Job fatality and injury risk, and compensating differentials

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.

Read more:

• The likely consequences of New Zealand's new value of a statistical life

This week in research #147

Here's what caught my eye in research over the past week (a very quiet week, it seems):

• Silva, Sá, and Biscaia (open access) find that a one-standard-deviation increase in high school GPA adds 5.9 first-year ECTS (European Credit Transfer System) at university, versus 1.8 ECTS for a one-standard-deviation increase in standardised national exam score, with the difference larger in the most selective university programs

The economic impact of the 2010 FIFA World Cup

Economic impact studies undertaken in advance of large sporting events typically anticipate large positive economic effects. However, studies undertaken after the event almost universally fail to demonstrate the anticipated effects. To that list (and see the links at the end of this post for specific examples), you can now add the 2010 FIFA World Cup, hosted by South Africa.

This 2025 article by Busani Moyo (University of South Africa) and Tendai Gwatidzo (University of the Witwatersrand), published in the Journal of Sports Economics (open access), provides the details. They apply the synthetic control method, which involves comparing the time series of outcome variables for South Africa with a counterfactual made up of a weighted average of other countries, chosen because that weighted average best replicates the trajectory of the outcome variable from before the treatment date.

In their main analysis, they use 2010 as the treatment date, in order to demonstrate any effect of the staging of the 2010 FIFA World Cup itself. The synthetic control they employ is made up of 31.7 percent Brazil, 21.3 percent Morocco, 18.1 percent Algeria, 15.5 percent Botswana, and small weightings of Kazakhstan, Malaysia, Mauritania, and Argentina. The results are shown in Figure 1 from the paper:

The solid blue line is the actual GDP per capita for South Africa, while the dashed red line is the counterfactual 'synthetic South Africa', which is supposed to show what would have happened to GDP per capita if South Africa hadn't hosted the FIFA World Cup. The results clearly demonstrate that actual South Africa performed worse than synthetic South Africa, suggesting that hosting the FIFA World Cup may have made South Africa worse off (at least, using GDP per capita as a measure).

But wait, not so fast. A lot of economic activity occurs in the lead-up to the hosting of the event. Moyo and Gwatidzo therefore change the treatment date to 2004, when South Africa was announced as the host, and check whether there was any impact then. The synthetic control changes (since they are using a different treatment date), now being made up of 31.3 percent Morocco, 24.7 percent Brazil, 17.9 percent Algeria, 14.3 percent Malaysia, and small weightings of Kazakhstan, Costa Rica, and Mexico. The results from this analysis are shown in Figure 3 from the paper:

Moyo and Gwatidzo interpret this as showing a positive effect on GDP per capita in the lead-up to the event, but I struggle to see evidence of any effect in Figure 3 (at least, before 2010 where, as in Figure 1, actual South Africa performs worse than synthetic South Africa). Actual GDP per capita tracks synthetic GDP per capita remarkably closely between 2004 and 2010, with little indication of any sustained positive effect. Moyo and Gwatidzo don't provide a clear quantitative estimate of the effect, which makes it difficult to assess whether the apparent positive effect is economically meaningful or statistically significant. Both seem unlikely to me.

Moyo and Gwatidzo then turn to looking at tourism arrivals, where the results are mixed. Using 2010 as the treatment date, actual tourism arrivals exceed those for synthetic South Africa for several years after the World Cup. However, using 2004 as the treatment date, synthetic South Africa clearly outperforms actual South Africa.

Moyo and Gwatidzo then turn to looking at tourism arrivals. In this case, the effect is modestly positive, as shown in Figure 10 from the paper:

Notice that in this case, there is a small positive difference in international tourism arrivals between actual South Africa and synthetic South Africa, at least up to 2013 or 2014. So, at least there is some good news for South Africa. Nevertheless, given the apparent negative effects on GDP per capita after the event, I am not convinced by their conclusion that:

These results, at least for South Africa, show that it is not the actual hosting of the World Cup that has a positive effect on GDP but the period of preparation for the tournament. The actual hosting of the tournament is only beneficial in the form of international tourism inflows.

Like many other studies, I think the results suggest that South Africa had a good party, which attracted extra visitors from outside the country, but failed to deliver the large positive economic benefits that were anticipated. I suggest that you file this study along with the multitude of others that cast doubt on the large positive economic benefits that are routinely predicted for major sporting events.

Read more:

• Tim Hazeldine on economic impact studies
• Beware economists bearing impact studies of the America's Cup
• Even less reason to believe in the economic impact of the America's Cup
• The overstated impact of the Super Bowl
• The economic impact of the 2010 World Cup in South Africa
• The economic impact of the 2000 Sydney Olympics
• Maybe hosting the Olympics just shuffles income around a country, rather than increasing it

Modelling the Nobel Prize in Economics

The Nobel Prize in Economics (technically, the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel) will be announced next Monday. Who will win? It is a closely guarded secret, but of course there are prediction markets - at the time of writing, Kalshi has Ariel Pakes as the favourite, with Susan Athey a close second, and Richard Blundell a distant third.

In a discipline where modelling is ubiquitous, it is worth asking whether it is possible to model who will win the Nobel Prize. This recent working paper by Peter Dolton and Richard Tol (both University of Sussex) makes a good attempt. They build a dataset of past winners and candidates (based on research performance as well as winners of other awards), and then estimate a model that shows the factors correlated with winning the Nobel Prize.

Dolton and Tol start with a simple assumption, which is that the Nobel Prize Committee first chooses a field to award the prize to, and then they choose the best candidate within that field. They justify this assumption by showing that there is some regularity in the way that the award goes from field to field over time (based on their categorisation of 14 fields of economics). They use this to construct a 'transition matrix', that records how often the Nobel Prize goes from one field in one year to another the next year. 

Which fields get Nobel Prizes? Dolton and Tol show that larger fields (those with more candidates), those that have waited longer since their last prize win, and the transition matrix, are all statistically significantly correlated with which field wins the prize.

Who wins the Nobel Prize within the winning field? Dolton and Tol find that winning candidates are older (although the relationship with age is non-linear, and peaks at age 70-71 before declining), and those who have had a student already win a Nobel Prize are more likely to win.

Some important things come out of this paper. First, who will win the Nobel Prize in 2026? The 2025 winners were Joel Mokyr, Philippe Aghion, and Peter Howitt. Their research field, according to Dolton and Tol's categorisation, is 'Growth'. According to the transition matrix in Table E.8 of the paper, the most likely field to follow 'Growth', is 'Equilibrium and Welfare' (although 'Development and Economic History' and 'Macro' are also possible). 

I got ChatGPT to comb through Dolton and Tol's candidate list and identify the top candidates in 'Equilibrium and Welfare'. ChatGPT suggested Andreu Mas-Colell or Partha Dasgupta. I have heard Dasgupta's name in people's shortlists before, but not Mas-Colell. Of course, if the Committee considered they had already ticked the 'Economic History' box with Joel Mokyr last year, then next according to the transition matrix would be 'Games and Market Structure', 'Information', or 'Macroeconomics'. Across those fields, ChatGPT suggested many names, but noted that David Kreps is the strongest overall, to which I would add Ariel Pakes (note the consistency with the Kalshi market prediction). ChatGPT rated Oliver Blanchard the top candidate in Macroeconomics. Anyway, we will see next week!

Second, I love the list in Table 4 of the paper, which shows the economists who, according to Dolton and Tol's model, have had the greatest chance of winning the Nobel Prize but have not done so. Top of this list is Michal Kalecki (died in 1970), followed by Lionel Robbins (1984), Jacob Marschak (1977), Arthur Burns (1987), and Frank Hahn (2013). Other notable names in that list (at least, according to me) are Bill Phillips (died in 1975), Harold Hotelling (1983), Bill Baumol (2017), and Henri Theil (2000). There are a few on the list who are still alive, including Tim Besley, Robert Barro, Guido Tabellini, George Loewenstein, and Torsten Persson.

One reason why so many outstanding economists died without receiving the prize is that it was only first awarded in 1969, by which time there was a long backlog of worthy candidates. The third important thing to come out of this paper is a counterfactual exercise, predicting who would have won the Nobel Prize each year if the prize had been first awarded in 1901 (along with the other Nobel Prizes). Table F.15 in the paper has the results (up to 1976, after which it is assumed that the awards would continue as they have been). A number of important names appear in this list, including the first three winners being Leon Walras, Carl Menger, and Francis Edgeworth. My students would no doubt recognise Alfred Marshall (1910), Corrado Gini (1924), Joseph Schumpeter (1930), Arthur Pigou (1935), John Maynard Keynes (1938), and Joan Robinson (1958), among others. Interestingly, in this counterfactual exercise, the first woman to win the prize would have been Beatrice Webb in 1924 (jointly with Sidney Webb and Corrado Gini), some 85 years before Elinor Ostrom.

The Nobel Prize announcement is one of the highlights of my year. Now that I've considered the results from the model, with some assistance from my special adviser ChatGPT, I'm prepared to make my prediction: Kreps and Pakes. We'll find out next week!

[HT: Marginal Revolution]