## Abstract

We estimate the marginal rate of substitution of income for reduction in current annual mortality risk (the “value per statistical life” or VSL) using stated-preference surveys administered to independent samples of the general population of Chengdu, China in 2005 and 2016. We evaluate the quality of estimates by the theoretical criteria that willingness to pay (WTP) for risk reduction should be strictly positive and nearly proportional to the magnitude of the risk reduction (evaluated by comparing answers between respondents) and test the effect of excluding respondents whose answers violate these criteria. For subsamples of respondents that satisfy the criteria, point estimates of the sensitivity of WTP to risk reduction are consistent with theory and yield estimates of VSL that are two to three times larger than estimated using the full samples. Between 2005 and 2016, estimated VSL increased sharply, from about 22,000 USD in 2005 to 550,000 USD in 2016. Income also increased substantially over this period. Attributing the change in VSL solely to the change in real income implies an income elasticity of about 3.0. Our results suggest that estimates of VSL from stated-preference studies in which WTP is not close to proportionate to the stated risk reduction may be biased downward by a factor of two or more, and that VSL is likely to grow rapidly in a population with strong economic growth, which implies that environmental-health, safety, and other policies should become increasingly protective.

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## Notes

- 1.
Compensating-wage-differential studies regress wage on occupational fatality risk; because wages are highly correlated with income, it is difficult to estimate the effect of income directly, though Evans and Schaur (2010) and Kniesner et al. (2010) use quantile regression to estimate how VSL differs across the wage distribution. Stated-preference studies have also been evaluated using meta-analysis (e.g., Lindhjem et al. 2011; Masterman and Viscusi 2018).

- 2.
This two-part test was first applied by Alolayan et al. (2017) in a stated-preference study to estimate VSL in Kuwait.

- 3.
Note that consistency with theory is a sufficient but not necessary condition for responses YY or NN. For example, a respondent who values the two risk reductions equally (violating proportionality) would respond YY if the common value is greater than the prices offered for both risk reductions.

- 4.
In the 2016 survey, rejecting either risk reduction when it is free violates the criterion.

- 5.
The exchange rate we use for both years is 7 RMB to 1 USD.

- 6.
Official population statistics for Chinese cities are notoriously difficult to cite and often conflicting in the literature because of: 1) varying use of terms, including the names of cities themselves, which can refer to the central urban jurisdiction or administrative regions that also include satellite cities, towns, and large rural areas; 2) conflicting categorizations, including two different terms generally translated into English as “urban”; and 3) focus of the census authorities on total residents and those with local residence permits (even if they live elsewhere), while non-registered migrant residents (who are generally poorer) are estimated separately by the Public Security Bureau using different methods.

- 7.
The 2005 survey also elicited WTP for a risk reduction of 10/10,000 from one-third of the respondents. These respondents are excluded from our analysis because if elicited WTP is less than proportional to risk reduction, including them could lead to lower estimates of VSL, biasing upward the observed change in VSL between the two periods. We report below the effect on estimated VSL if these respondents are included.

- 8.
For the 2016 survey, a respondent who rejects at least one of the treatments when it is free is classified as failing the positivity criterion.

- 9.
An additional 322 respondents valued a larger risk reduction (10/10,000) and are excluded from the analysis.

- 10.
Of the 111 respondents with WTP > 0 excluded by the proportionality test, 71 (64%) responded YN and 40 (36%) responded NY to the smaller and larger risk reductions, respectively.

- 11.
Income statistics are calculated excluding individuals who declined to answer. For comparison, GNI per capita in China was 14,300 RMB in 2005 and 53,800 RMB in 2016 the estimated median incomes are 73% and 57% of these values, respectively. The CPI increased by a factor of 1.36 over the period (https://data.worldbank.org/).

- 12.
For the 2016 survey, only one bid (1500 RMB) is used for both risk reductions; the fraction accepting that bid is larger for the larger than the smaller risk reduction.

- 13.
The Turnbull lower-bound means are non-parametric estimates of mean WTP; the estimates from the simple regression models are parametric estimates of the median WTP over the error term. Hence the parametric estimates can be smaller than the non-parametric lower bounds.

- 14.
This elasticity is calculated comparing estimates from the subsamples that satisfy the positivity criterion; using estimates from the full samples, the elasticity is 3.4.

- 15.
Including respondents to the 2005 survey who valued a larger risk reduction (10/10,000) has a modest downward effect on the estimated VSL. The estimated coefficients (standard errors) on log(risk reduction) are 0.633 (0.160) and 0.744 (0.120) for the full sample (

*N*= 993) and the subsample with WTP > 0 (*N*= 694). The estimated intercepts (standard errors) are 8.147 (1.202) and 9.829 (0.897), respectively. VSLs calculated for a risk reduction of 4/10,000 are 8710 and 19,700 USD, respectively, about 4 and 9% smaller than the values in Table 3. - 16.
The rapid income growth in Chengdu is characteristic of China overall; indeed GNI per capita has grown even more rapidly than personal income as measured in our survey.

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## Acknowledgements

Kip Viscusi and Sue Chilton provided careful reviews and valuable comments. Other helpful comments were provided by Hugh Metcalf, participants at the “Risk Guidelines for a Safer Society” symposium (Vanderbilt Law School, 2018), the Chinese Economists Society North America Conference (University of Georgia, 2018), the Society for Benefit-Cost Analysis annual conference (George Washington University, 2018), the Harvard University environmental economics and policy seminar (2017), and the early career workshop in honour of emeritus professor Michael Jones-Lee (Newcastle University, 2019). Generous funding was provided to the Harvard-China Project from the Harvard Global Institute for the 2016 household survey and subsequent analysis, and from the V. Kann Rasmussen Foundation, Volvo Educational and Research Foundations, Luce Foundation, and Harvard University Asia Center for earlier work, including the 2005 household survey. The authors also thank Mingming Shen, Jie Yan, and other collaborators at the Research Center for Contemporary China at Peking University for leading the field implementation of both surveys.

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Hammitt, J.K., Geng, F., Guo, X. *et al.* Valuing mortality risk in China: Comparing stated-preference estimates from 2005 and 2016.
*J Risk Uncertain* **58, **167–186 (2019) doi:10.1007/s11166-019-09305-5

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### Keywords

- Value of statistical life
- Stated preference
- Willingness to pay
- China

### JEL Classifications

- D61
- H43
- I18
- Q51