Last week, my ECONS102 class covered health economics. Part of that topic involves discussion of approaches to measuring the 'value of a preventable fatality' (sometimes also called the 'value of a statistical life', or VSL). One of those approaches is the willingness-to-pay (WTP) approach, which involves estimating what people would be willing to pay in order to avoid small increases in risk. One way of applying the WTP approach in practice is to look at revealed preferences, based on people's actual risk avoidance behaviour. And one example that I use in class to illustrate the revealed preference method is to measure compensating differentials which, rather than measuring willingness-to-pay to avoid risk, measure workers' willingness-to-accept additional risk.
Compensating differentials recognise that jobs that differ in non-monetary characteristics may offer different wages. For example, consider two jobs that are similar in terms of skill requirements. If one of the jobs has positive non-monetary characteristics (e.g. it is safe, clean, and engaging), then more people will be willing to do that job. This leads to a higher supply of labour for that job, which leads to lower equilibrium wages. In contrast, if the other job has negative non-monetary characteristics (e.g. it is dangerous, dirty, and boring), then fewer people will be willing to do that job. This leads to a lower supply of labour for that job, which leads to higher equilibrium wages. The difference in wages between the attractive job that lots of people want to do and the unattractive job that fewer people want to do is called a compensating differential. The compensating differential essentially compensates workers for working in jobs with negative non-monetary characteristics compared with working in jobs with positive non-monetary characteristics.
The risk of being injured on the job is a substantial negative non-monetary characteristic for some jobs. Based on the idea of compensating differentials, workers should only be willing to take on a job with a higher risk of death or injury if that job comes with a higher wage. Measuring that additional wage would provide a measure of the compensating differential, which could then be used to estimate the value of a preventable fatality.
As an example, consider this 2022 article by Zac Reynolds, Daehoon Nahm and Craig MacMillan (all Macquarie University), published in the journal Economic Record (open access). They estimate compensating differentials for job fatality and injury risk in Australia, using income data from the Household, Income and Labour Dynamics in Australia (HILDA) survey from 2010-2018, and risk data from Safe Work Australia. Their regression model estimates the compensating wage differential (CWD) controlling for industry and occupation, as well as for a range of demographic and labour force characteristics of the workers in the sample. In their preferred set of results:
...the CWD and corresponding VSL for fatal risk are 0.13% and $9.7 million respectively.
Interestingly, union members receive significantly higher compensation for fatality risk. In their preferred model, the CWD for union members is 0.44 percent for an increase in fatality risk of one in 100,000 workers, significantly higher than for non-members. If you need a good reason to join a union, this might provide it.
Surprisingly, Reynolds et al. find no evidence of a CWD for non-fatal risk overall. In fact, their preferred results suggest that higher non-fatal injury risk is associated with lower wages, rather than higher wages, for non-union workers. However, alongside that there is a significant CWD for union members, where:
...union members receive a CWD of 0.09% for a unit increase in injury risk from the mean level which corresponds to a VSI of $65,300.
VSI is the 'value of a statistical injury', which is the non-fatal equivalent of the VSL. One limitation of Reynolds et al.'s analysis is the potential for omitted variable bias. Their models include either fatal risk or non-fatal risk, but never both together. Since these risks are positively correlated, omitting one may bias upwards the estimated effect of the other. However, Reynolds et al. explain that including both risks would create multicollinearity problems, meaning that the results would potentially be less biased, but also less precise.
Finally, Reynolds et al. compare their results with the 'official' VSL applied by the Australian government, noting that:
For Australian workers who belong to a union, this estimate implies a VSL of $34.9 million. Ignoring union coverage results in a VSL of $9.7 million. These estimates are both well above the Australian government VSL estimate of $5.1 million...
For comparison, the New Zealand government currently applies a VSL of $12.5 million (in 2021 dollars, which is comparable with the 2021 VSL that Reynolds et al. report for Australia) for measuring the benefits of road safety improvements. This is equivalent to about AU$10 million at the current exchange rate.
The 'value of a preventable fatality' (or value of a statistical life, if you prefer) isn't a price tag on anyone's life, but an estimate based on how people trade off money against small changes in the risk of death. As Reynolds et al. demonstrate, those estimates can vary substantially, which is worth remembering when governments use a single number to represent the benefits of increased safety and in other applications.
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