sup>_u_</sup> _i_<sup>:</sup> random error term

Results are often sensitive to the equation specification. Clearly, without controlling for other worker characteristics, the coefficient on fatal job risk would be negative rather than positive—jobs with the highest risk of death often pay the least. However, the magnitude of the coefficient on fatal risk ( _γ0_ ) is often sensitive to what other variables are included in the equation.<sup>22</sup> Because _γ0_ represents the proportionate increase in the wage for a one unit change in fatal job risk on the wage, the VSL is calculated by multiplying _γ0_ by the average wage and dividing by a one-unit change in risk.

The published literature includes over four dozen hedonic wage (HW) studies conducted in high income countries.<sup>23</sup> The mean VSL, in 2000 USD, is between $5 and $6 million; however, the range of estimates is large. Four recent studies attempt to explain variation in VSL estimates across studies as a function of study and respondent characteristics (Bowland and Beghin, 2001; Miller, 2000; Mrozek and Taylor, 2002; Viscusi and Aldy, 2003). Using VSL estimates from various studies, the authors run meta-regressions in which the VSL is the dependent variable and covariates include mean worker income, the mean size of the risk reduction, the proportion of workers unionized, whether the study included controls for inter-industry wage differentials or for non-fatal job risk. All four studies find that the VSL increases with the average income of workers in the study, and declines with the mean level of risk, at least after some point. Mrozek and Taylor (2002) find that studies that fail to control for inter-industry wage differentials report larger VSLs.

Meta-regressions are useful as empirical literature reviews—they indicate which factors raise or lower a VSL estimate, holding other features of study design constant. Sometimes they are used to predict the VSL for a preferred set of covariates.<sup>24</sup> However, care must be taken in interpreting the coefficients in a meta-regression. The coefficient on average worker income in a meta-regression should not be interpreted as the income elasticity of the VSL, for two reasons. Because most models use the semi-log specification in (8), the VSL = _γ0_ *Wage/(one unit change in risk). The elasticity of the VSL with respect to the wage (assuming no other covariates are included in the equation)

> 22 Black et al. (2003), in a reanalysis of data from compensating wage studies requested by the USEPA, show that the magnitude and sign of _γ0_ vary significantly depending on whether industry and/or state dummies are included in the hedonic wage equation.  In 4 different equation specifications for each of 10 datasets they find only 16 (out of 40) coefficients on fatal risk that are positive and statistically significant for men and 14 (out of 40) coefficients that are positive and statistically significant for women. 23 Viscusi and Aldy (2003) list 30 HW studies using US data.  They also cite 23 HW studies conducted in countries outside of the US, 18 of which were conducted in OECD countries.  Kochi et al. (2006) and Mrozek and Taylor (2002)cite 47 HW studies in high-income countries.  The five recent meta-analyses are Miller (2000), Bowland and Beghin (2001), Mrozek and Taylor (2002), Viscusi and Aldy (2003), and Kochi et al. (2006).

> 24 Both Mrozek and Taylor (2002) and Viscusi and Aldy use the meta-regressions in this way.

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