Using data from the Census of Fatal Occupational Injuries to estimate the “value of a statistical life”
Using the CFOI to estimate the VSL
Economists estimate the VSL by matching fatality rate data to workers in large employment datasets on the basis of worker characteristics. Tables 2 and 3 use 2008 CPS data in which each worker is matched with the pertinent industry–occupation fatality rate calculated for each of 50 industries and 10 occupational groups. Table 2 summarizes some sample characteristics. The standard procedure is to estimate a regression equation in which the hourly wage or the logarithm of the hourly wage is the dependent variable. The set of explanatory variables included a variety of personal and job characteristics.6 The sample is restricted to full-time nonagricultural workers.
|Logarithm of hourly wage||2.88||.55|
|Gender (1 = male)||.55||.50|
|Marital status (1 = married)||.59||.49|
|Race (1 = White)||.83||.38|
|Union (1 = member)||.15||.36|
|Years of schooling||14.77||2.57|
|Average number of hours per week||42.57||6.41|
|Fatality rates (per 100,000):|
Employment-based fatality rate
Hours-based fatality rate
|Source: Author’s calculations, based on U.S. Bureau of Labor Statistics, Current Population Survey.|
The estimates in table 3 are of particular interest in that they comprise estimates based on the new hours-based fatality rate approach as well as estimates based on the earlier employment-based fatality rate. All studies using CFOI data to estimate the VSL are based on the previous employment-based measure, so it is worthwhile to assess whether the fatality rate measure influences the estimates. The hours-based fatality rate is somewhat lower than the employment-based rate. The hours-based fatality rate is 3.29 per 100,000 workers for the sample used in the estimation and 3.53 for the 2008 CPS more generally. By comparison, the employment-based rate is 3.41 for the sample and 3.66 for the 2008 CPS.
|Category||Wage equation, based on—||Logarithm of wage equation, based on—|
|Hours-based fatality rates||Employment-based fatality rates||Hours-based fatality rates||Employment-based fatality rates|
|Fatality rate||0.0395 (0.0078)||0.0437 (0.0067)||0.0024 (0.0003)||0.0026 (0.0003)|
|Value of a statistical life (in millions of dollars)||7.9||8.7||9.9||11.1|
Note: Standard errors are in parentheses following the estimate. All coefficients are statistically significant at the 99-percent level or better. Endnote 5 in the text gives other variables included in the equation. The sample size is 126,225.
Source: Author’s calculations, based on U.S. Bureau of Labor Statistics, Current Population Survey.
As the results shown in table 3 indicate, the fatality rate variable is positive and statistically significant in each case. Calculating the VSL on the basis of the estimates obtained from the wage equation entails multiplying the fatality rate coefficient by 100,000 (because the fatality rate is expressed per 100,000 workers) and by the average number of hours worked per year, to convert the hourly wage into an annual compensation amount.7 The calculation of the VSL for the logarithm of the wage equations is similar, except that the estimates also must be multiplied by the average hourly wage rate.
The VSL estimates in table 3 range from $7.9 million to $11.1 million. The estimates based on the hours-based fatality rates are $0.8 million to $1.2 million smaller, but the confidence intervals for the VSL estimates overlap. Although there is a consistent difference, the narrowness of the gap is indicative of the relative stability of the VSL estimates, whether the hours-based fatality rate or the employment-based measure is used.
Previous studies using the CFOI to estimate the VSL
To date, 16 previous studies have used CFOI data. Table 4 summarizes some of the principal characteristics and results of these studies. In addition to listing the particular study, the CFOI measure used in the analysis, and the employment sample, the table reports one or more empirical estimates of the VSL (in 2012 dollars) from the article in question, based on representative log–wage equations estimated in the article. All of the articles listed report many different estimates of the VSL, in one case as many as 80 different equations. All but one of the articles match CFOI risk variables to individual employment data, rather than industry averages. Studies based on individual data control for a detailed set of personal characteristics and job characteristics. The lone exception to the use of microdata is the article by William P. Jennings and Albert Kinderman, which analyzes average industry wage rates rather than utilizing a large sample of individual data, as is the norm in the labor economics literature.8 The model set forth by those authors, which includes no controls for worker characteristics or job characteristics other than average industry risk levels, yielded no significant evidence of aggregate premiums for risk across broad industry groups.
6 More specifically, the variables were potential work experience, potential work experience squared, years of education, and indicator variables for male, married, Black, Native American, Asian, Hispanic ethnicity, doctorate or professional degree earned, paid hourly rate, full-time employment, union or employee association membership, government employment, six metropolitan and nonmetropolitan areas, eight regional areas, nine largely blue-collar occupations, and professional occupational group. The sample is restricted to those working at least 35 hours per week with hourly wages between $2 and $100. Excluded are workers in agriculture and those in the Armed Forces.
7 For both the employment- and hours-based measure, the annual number of hours is 2,000, representing a standard 40 hours per week for 50 weeks.
8 William P. Jennings and Albert Kinderman, “The value of a life: new evidence of the relationship between changes in occupational fatalities and wages of hourly workers, 1992 to 1999,” Journal of Risk and Insurance, September 2003, pp. 549–561.