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Journal of Benefit-Cost Analysis

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New risk rates, inter-industry differentials and the magnitude of VSL estimates

Carol R. Scotton
Published Online: 2013-03-28 | DOI: https://doi.org/10.1515/jbca-2012-0015


The Census of Fatal Occupational Injury (CFOI) provides data for creating objective measures of workplace risk used in estimations of wage-risk premia for value of statistical life (VSL) calculations. This relatively new data set enables a more theoretically defensible measure for use in hedonic wage equations. However, constructing these rates from the CFOI data necessarily involves creating an industry-occupation matrix defining the “jobs,” deciding whether or not to include the self-employed, and selecting a denominator. These choices in the construction of the risk measure alone, as shown here, result in variations of VSL estimates ranging from $8 million to $18 million. Further, risk measures based on the CFOI data, regardless of construction, are sensitive to simple changes in the specification for the hedonic wage equation. In particular, fixed effects describing the industry in which a worker is employed, as well as the worker’s occupation, are primary influences on the magnitude of the VSL estimates.

Keywords: compensating wages; hedonic wage model; inter-industry differentials; value of a statistical life; workplace fatalities; JEL codes: J17; J31; I1


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About the article

Corresponding author: Carol R. Scotton, Department of Economics, Knox College, Galesburg, IL 61401, USA, Tel.: (309) 341-7115

Published Online: 2013-03-28

There is a vast literature on the VSL and the debates and concerns about it, prompting specialty websites such as VSL Research at the Maxwell School of Syracuse University found at <http://sites.maxwell.syr.edu/vsl/vsl.html> last accessed August 7, 2012.

The VSL represents the minimum amount that the workers would, collectively, be willing to pay to reduce the risk of death by one person. For example, a VSL of $6 million is computed from an estimated annual wage-risk premium of $600 from risk rates based on 1 in 10,000 workers. Each of 10,000 workers, on average, receives an annual compensating differential of $600 for facing the increased risk that one more person among them will be fatally injured on the job. In other words, the VSL is computed the same way willingness to pay estimates for a public good are: individual wage-risk premia are summed vertically.

This is true regardless of whether the terminology used refers to “job,” “industrial,” “work-place” or “occupational” fatalities.

Data was also available by occupation group only, i.e., regardless of industry, from the National Institute of Occupational Safety and Health (NIOSH). Moore and Viscusi (1988) and Black and Kniesner (2003) compare risk rates by industry only, produced by the BLS, and by occupation only available from NIOSH.

The common example of coal miners and secretaries obscures the point that both men and women face risks in the workplace and men and women face the same risk if they are doing the same job. Because risk rates were primarily only at the industry level and most fatalities were male, women were routinely excluded from the labor force samples in VSL estimations. Importantly however, female deaths were likely included in the computation of the risk rates. In other words, if the coal miner was a woman, it is still the death of a coalminer. This would have increased the risk rates for the labor force sample and decreased the wage-risk premiums estimated in the wage equations. This study will not distinguish between men or women holding a particular job. The point is to measure the risk inherent in the job, that is, due to the nature of the job, not if the coal miner, secretary, electrician, doctor or driver is a man or a woman.

Leigh found that including industry controls rendered the coefficient on risk not statistically significant. The meta-analysis by Mrozek and Taylor 2002 included 25 (out of 142) estimates where industry dummy variables were included in the wage equation. The presence of industry dummies significantly lowers the VSL estimate.

See Drudi (1995) for a comprehensive summary of the history of occupational risk data. The CFOI research data file provides micro-level data on all workplace deaths in the US; importantly, it identifies both the industry and occupation of the worker at the time of death, the circumstances of death, employment status and more. Researchers can gain access to the CFOI data file via a confidentiality agreement with the BLS.

The BLS continues to produce fatal occupational injury rates, but only by either industry or by occupation and then only for selected industries and occupations. See <http://www.bls.gov/iif/oshnotice10.htm> last accessed August 7, 2012.

An annual average over a series of years for deaths and the size of the labor force is generally used to smooth out anomalies given the rarity of deaths and the freak, and unfortunate, occurrence of multiple deaths in a particular occupation/industry pair happening in one event.

There are other choices that could be made to construct more specific rates, for example, by gender, by geographic region or by length of experience on the job (if it were possible to obtain valid estimates of Woi ). In any case, decisions regarding the three factors considered in this study would have to be made; the finer distinctions would just make the task that much more challenging. Further, and more usefully, the risk rates can be constructed to differentiate the type of risk faced, such as transportation-related vs homicides [see, for example, Scotton and Taylor (2011) or Kochi and Taylor (2011)].

Beginning in 2008, the BLS is computing fatal injury rates based on hours worked, rather than employment-based rates (Northwood, 2010). This changes how the denominator is calculated but does not resolve matters concerning the source of the denominator data. The BSL published rates are still computed only either by industry or by occupation, regardless if hours based or employment based. Because of data limitations across my comparisons, I only use employment-based rates in this study.

Further, the accuracy and reliability of survey responders and coders producing the datasets are a factor. For example, Mellow and Sider (1983) and Mathiowetz (1992) show there is less correspondence in identifying the occupation and industry category between an employee and the firm as the coding is more detailed. This favors more aggregated industrial and occupational groups.

The CPS, the most common source for Woi, uses census coding for industry and occupation. The CPS coding includes a mapping to the SOC and NAICS. This additional crosswalk on coding presents practical hurdles. When the CPS is used, for example in estimating the denominator for the risk rate or as the source for the labor market sample, some coding anomalies have to be addressed, which are not fully discussed here.

The resulting matrix would have to account for the same level of detail in occupations across all industries. This does not mean that every occupation would be found in each industry.

All studies to date using the CFOI data are constructed from death data prior to the year 2000. (This includes both Viscusi and Scotton and Taylor referenced in this study.) Over a period of years beginning in 21st century, industry coding in the US has changed from the Standard Industrial Code (SIC) to the NAICS. This coding change affects most all US labor force data. This study uses the new NAICS coding system and therefore uses the current data on deaths (from 2003–2006) and labor force composition. While new coding does not map exactly to the old, the data – and coding – used here will be comparable for studies going forward.

Every effort was made to minimize any variation from the standard aggregation categories for each matrix while at the same time not losing available data. However, there are a few deaths in the CFOI (over this period) where industry coding was at the 2-digit level only. Consequently, the long matrix, with the industries at the 3-digit level, creates probabilities based on a total of 22,356, instead of the 22,421 deaths (over 4 years) in the square matrix.

Since not all occupations are found in every industry, the number of distinct “job clusters” in a matrix is less than the matrices’ dimensions would suggest. In other words, what drives the number of cells in a matrix is the denominator. There can be a job with zero risk (i.e., no deaths), but there is not a job if no one is employed in it.

The CFOI has established work relationship criteria, including location on or off premises and work-related travel, and all cases are corroborated by two or more independent sources. Someone is “at work” while producing a (legal) product or result “in exchange for money, goods, services, profit or benefit” (US BLS, 2007a). For example, commuting to a job is not in scope; traveling required to do a job is in scope.

With the CFOI, deaths among wage earners can be distinguished from those among the self-employed. Personick and Windau (1995) find “several important differences in fatality patterns between the two” (pp. 25–26) Similarly, the CFOI identifies those deaths that are specifically work-related from suicides or deaths stemming from domestic violence or terrorism which also occur while someone is at work. Further, the CFOI research file provides variables on the mode and circumstances of the fatal injury. See Kochi and Taylor (2011) and Scotton and Taylor for a discussion of disaggregated risk rates, that is, rates based on the mode of death. These explorations of heterogeneity in risk are markedly different than considering differences in demographics.

This study does not distinguish full-time from part-time work, neither in the death counts or employment levels.

Ruser (1998) proposes the denominator ought to be based on hours worked rather than a count of workers. This is now how the BLS computes rates (Northwood, 2010); the estimates for the hours worked are from the CPS. However, since the necessary data for comparisons examined in this study are not available, I continue to use employment-based estimates. Another denominator possibility proposed by Gittleman and Pierce (2006) is to compute the relative risk in terms of output, that is, real GDP. Their direction for a relative risk measure for a VSL estimate would not be appropriate.

Another important quality of the source for the denominator is the coding compatibility for occupations and industries with the CFOI data and the subsequent labor force data set used to estimate the VSL. This is addressed in Section 2.1.

See the technical notes in USDL 07-0712 (US BLS, 2007b), for example, for a description of the OES survey (US BLS, 2007c).

As reported in Appendix 2, there is a pronounced difference in the distribution of risk based on the choice of denominator, with greater variability from the OES estimates.

All of the measures created are based on the annual average number of deaths – and level of employment—for the US labor force of 2003–2006. The six different sets of fatal risk measures can be made available upon request to the author and through an agreement with the BLS CFOI office after meeting confidentiality requirements.

The oi designation show in Equation 1 has been dropped for ease of reference since all risk rates used in this study are computed for occupation within industry.

FIRE is Finance, Insurance and Real-Estate.

No agricultural workers, as designated by the MORG, are in either sample. Also, both samples are restricted to workers in job clusters with annual average employment estimates of at least 1000 workers (as computed for the denominator for the risk rates). This restriction excludes very few workers.

See Bollinger and Hirsch (2005) and Hirsch and Schumacher (2004) for a discussion on the use of earning imputation in the CPS. As noted in Table 1, the wage data for 31% of the larger sample has been imputed by the CPS. Bollinger (2001) shows that including workers with imputed wages biases estimates of compensating wage differentials. As a result, Hirsch (2008) suggests “the simplest approach, and not a bad one at that, is to omit imputed earners from the estimation sample” (p. 4). I follow this advice when I have finished making the comparison. This should make my results more relevant for future studies.

The model and theory used here are well-documented. See reviews indentified in the introduction.

None of the models described in this study include a non-fatal workplace injury measure because, currently, data on non-fatal injury and illness is only available either by industry or by occupation. Including one or both of these non-fatal rates along with the various industrial and occupational controls adds little and changes nothing about the results of this study. See note 46.

Note that Viscusi presents risks in terms per 100,000 workers, while this paper reports values per 10,000 workers. All references to the coefficients from Viscusi in this study are presented in terms per 10,000 workers. The decimal point for the coefficients, and their standard errors, has been moved one place. Also, note that the risks represented in Viscusi’s 2004 study are based on workplace deaths during the period of 1992–1997. His MORG labor force sample is from 1997. See the notes at Table 2 for more information.

The full regressions results are available at <http://faculty.knox.edu/cscotton/expcover.pdf>.

The number of clusters is the number of different jobs (i.e., the matrix for the risk rates) represented in the labor force sample. See notes at Tables 2 and 3.

The standard errors reported here from Viscusi are also robust and clustered, but he does not report on the number of jobs (clusters) represented by his sample. His underlying job matrix has 707 cells, compared to a possible 714 in the long matrix in this study.

Sample restrictions on age and level of education are slightly different. The Viscusi sample excludes the highest earners. The independent variables used here differ in that they include a control for hourly wage, more levels of education, fewer racial groups and regional controls and no control for public versus private industry. Also, the sample used in this study excludes any jobs, and therefore workers in those jobs, when the number of workers employed in that job are fewer than 1000 nation-wide for any of the matrices.

Costa and Kahn (2002) argue that VSL estimates, in real terms, would not be constant over time. Their findings suggest that workplace risk rates need to be computed on current injury data for the workforce, rather than considering that an inflation adjustment is sufficient.

The Viscusi study replicated here only reported on models with occupation controls. The replications presented in Table 2 also only use nine occupational controls.

There are also intra-industry differentials as described in Fairris and Jonasson (2008).

While this literature studies establishments, the phenomena is, nevertheless, characterized by industry groups (such as were described by the SIC and now by the NAICS), hence the term, inter-industry differentials. This interchange of the terms industry and establishment has deep roots, e.g., industrial goodwill and industrial relations.

Mrozek and Taylor’s meta-analysis found that the presence of five or more industry controls significantly affects the VSL estimate.

For example, the CPS uses census code classifications which are analogous to 3, 4, 5, and, in some cases, 6-digit NAICS or SOC codes. In the restricted sample described in Table 1, there are 240 industry categories and 480 occupation categories; in the unrestricted, 240 industries and 482 occupations.

Assuring compatibility between the data used for Doi and Woi requires careful fine tuning so that no data is lost.

The NAICS sub-sectors (3-digit code) define the least aggregated industry groups. These 73 industry controls are primarily the same industry groups represented in the long matrix. Slightly more aggregated are the 52 CPS detailed industry recodes, followed by the 19 CPS intermediate groups (similar to industry groups in the square matrix). The CPS major industry groups (closely mapped to the NAICS sectors) are more highly aggregated, with 11 groups. The highest degree of aggregation is the seven 1-digit NAICS groups. For occupations, the most detail is the 21 occupation groups (the same occupation groups as in the square matrix) as defined by the 2-digit SOC major groups. The nine SOC intermediate aggregation groups (the same occupation groups used in the long matrix) are less detailed; these are also the CPS major occupational groups. Finally, the five SOC high-level aggregation groups provide the highest level of aggregation for the occupational controls.

Models were estimated that also included non-fatal injury rates, which can only be computed by industry alone or by occupation alone (and have several other flaws), to assure nothing was lost or gained regarding control for industry or occupation. Further results from these models are not presented or discussed here since they yield no additional insight into the main issue on the construction of the fatal risk measure or the effect of industry-occupation controls.

To avoid multicollinearity, these models were estimated as follows: When using risk* from the square matrix, the long matrix categories are used as controls; when risk* is from the long matrix, the square matrix categories are used as controls.

Burnham and Anderson (2004) propose pooling the information from multiple model variations. In this study, the AIC and BIC are used only to compare the effects of the various combinations of industry and occupation controls.

Restricting the sample to reported, rather than imputed, wages is discussed in note 29.

The weekly wage as dependent variable is likely to be a more consistent estimate than hourly wage for a sample of both salary and hourly workers. Studies using hourly wages from the CPS data convert weekly wages for those earning a salary into hourly wages by dividing the weekly wage by the usual number of hours worked per week. For salaried workers, the usual hours reported is difficult to interpret and over 40% of the sample are paid a salary rather than an hourly wage. On the other hand, the gross weekly wage for hourly workers is hourly wages times the reported usual hours. I follow the recommendation of Thaler and Rosen (1976) and use the weekly wage.

The results for all models for each of the 6 measures can be found at <http://faculty.knox.edu/cscotton/expcover.pdf>. For all models, regressors have the expected sign and are stable with respect to risk*. The results for the model used in the comparison described on Table 2, with no industry controls and nine occupational controls, are included there. The coefficients, however, are not comparable with those on Table 2 because the dependent variables and sample are different. Models with hour wage, or ln (hour wage), as the dependent variable and the sample restricted to those reporting wages only do yield the same pattern of results. Consistent with Bollinger (2001) and Hirsh (2008), the coefficient estimates on death risk are larger in the restricted sample while most of the other regressors are slightly smaller.

Not reported on the table but worth noting is that all but eight of the 72 industry controls are statistically different from zero (p<0.1 or less) when the risk measure is from the square matrix. This is robust across all risk* and regardless of the number of occupational controls. When the risk measure is from the long matrix – defined by more detailed industries – only as many as 10 industries may be no different from zero. The excluded industry is oil and gas extraction. Similar results are found when no risk measure is included. The magnitude, and the level of significance, of the inter-industry wage differential is influenced by the use of occupational controls.

With or without a fatal risk measure in Model 3 (with no industry controls, 21 occupational controls), 18 of the 20 occupational controls are statistically different from zero (p<0.01). There is no appreciable effect on the statistical significance of the occupational controls themselves as compared to the model with no fatal risk measure.

The pattern found with industry and occupational controls, individually or combined, holds with just a few categories of either. The estimates are much more sensitive to few controls, suggesting that industry differentials are very predominate and specific to how the industries are aggregated.

See Table 4 with the maximum number of controls. The results are mixed depending upon the denominator and as the number of controls vary as shown in Table 3 Panels B and C compared to Panel A.

Indeed, how one dies is also an issue for consideration not dealt with in this study. Consider, for example that “nearly half (45.8%) of the self-inflicted fatalities [among mechanics] were by self-employed mechanics, although only 16% of mechanics are self-employed”. (Smith 2007). See also Scotton and Taylor for an illustration of how the risk rate can be disaggregated to better reflect how to value the type of risk faced or being reduced.

All risk rates are per 10,000 workers.

Appendix 1 shows the industries and occupations in each matrix.

At least one of the service occupations has zero risk in this industry group.

It would be possible to disaggregate TMM occupations up to seven sub groups at the 3-digit SOC level.

With any disaggregation beyond the square matrix, the matching and merging of data needed for Doi and Woi becomes more problematic. And, the rate produced must be able to be matched to a labor force data set.

If the CPS is used for the labor force sample where workers are not distinguished by type of Construction industry this would have no advantage.

All fatal injury rates were generated by the author with restricted access to the BLS CFOI microdata.

Citation Information: Journal of Benefit-Cost Analysis, Volume 4, Issue 1, Pages 39–80, ISSN (Online) 2152-2812, ISSN (Print) 2194-5888, DOI: https://doi.org/10.1515/jbca-2012-0015.

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