Estimating the value of safety with labour market data: are the results trustworthy?

Abstract

We use a panel dataset of UK workers, combined with risk data at the four-digit industry level, to look for evidence of compensating wage differentials for workplace risk. We discuss various econometric problems associated with the hedonic wage approach, namely the instability of the estimates to specification changes, unobserved heterogeneity and endogeneity. We find evidence of significant compensating wage differentials and Values of a Statistical Life (VSL) figures only under the most restrictive assumptions, i.e. when we assume that there is no unobserved heterogeneity and that all regressors are exogenous. However, the VSL values are large and vary dramatically with the inclusion or exclusion of industry and/or occupation dummies, as well as with the addition of nonfatal risk. When we specify models that allow for heterogeneity and endogeneity of risk and of other regressors, we find no evidence of compensating wage differentials. We conclude that if compensating differentials for risk exists, econometric problems and the changing nature of labour markets prevent us from observing them. We also conclude that models and techniques for panel data that account for unobserved heterogeneity and endogeneity present a completely different picture about compensating wage differentials than that inferred by most wage-risk studies, which have generally used single cross-sections of data.

Notes

¹ In some cases, studies based on UK data have found the VSL to be much larger than the upper bound of this range. For example, Siebert and Wei (1994), Sandy and Elliott (1996), Arabsheibani and Marin (2000) and Sandy (2001) peg the VSL in the range between €4.3 million and €74.4 million (equal to $4.0 million to $68.5 million at the 2000 exchange rate). A meta-analysis by CSERGE (1999) generates a range of VSL figures between €2.9 million and €100 million, resulting in weighted average equal to €6.5 million (all 2000 €, the corresponding dollar amounts being $2.7, $92.1 and $6.0 million).

² Using the 1995 Swiss Labor Force Survey (SLFS) and the 1994 Swiss Wage Structure Survey (SWSS), Baranzini and Ferro Luzzi peg the VSL implicit in the choices of Swiss workers in the range of CHF 10–15 million (Swiss Francs, equivalent to $6.5–9.5 million 2000 US dollars). They find that the VSL depends on risk level, union coverage and age.

³ Clearly, doing so assumes that individuals would apply the same marginal rate of substitution between income and risk in both the original and the new policy context. This reliance on labour market estimates of the VSL–which occurs when original estimates of the willingness to pay to reduce the risk of dying in a specified environment context are not available–is not uncontroversial. The use of VSL figures from compensating wage studies when computing the mortality benefits of environmental policies has been criticized on the grounds of the fact that it mirrors the preferences of healthy males whose average age is 40, rather than those of the primary beneficiaries of environmental policies–the elderly and those in compromised health. Adjustments to the VSL for remaining life years were subsequently proposed, and eventually repealed.

⁴ See Kniesner et al. (2006) for use of longitudinal data for US workers.

⁵ In empirical work, the logarithmic transformation of the wage rate often replaces w as the dependent variable in the regression. The wage rate, w, and fatality risk, p, are usually measured on an annual basis.

⁶ In addition, Viscusi (1993) recommends that Equation 3 should include expected worker compensation in the event of a nonfatal workplace accident, i.e. (WC × q), where WC is the level of workers compensation paid out to the worker if he experiences an accident at work.

⁷Dorman and Hagstrom (1998) question the existence of wage-risk compensation for nonunion workers in the US.

⁸ When treating workplace mortality as exogenous, they find evidence of the existence of compensating wage differentials consistent with an average VSL to be around £9.7 million, with lower values for manual workers and larger values for managerial/professional workers.

⁹ Wei (1999) instruments for risk and assumes that the north and south of England are separate labour markets to identify the VSL using a structural approach similar to that previously used in Biddle and Zarkin (1988).

¹⁰ The labour economics literature has devoted considerable attention to the issue of mismeasured wages (e.g. Griliches and Hausman, 1984; Bound and Krueger, 1991; Bound et al., 2001; Kim and Solon, 2005) and the possible correlation between the measurement error and wages, deriving under which conditions the biases of the coefficients are exacerbated or mitigated by the use of panel data and first-differences. We do not have social security earnings against which to compare the reported wages, so in this article we are forced to ignore this issue and to take wages at face value. We are also forced to ignore the issue that risks might be mismeasured, with similar consequences, but first-differencing should reduce the seriousness of the risk mismeasurement.

¹¹ This type of heterogeneity is thus conceptually distinct from the heterogeneity usually represented by individual-specific fixed or RE.

¹² Specifically, we average the risk of the current year with those of the two previous years.

¹³ SIC 92 categories A, B, P and Q and SOC 90 codes 600–619, 900–903.

¹⁴ We define as blue-collar jobs SOC 80 codes 500–599 (craft and related occupations), 620–699 (personal occupations), 719–722 (sales assistants and check-out operators plus other sales representatives, 733 (scrap dealers and scrap metal merchants), 800–899 (plant and machine operatives) and 910–990 (other occupations except for agriculture, forestry and fishing).

¹⁵ For the 2001–2003 period, the BHPS contains 26 703 observations. We lose about half of this sample once we exclude women, 979 observations when we restrict attention to persons aged 18–65, and 734 when we rule out persons in high-risk professions. Of the 11 921 remaining observations, for 285 we were unable to match risk data. For 1139, we did not have income information; 600 are excluded because these workers report being employed full time, but wages are less than £4000 a year, and 539 are excluded because the workers do not work full time. This leaves us with 9358 observations, from which we drop persons that live in Wales or Northern Ireland (losing 2878 observations) and observations for which 3-year average risk rates could not be computed (49 observations). This leaves us with a sample of 6431 observations, but the usable sample is 4940 because of missing values for a number of covariates.

¹⁶ We are, however, concerned that in some cases this change might be only apparent, perhaps due to a better identification of the industry the worker belongs to. For example, when we look at blue-collar workers whose SIC code changes over the period covered by our study and at the same time report a tenure of 0 years (indicating that they are beginning a new job); about 665 appear to be in this situation.

¹⁷ Fatality rates declined by 3.1 per 100 000 in the 10 years between 1959 and 1969, but the corresponding decrease between 1994 and 2004 was only 0.36. If this process continues at the same rate, only 0.28 lives per 100 000 employees will be saved by safety measures imposed between 2004 and 2014. Further, workplace accidents account for a smaller and smaller share of all-cause mortality risks. For males aged 25–35, for example, the ratio of job mortality risk to the risk of dying for all causes fell from 2.7% in 1976 to 0.7% in 2003, the year of wave 13 of the BHPS. Similar trends are seen for other age groups as well.

¹⁸ In the full sample, there are 1540 and 3400 union and nonunion workers, with mean fatality risks of 1.29 in 100 000 and 1.23 in 100 000, respectively. The SDS are 2.98 and 2.41 in 100 000, and the t-statistic for the difference in means is 0.879, which means that there are no significant differences across the two groups. Among blue-collar workers, 842 are unionized and 1510 nonunionized. The corresponding means (SDS) are 1.86 (3.6) and 1.75 (1.7) per 100 000, with a resulting t-statistic of 0.766.

¹⁹ The VSL is calculated as the product of β ₂ by average wage, times 100 000 (because risk is expressed as XE − 05).

²⁰ As Leigh (1995) has shown, apparent wage/risk differentials can be caused by inter-industry wage differentials. In our data, coefficients remained significant even after including industry dummies, which is probably due to the fact that risk is measured on the four-digit SIC level, whereas the industry dummies were based on major categories.

²¹ One possible explanation for this is that only roughly 3–5% of the variation in job risk for all workers can be predicted using the instruments, with the remainder being absorbed into the residuals . As a consequence, the residuals are highly correlated with job risk and with in Equation 9. The correlation coefficient between and p_i is 0.98 for all workers and also for blue-collar workers, which explains why the regression coefficient β ₂ is so sensitive to the inclusion of the residuals. Arabsheibani and Marin (2001) report that they encountered the very same problem, despite using a broader set of instruments and obtaining much better first-stage R ², and conclude that compensating risk differentials extracted in this way should be viewed with great caution due to multicollinearity.

²² Black and Kniesner illustrate this case for the fast-food industry. If younger and female clerks are assigned to daytime shifts, while older males do nighttime shifts, when the likelihood of robberies is higher, then the risks of younger and female clerks are overstated and those of older males are understated. Clearly, the measurement error is correlated with age and gender.

²³ This would happen because we infer the compensating wage differential from a marginal worker–a low-skill, high-risk worker–who is the one that demands the most compensation for workplace risks. But this maximum compensating differential is divided by the average risks to get the VSL, resulting in an overestimate of the latter.