Anchoring biases in international estimates of the value of a statistical life

Abstract

U.S. labor market estimates of the value of a statistical life (VSL) were the first revealed preference estimates of the VSL in the literature and continue to constitute the majority of such market estimates. The VSL estimates in U.S. studies consequently may have established a reference point for the estimates that researchers analyzing data from other countries are willing to report and that journals are willing to publish. This article presents the first comparison of the publication selection biases in U.S. and international estimates using a sample of 68 VSL studies with over 1000 VSL estimates throughout the world. Publication selection biases vary across the VSL distribution and are greater for the larger VSL estimates. The estimates of publication selection biases distinguish between U.S. and international studies as well as between government and non-government data sources. Empirical estimates that correct for the impact of these biases reduce the VSL estimates, particularly for studies based on international data. This pattern of publication bias effects is consistent with international studies relying on U.S. estimates as an anchor for the levels of reasonable estimates. U.S. estimates based on the Census of Fatal Occupational Injuries constitute the only major set of VSL studies for which there is no evidence of statistically significant publication selection effects. Adjusting a baseline bias-adjusted U.S. VSL estimate of $9.6 million using estimates of the income elasticity of the VSL may be a sounder approach for generating international estimates of the VSL than relying on direct estimates from international studies.

Appendix: Description of fatality risk data

U.S. Government fatality rate data

The U.S. Government subsample contains all studies using fatality data published by the U.S. federal government, other than studies that used the Census of Fatal Occupational Injuries (CFOI). Nearly all studies in the subsample used fatality rates from either the Bureau of Labor Statistics (BLS) or the National Institute of Occupational Safety and Health National Traumatic Occupational Fatality (NTOF) data. The only exception is Low and McPheters (1983), which constructed police officer death risks using the U.S. Department of Justice’s statistics on police officer deaths.

The earlier BLS data extrapolated fatality rates from a sample of compliance surveys administered under the Occupational Safety and Health Act of 1970. All survey responses were voluntary. The BLS indexed fatal injury rates by three-digit SIC industry code. In the early years of the data, it included limited information about the workers involved and the circumstances of the injury, but even these details were available only in a limited number of states and were not generally used in VSL studies. In 1992, the BLS stopped gathering information on fatal injuries through the Survey of Occupational Injuries and began the CFOI.

The BLS fatality rates suffered from multiple shortcomings. Because BLS fatality rates were extrapolated from a partial sample of firms, there existed sampling error in the fatality rates calculated from BLS data. The sample likely also exhibited selection bias because all responses to the survey were voluntary. Further, BLS indexed the data only by industry, limiting researchers’ ability to accurately match workers with fatality rates. The BLS data were the most common fatality rates in the early VSL literature.

In 1987, the National Institute of Occupational Safety and Health created the NTOF data series. The NTOF data differed from the BLS data in a few important ways. Fatality rates were calculated with a census of all occupational fatalities recorded on death certificates, reducing the sampling error present in BLS data. The NTOF data were indexed by state and one digit SIC industry code. The finer NTOF indexing allowed researchers to assign fatality rates to workers with less measurement error. Moore and Viscusi (1988), the first article to use the NTOF data to estimate the VSL, found that use of the NTOF data generated an average fatality rate 84% higher than the BLS data and doubled the VSL relative to BLS data.

Together, 18 studies containing 173 VSL estimates utilized the BLS, NTOF, and FBI fatality rates to estimate a VSL. The mean VSL in these estimates was $7.3 million, $4.7 million less than the whole sample mean of $12.0 million. The mean fatality rate for these studies was 1.685 fatalities per 10,000 full-time equivalent workers, more than the sample mean and more than three times higher than the mean fatality rate in the CFOI studies.

CFOI Subsample

The CFOI subsample contains all studies whose fatality data is from the CFOI’s restricted access microdata file. While the Bureau of Labor statistics provides summary figures from the CFOI on its website, the microdata file provides much more detailed information. In 1992, the BLS launched the CFOI data series as a cooperative program between the federal and state governments to accurately catalogue fatal workplace injuries. The CFOI uses multiple data sources, such as accident reports, coroners’ records, and workers’ compensation records to identify fatal injuries. Each injury is substantiated with two or more independent source documents. For each injury in the data, the CFOI provides diverse personal characteristic data, the type of injury, and details regarding the circumstances of the accident. An average of four source documents supports each fatality that the CFOI records (Wiatrowski 2014).

Initially, the CFOI utilized Standard Industry Classification and U.S. Census Bureau Occupation codes to classify workers according to industry and occupation. In 2003, the CFOI adopted the North American Industrial Classification codes for industries and the Standard Occupational Classification Codes for occupations. Since 2003, the CFOI has been the dominant source of fatality data for studies calculating the VSL in the United States. When using labor market studies to define a VSL for policy, the U.S. government exclusively uses studies using the CFOI fatality rates. For example, the United States Department of Transportation (2015) Revised Departmental Guidance on the VSL lists nine CFOI studies that it uses to reach the agency’s preferred VSL of $9.4 million. Likewise, the Environmental Protection Agency (2016) report on calculating the VSL using meta-analytic methods restricted its analysis to stated preference studies and studies utilizing CFOI data to calculate a VSL of $10.5 million.

The CFOI data provide a greater level of detail, dramatically reducing the amount of measurement error inherent in the construction of a worker’s fatality rate. The CFOI allows researchers to construct fatality rates by industry, occupation, demographic variables, and any combination thereof, limited only by the imprecision introduced by defining fatality rates by a very large set of categories. The dimensions that studies in the CFOI literature have utilized include occupation, industry, sex, race, age, and immigrant status (Viscusi 2013).

The CFOI subsample is the largest subsample in this study, containing 20 studies and 621 VSL estimates. The mean VSL estimate in the CFOI subsample is $13.1 million, which exceeds the mean in the whole sample. This pattern is consistent with the finding that studies using CFOI fatality rates have less classical measurement error. The mean fatality rate in the CFOI studies is 0.469 per 10,000 workers, with a small standard deviation of 0.192. The CFOI subsample has the lowest fatality rate; the lower rate likely results because of a combination of increased workplace safety in the modern era and reduced sampling error in the data collection.

U.S. Non-Government

The U.S. Non-Government subsample contains all studies whose fatality data was based on the United States labor force, but that a United States federal government agency did not compile. The most common source of data in the U.S. Non-Government subsample was the 1967 Occupation Study from the Society of Actuaries (SOA). The SOA data measured occupational risks using a sample of insurance company records from 1955 to 1964. The SOA indexed the data by industry and occupation, possibly reducing the measurement error relative to the early BLS data. However, the critical deficiency in the SOA data was the measure of death risk it utilized. Rather than tabulating the probability of a fatal accident due to occupational risks, the data calculated mean mortality rates. The SOA fatality rates were thus probabilities of death from any cause, rather than a workplace fatality. Actors, for example, had very high mortality rates.

The remaining fatality rate sources in the U.S. Non-Government subsample were unique to the studies that used them. Leigh (1991) constructed fatality rates from workers’ compensation files from 11 state governments. Gegax et al. (1991) constructed fatality rates using a survey instrument to directly elicit workers’ perception of workplace fatality risks.

Together, six studies comprise the U.S. Non-Government subsample, containing 24 VSL estimates. The mean VSL estimate in the U.S. Non-Government subsample is $3.10 million, which is smaller than the other U.S. subsamples and less than one-third of the whole sample mean. The mean fatality rate in the U.S. Non-Government subsample is 6.671, dwarfing the fatality rate in the other samples. The SOA studies, by calculating total mortality rather than workplace fatality rates, drive this exceptionally high rate.

Non-U.S. Government

The Non-U.S. Government subsample contains all studies measuring the VSL using non-U.S. workers with fatality data from a government source. The countries in this subsample include the United Kingdom, Canada, Australia, South Korea, India, Poland, Pakistan, Japan, Taiwan, and Chile. The type of government agencies providing fatality rates varied significantly among studies. Siebert and Wei (1994), whose data was from the U.K. Health and Safety Executive, and Kim and Fishback (1999), whose data was from the Korean Ministry of Labor, both used data from labor ministries that are analogous to the U.S. Bureau of Labor Statistics or National Institute of Occupational Safety and Health. Shanmugam (2000; 2001) used the Administrative Report of the Chief Inspector of Factories in Madras. Other studies used data from national government agencies that resemble workers’ compensation boards. For example, Meng (1989) and Meng and Smith (1990) both used data from Canadian Workmen Compensation and Liu et al. (1997) utilized fatality data from the Taiwanese Labor Insurance Agency.

The Non-U.S. Government subsample includes 21 studies containing 188 VSL estimates. The mean VSL estimate in the subsample is $13.8 million, the largest of any of the subsamples. The estimates in the Non-U.S. Government subsample were the least precisely measured, with an average standard error greater than the average VSL and more than twice as large as the average standard error in the whole sample. The average fatality rate per 10,000 workers in the Non-U.S. Government sample was 1.556, comparable to the average fatality rate in the U.S. Government subsample. However, the standard deviation of the fatality rate in the Non-U.S. Government subsample is quite large at 2.430. The heterogeneity of the fatality rates is unsurprising, given that they measure risks in ten different countries with very different labor conditions.

Non-U.S. Non-Government

The final subsample is the Non-U.S. Non-Government sample, which contains all studies that estimate a VSL for non-U.S. workers using fatality data that was not released from an agency in a foreign government. The countries in this subsample include Austria, Switzerland, and Germany. Weiss et al. (1986) constructed fatality rates using data from Austrian insurance companies. Baranzini and Ferro Luzzi (2001) collected fatality rates by industry from the Swiss National Accident Insurance Company, an independent, non-profit company established under Swiss Law to manage Switzerland’s public worker insurance. Schaffner and Spengler (2010) collected risk information from German statutorily created independent accident insurance corporations. These three studies comprise the entire Non-U.S. Non-Government subsample and contain 19 VSL estimates. The mean VSL estimate in these studies was $8.7 million, which is substantially lower than the other non-U.S. subsample. The mean fatality rate for these studies was 0.592 per 10,000 workers.