Estimation of social value of statistical life using willingness-to-pay method in Nanjing, China

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Estimation of social value of statistical life using willingness-to-pay method in Nanjing, China Zhao Yang a , Pan Liu b,∗ , Xin Xu b a National Key Laboratory of Air Traffic Flow Management, Civil Aviation College, Nanjing University of Aeronautics and Astronautics, Jiangjun Road No. 29, Nanjing 211106, China b Jiangsu Key Laboratory of Urban ITS, Jiangsu Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Si Pai Lou #2, Nanjing 210096, China

a r t i c l e

i n f o

Article history: Received 29 January 2015 Received in revised form 19 March 2016 Accepted 25 April 2016 Available online xxx Keywords: Willingness-to-pay Value of statistical life Mixed logit Random coefficient

a b s t r a c t Rational decision making regarding the safety related investment programs greatly depends on the economic valuation of traffic crashes. The primary objective of this study was to estimate the social value of statistical life in the city of Nanjing in China. A stated preference survey was conducted to investigate travelers’ willingness to pay for traffic risk reduction. Face-to-face interviews were conducted at stations, shopping centers, schools, and parks in different districts in the urban area of Nanjing. The respondents were categorized into two groups, including motorists and non-motorists. Both the binary logit model and mixed logit model were developed for the two groups of people. The results revealed that the mixed logit model is superior to the fixed coefficient binary logit model. The factors that significantly affect people’s willingness to pay for risk reduction include income, education, gender, age, drive age (for motorists), occupation, whether the charged fees were used to improve private vehicle equipment (for motorists), reduction in fatality rate, and change in travel cost. The Monte Carlo simulation method was used to generate the distribution of value of statistical life (VSL). Based on the mixed logit model, the VSL had a mean value of 3,729,493 RMB ($586,610) with a standard deviation of 2,181,592 RMB ($343,142) for motorists; and a mean of 3,281,283 RMB ($505,318) with a standard deviation of 2,376,975 RMB ($366,054) for non-motorists. Using the tax system to illustrate the contribution of different income groups to social funds, the social value of statistical life was estimated. The average social value of statistical life was found to be 7,184,406 RMB ($1,130,032). © 2016 Elsevier Ltd. All rights reserved.

1. Introduction With the rapid development of social economy and road transport industry in China, increased attention has been given to improving safety of the roadway system. The valuation of crashes has become an emerging public policy issue, because the value of crashes is a crucial input parameter in the cost-benefit analysis of safety related projects. The costs associated with crashes account for a large proportion of the monetized component in the costbenefit analysis of major road schemes (Cambridge Systematics,

Abbreviations: VSL, value of statistical life; FHWA, federal highway administration; GDP, gross domestic product; AIS, abbreviated injury scale; SVSL, social value of statistical life; AIC, Akaike information criterion; MC, Monte Carlo; WTP, willingness-to-pay. ∗ Corresponding author. E-mail addresses: [email protected] (Z. Yang), pan [email protected] (P. Liu), xuxin [email protected] (X. Xu).

2008). Rational decision making regarding the safety related investment programs greatly depends on the valuation of crashes. The valuation of fatalities and injuries are critical for estimating the costs associated with crashes. Usually, the costs for property damage only crashes can be directly obtained, while the costs associated with fatalities and injuries require more investigation. The idea is not to put a tag price on a fatality or an injury, but on reductions in the probability of a fatality or an injury (Iragüen and Ortúzar, 2004). This concept gives rise to the value of statistical life (VSL). More specifically, the VSL represents the value of the improvements in safety that results in a reduction by one expected number of fatality, which is equal to the population average of the marginal rate of substitution between income and fatality risk. Different methods can be used for estimating VSL. So far the most widely accepted method is based on the maximum utility theory (Rizzi and Ortúzar, 2003; Iragüen and Ortúzar, 2004; Andersson, 2007). This method quantifies the individual perception of the utility of safety improvements when facing fatality risks, which is also

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called the subjective value of statistical life. The subjective value of statistical life is the marginal amount of money that respondents are willing to sacrifice in order to reduce one expected number of fatality. The assumption is that rational decision makers always choose the alternative with the maximum utility. They would like to pay a specific amount of money to reduce fatality risks through traffic improvements if they think their utilities can be increased. Discrete choice models are developed to establish a relationship between the chance that an individual choices an alternative and various influence factors. Usually the models are developed using data obtained through stated preference or revealed preference surveys. With the discrete choice models, the subjective value of statistical life can be estimated as the marginal rate of substitution of the estimated coefficients of fatality risks and costs. Periodically, the Federal Highway Administration (FHWA) in the United States develops guidance on estimating VSL. The reported VSL estimate was updated over time according to the implicit gross domestic product (GDP) price deflator, which was $2.5 million in 1993, $3.0 million in 2002 and $3.25 million in 2006 (FHWA, 2008). In 2008, rather than simply increasing the 1993 estimate incrementally, the FHWA reported a new estimate of VSL of $5.8 million (value in 2007) based on five most recent research results (Kochi et al., 2006; Mrozek and Taylor, 2002; Miller, 2000; Viscusi, 2003, 2004). Numerous studies have also been conducted to evaluate the VSL in different countries. Miller (2000) compared the estimated VSL from 68 studies spread across thirteen countries. It was found that the estimated VSL vary significantly across nations. The values are typically about 120 times GDP per capita. Trawe´ın et al. (2002) compared the costs per fatal casualty in crashes adopted by authorities in different countries. It was found that the average cost per fatality has increased between 1990 and 1999 due to both changes in the methodology and changes of valuations. Blaeij et al. (2003) conducted an international meta-analysis of the values of statistical life in road safety that summarized the results of previous research. The study reported the estimates of VSL from thirty different studies. The meta-analysis also sheds some new lights on the variation of the VSL by country, survey method, elicitation method, safety enhancing measure and the format of VSL, etc. The severity level of a crash could range from a slight injury to a life threatening event. While lots of studies have been conducted regarding the estimation of VSL, few of them used the similar methods for estimating the value of injuries. The major concern is that respondents can hardly perceive the severity of crashes accurately. That is, they cannot distinguish clearly between the money that needs to be devoted to reducing fatal and injury risks. To determine the value of injuries, FHWA proposed the abbreviated injury scale (AIS) to estimate the costs associated with different types of injuries as a percentage of the assumed VSL estimate. A total of six AIS levels were defined according to crash severity, including minor crash, moderate crash, serious crash, severe crash, critical crash, and fatal crash. For each type of crash, the fraction of VSL was determined (FHWA, 2008). Until recently, little documentation has been available with regard to the estimation of VSL in developing countries like China. Due to the socioeconomic and demographical disparities, people’s willingness to pay can be quite different across nations. For example, a large proportion of people in China did not had driver licenses. Their perception of the increased utility due to risk reduction might be different from that of drivers. Also, various factors may affect people’s choice behaviors in different ways. The heterogeneity of travelers, compounded by the existence of various trip characteristics, makes the analyses more complicated. In addition, the VSL captures individuals’ willingness-to-pay with the consideration of the trade-off between costs and fatality risks. However, in the evaluation of safety related projects, the social view of individ-

ual benefits is not necessarily equal to the private view. It is doubted that the subjective value of statistical life cannot be directly used in the cost-benefit analysis of safety related projects. Instead, the social value of statistical life should be used, which represents the ratio between a margin of utility of fatality and a social utility of money (Jara-Díaz et al., 2000). The social benefits of risk reduction require further elaboration. The present study aims to estimate the social value of statistical life through an empirical application in the specific nature of China. More specifically, this paper tries to: (a) identify how the various factors influence people’s willingness-to-pay for the reduction of crash risks; (b) estimate the subjective value of statistical life using discrete choice models, while considering the random tastes that may exist among different respondents; and (c) estimate the social value of statistical life that can be used in the evaluation of transport related projects. 2. Methodology 2.1. Subjective value of statistical life According to the rational choice theory, if a decision maker is faced up with two alternatives (i and j), with the Ui higher than Uj , the decision maker always chooses alternative i. The expression can be expressed as follows (Train, 2003): Pi, m = Pr(Ui,m > Uj,m )

(1)

where Pi ,m represents the probability that the decision maker m chooses alternative i; Ui,m represents the utility that decision maker m obtains from alternative i; and Uj,m represents the utility that decision maker m obtains from alternative j. The random utility can be expressed as the sum of the systematic utility and an unobserved error term. The expression can then be transformed to: Pi, m = Pr(Vi,m + εi,m > Vj,m + εj,m ) = Pr(εj,m − εi,m < Vi,m − Vj,m )

(2)



=

I(εj,m − εi,m < Vi,m − Vj,m )f(ε)dε

where Vi,m represents the systematic utility that decision maker m obtains from alternative i; Vj,m represents the systematic utility that decision maker m obtains from alternative j; ε represents the unobserved error term; I represents if the statement that the difference between the error terms εj,m and εj,m is lower than the difference between the systematic utility Vi,m and Vj,m is true or not (=1 if the statement is true, 0 if the statement is false); f(ε) represents the priori assumed density function of the unobserved error term ε. The systematic utility Vi,m and Vj,m can be expressed as a linear function of the attributes of an alternative, multiplied by their coefficients. The expression is shown as follows: Vi,m = ˇcost × ci, m + ˇcau × caui, m +



ˇk × Xk, i, m

(3)

k

Vj,m = ˇcost × cj, m + ˇcau × cauj, m +



ˇk × Xk, j, m

(4)

k

where ci,m represents the cost if decision maker m chooses alternative i; cj,m represents the cost if decision maker m chooses alternative j; caui,m represents the fatality rate if decision maker m chooses alternative i; cauj,m represents the fatality rate if decision maker m chooses alternative j; Xk,i,m and Xk,j,m represents other influence factors that are known to the decision maker for alternative i and j, respectively; ˇcost represents the coefficient of cost; ˇcau represents the coefficient of fatality rate; ˇk is the coefficient of the

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other influence factors are known to decision makers. The subjective value of statistical life (VSL) is then estimated as the ratio of the marginal utility of fatality rate to the marginal utility of cost, which can be estimated as: VSL =

∂U/∂cau ˇcau = ˇcost ∂U/∂c

(5)

2.2. Social value of statistical life The social utility due to fatality reduction can be estimated as the sum of the utility of each individual group, which is given as: Us = U1+· · ·+Uq+· · ·+Un

(6)

where Us represents the social utility due to fatality reduction; Uq is the utility for individual group q (q = 1,. . .,n). The individual utility is a function of fatality rate (cau), cost (c) and individual income (Iq ), which is shown as follows: Uq = f(Iq, c, cau)

dUs =

 ∂Uq ∂Iq

q

dBq =



qdBq

(8)

1 qdBq s

(9)

It is assumed that the safety investments that aim at risk reduction are funded through the collected taxes. Thus, the social welfare loss due to contributed taxes should be equal to the social funds used for investments (Jara-Díaz et al., 2000). If the individual group q pays a marginal tax dTq , the marginal social welfare loss dL is calculated as:



qdTq

(10)

q

According to the definition of s , the social utility of income is the ratio between the marginal social welfare loss and the marginal amount of taxes collected:



dL s = = dT

In the binary logit model, the coefficients of the parameters are fixed, and the error term εi and εj are assumed to be independently and identically distributed with a Gumbel distribution. In this study, data from stated preference surveys were used to estimate the coefficients of logit models. The respondents were asked if they were willing to pay a certain amount of money to reduce the fatality rate by a certain amount. Let 1 indicate that they are willing to pay for fatality rate reduction and 0 that they are not. Given a sample of respondents who have provided socioeconomic information and their choices, a model with these variables can be estimated. The logit model is shown as follows: Y = LN(

qdTq

q



= dTq

Pi,q Pj,q

)

= Vi,q − Vj,q = ˇcost (ci, q − cj, q) + ˇcau (caui, q − cauj, q)



+



qq

(11)

q

q

where  q is the proportion of marginal taxes paid by group q. Theoretically, an increase in the cost (dc) would result in a reduction in utility (s × dc) due to loss of money on one hand, and an increase of utility (ˇcau × dcau) due to risk reduction on the other hand. Thus, the change in social utility is given as: dVs = −s × dc + ˇcau × dcau

(12)

(14)

ˇk × (Xk, i, q − Xk, j, q)

k

q

dL =

2.3. Binary and mixed logit models

q

where q is the marginal utility of income for group q; dBq represents the change in individual benefit for group q. According to Eq. (8), the social utility due to fatality rate reduction is the weighted sum of all individual benefits (in terms of monetary values). A social conversion factor s is then used to convert the social welfare into monetary terms: dB =

where SVSL is the social value of statistical life; s is the social utility of money.

(7)

When the fatality rate is changed due to safety related projects, the change in social utility (dUs ) can be estimated as:

3

= ˇcost c + ˇcau cau +



ˇk × Xk

k

where Y is the LN of the odds, or likelihood ratio, that the dependent variable is 1. Pi,q represents the probability that q chooses alternative i; Pj,q represents the probability that q chooses alternative j; Vi,q and Vj,q represent the systematic part of the utility function for alternative i and j, respectively; ␣ represents the change in the other factors influencing decision making that are known to the decision maker; c represents the change in travel cost; cau represents the change in fatality rate; and Xk represents the change in influencing factor k. The binary logit model is easy to implement and estimate. However, previous studies indicated that this method is limited in its scope due to a set of stringent assumptions, notably with regards to the nature of substitution patterns across alternatives, the absence of random taste heterogeneity across decision makers, and the ignorance of the correlation in unobserved factors over time (McFadden and Train, 2000). As compared with the binary logit model, the mixed logit model is a highly flexible model that can approximate the utility model with random parameters. It obviates the limitations of the standard logit model by allowing for random taste variation, unrestricted substitution patterns and correlation in unobserved factors over time (McFadden and Train, 2000). A mixed logit model can be developed by considering the coefficients of parameters to be random. Let ˇr represent the rth coefficient. The coefficients vary over decision makers in the population with density f(ˇr ). The probability that individual n chooses alternative i over alternative j can be expressed as:



Pi =

(

eVi eVi +eVj

)f (ˇr )dˇr

(15)

where f(ˇr ) represents the function of coefficient ˇr . 3. The stated preference survey

Accordingly, the social value of statistical life (SVSL) is estimated as: ˇcau ∂Vs/∂cau ˇcau SVSL = = − = −s ∂Vs/∂c qq q

(13)

A stated preference survey was conducted in the city of Nanjing from April to June, 2014 and from September to October, 2015. Nanjing is the capital city of the Jiangsu province, which is one of the most developed provinces in China in terms of the gross domestic product (GDP) per capita and human development index. The total

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4 Table 1 Sample sizes for different districts in Nanjing. District

Population (10,000)

Urban

Xuanwu District Qinghuai District Gulou District Jianye District Yuhuatai District Qixia District

66.05 103.48 129.22 44.68 41.58 66.41

264 414 517 179 166 266

8.07% 12.64% 15.78% 5.46% 5.08% 8.11%

Suburban

Jiangning District Pukou District Lishui District Gaochun District Luhe District Total

117.86 72.87 41.95 42.04 92.64 733.9

471 291 168 168 371 2,936

14.39% 8.90% 5.12% 5.13% 11.31% 100%

population in the Nanjing metropolitan area exceeds 8.2 million by the end of 2014. The GDP per capita in Nanjing reached 107,545 RMB (16,210 US dollars) in the year of 2014 (Nanjing Municipal Bureau of Statistics, 2015). This study takes the case of Nanjing to illustrate the sampling methods and the survey process to estimate the VSL. The procedure can also be used to estimate the VSL for other cities in China. Face-to-face interviews were conducted at stations, shopping centers, schools, and parks in eleven districts in the urban area of Nanjing. The sample size for each district and for different age groups was determined according to the proportion of population. Within each age group, the surveyed people were randomly selected from different days of week and time of day so as to ensure that each individual in the population had an equal chance of being selected, as shown in Table 1. A questionnaire was handled out for each surveyed individual. Before the initiation of the interview, some background information was presented, including the purpose of the survey, the current crash rate and fatality rate in the city of Nanjing, and a brief description about the safety improvements that may help to reduce fatality risks. In order to mitigate the problem of individuals’ judgement of small probabilities, the fatality risk was transformed into the average number of fatalities per year. Respondents were then asked to express their choices under a series of hypothetical situations. The questionnaire contains three sections. The first section is about respondents’ socioeconomic characteristics, including gender, age, income, education, occupation, etc. The second section is about respondents’ safety related behaviors if the respondent has a driver license, such as the age of driving, whether they had red running or drunk driving behaviors, and if they are used to wearing seatbelts when driving. The third section presents a series of assumed choice situations reflecting the respondents’ tradeoff between cost and level of risk. The respondents were asked if they were willing to contribute a specific amount of money for safety improvements so as to travel with lower number of fatalities per year. The charged fees can be used to implement road safety countermeasures, or to improve private vehicle equipment. For example, a respondent was asked “Are you willing to pay 50 RMB per year to reduce the fatality rate from 500 fatalities per year to 250 fatalities per year in Nanjing, if the charged fees were used to implement road safety countermeasures?” If the answer was “Yes”, a following question would be asked as “How about paying 100 RMB per year?” If the answer was “No”, another following question would be asked as “How about if the charged fees were used to improve your private vehicle equipment?” To prevent the respondents being tied to the questions and ensure the quality of the data, each respondent was only asked to make three to four choices. Out of the 2,202 interviewees in the initial sample collected from April to June, 2014, 1,277 responded, indicating a total response rate of 58%. To ensure that the sample is representative of the whole

Sample Sizes

Proportion

population, a second stage stated preference survey was conducted among the group of people who had not been interviewed in different districts of Nanjing and for different age groups. For the purpose of model calibration for different groups of people, a supplementary investigation was carried out from September to October, 2015. The final sample size of each district follows that in Table 1. After eliminating the illogical data, a total of 2,857 questionnaires were collected, resulting in a sample size of 10,085 choices. Table 2 describes the social-economic characteristics of the respondents.

4. Results of analyses Considering the fact that the parameters influencing the choice behaviors may be different between motorists (people who have driving license) and non-motorists (people who do not have driving license), the collected data were subdivided into two groups. For each group of data, two types of models were developed, including a fixed coefficient binary logit model and a mixed logit model. The dependent variable is the answer made by the respondents—whether he or she is willing to pay a specified amount of money for a hypothetical situation. It is a dummy variable which equals 1 if the respondent is willing to pay for fatality rate reduction and 0 if not. The initially considered explanatory variables are summarized in Table 3. Using the software package STATA, the coefficients for the two types of discrete choice models for each group were estimated. Considering the diversity in the marginal utility of each independent variable across individuals, the selected variables may have random coefficients. The variables with random parameters were determined by allowing each variable to have a random parameter and checking the t-statistic of the standard deviation of the distribution of each parameter. The results indicated that in the model for motorists, both DELTACAU and DELTAC had random parameters, while in the model for non-motorists, only DELTAC had a random parameter. Different types of distributions for coefficients were testified, including the normal distribution and lognormal distribution. The likelihood ratio test was conducted and the relative quality of statistical models were compared according to Akaike information criterion (AIC) and the relative likelihood of different models. The results suggested that for the model for motorists, the best estimation results can be obtained when both the coefficients of DELTACAU (ˇcau ) and DELTAC (ˇcost ) followed the normal distribution; while for the model for non-motorists, the best estimation results can be obtained when the coefficient of DELTAC (ˇcost ) followed the normal distribution. The results are summarized in Table 4 for motorists and Table 5 for non-motorists. All of the selected variables are statistically significant at a 95% level of confidence. For both models, the random coefficient models provide higher log likelihood values and lower AIC values than the fixed coefficient models do, indicating that the random coeffi-

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5

Table 2 Socio-Economic Characteristics of Respondents. Variable Notation

Definition

Total

Frequency

GENDER

Male Female

2,857

1,460 1,397

51.10% 48.90%

AGE

≤29 30–49 ≥50

2,857

920 1,311 626

32.20% 45.90% 21.90%

INCOME

Monthly income of the interviewee in RMB

2,857

954 926 597 289 91

33.40% 32.40% 20.90% 10.10% 3.20%

EDUCATION

Uneducated/Elementary or Secondary school Bachelors Graduates or higher

2,857

1,520 1,146 191

53.20% 40.10% 6.70%

OCCUPATION

Student Labor/Employee Professional & technical Government officer Private Employer No job/Retired Others

2,857

403 780 614 225 213 216 406

14.10% 27.30% 21.50% 7.88% 7.46% 7.55% 14.21%

DRIVAGE

No driving license Less than 1 year 1 to 5 years Over 5 years

1,255 397 708 497

43.94% 13.88% 24.80% 17.39%

≤3,500 3,500–5,000 5,000–8,000 8,000–12,500 ≥12,500

2,857

REDRUNa

Whether have red light running behaviors (For motorists)

Yes No

1,602

915 687

57.10% 42.90%

DRINKDRVa

Whether have drunk driving experiences (For motorists)

Yes No

1,602

813 789

50.76% 49.24%

SAFEBELTa

Whether used to wearing safety belt (For motorists)

Yes No

1,602

1,508 94

94.16% 5.84%

a

The last three questions were only for motorists who had driving license.

Table 3 Definition of Candidate Explanatory Variables. Variable Notation

Type

Definition

GENDER AGE1 AGE2 EDU OCCUPA1 OCCUPA2 OCCUPA3 OCCUPA4 OCCUPA5 INCOME1 INCOME2 INCOME3 INCOME4 DRIVAGE DRINKDRV SAFEBELT PRIVATE DELTACAU DELTAC

Dummy Dummy Dummy Discrete Dummy Dummy Dummy Dummy Dummy Dummy Dummy Dummy Dummy Discrete Dummy Dummy Dummy Continuous Continuous

1 if male, 0 otherwise 1 if 30≤ age ≤49, 0 otherwise 1 if age ≥50, 0 otherwise 1 = junior or senior high school student, 2 = undergraduate students, 3 = graduates and above 1 if labor/employee, 0 otherwise 1 if government officer, 0 otherwise 1 if professional & technical, 0 otherwise 1 if private employer, 0 otherwise 1 if unemployed or retired, 0 otherwise 1 if 3500 ≤ income < 5,000, 0 otherwise 1 if 5000 ≤ income < 8,000, 0 otherwise 1 if 8,000 ≤ income < 12,500, 0 otherwise 1 if income ≥ 12,500, 0 otherwise 1 = 0 to1 year; 2 = 1 to 5 years; 3 = over 5 years 1 if yes, 0 otherwise 1 if yes, 0 otherwise 1 if the charged fees were used to improve private car equipment, 0 otherwise Change in casualty rate Change in travel cost (RMB)

cient models provide better goodness-of-fit to the collected data. With regard to the mixed logit model for motorists, the relative likelihood for the model with lognormal distribution for ˇcost and normal distribution for ˇcau is 0.037; and the relative likelihood for the model with normal distribution for ˇcost and lognormal distribution for ˇcau is 0.003, indicating that the two models are 0.037 and 0.003 times as probable as the mixed logit model with normal distribution for both ˇcost and ˇcau to minimize the information loss. Similarly, for the mixed logit model for non-motorists, the relative likelihood for the model with lognormal distribution for ˇcost is 0.171, indicating that the model is 0.171 times as probable as the

model with normal distribution for ˇcost to minimize the information loss. As a result, the mixed logit model with normal distribution for both ˇcost and ˇcau was selected for evaluating the effects of contributing factors that affected respondents’ willingness to pay for fatality rate reduction for motorists; and the model with normal distribution for ˇcost was selected for non-motorists. 4.1. Factors affecting willingness to pay for risk reduction Table 4 summarized the significant factors that affect people’s willingness to pay for risk reduction for motorists. Ten explanatory

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6 Table 4 Model Estimation Results for Motorists. Variables

Binary logit model

Mixed logit model I 2 ˇcost ∼-N(1 , 1 ), ˇcau ∼−N(2 , 2 2 )

Mixed logit model II ∼-logN(3 , 3 ), 2 ˇcau ∼−N(4 , 4 )

Mixed logit model III ∼-N(5 , 5 2 ), ˇcau ∼−logN(6 , 6 )

ˇcost

ˇcost

Coef.

Std. Err.

z

Coef.

Std. Err.

z

Coef.

Std. Err.

z

Coef.

Std. Err.

z

INCOME EDU GENDER AGE1 AGE2 DRIVAGE PRIVATE OCCUPA4 DELTACAU DELTAC Std. of DELTACAU Std. of DELTAC Constant

0.243 0.165 1.018 0.520 −3.116 −0.316 3.318 0.626 −2,587.53 −0.003

0.055 0.095 0.178 0.177 0.237 0.098 0.164 0.242 1252.57 0.001

4.45 1.73 5.73 2.94 −13.13 −3.23 20.24 2.58 −2.07 −2.95

0.177 1.017 1.320 0.889 −4.217 −1.229 5.313 0.926 −30,486.81 −0.009 15,987.66 0.006

0.086 0.188 0.298 0.301 0.448 0.208 0.545 0.412 6,246.37 0.002 3,270.57 0.003

2.06 5.42 4.43 2.95 −9.42 −5.91 9.75 2.25 −4.88 −4.21 4.89 5.59

0.259 0.941 1.338 0.766 −4.197 −1.103 4.841 0.855 −30,486.81 −5.184 −16,698.52 1.223

0.086 0.176 0.288 0.292 0.434 0.192 0.429 0.382 5,540.10 0.273 3133.59 0.147

3.00 5.34 4.64 2.63 −9.67 −5.76 11.28 2.24 5.35 −19 −5.33 8.34

0.188 0.948 1.304 0.833 −4.332 −1.147 5.331 0.991 −9.841 −0.007 0.731 −0.016

0.087 0.185 0.300 0.296 0.542 0.210 0.566 0.415 0.232 0.002 0.140 0.003

2.17 5.13 4.35 2.81 −7.99 −5.46 9.42 2.39 −42.49 −3.73 5.2 −5.78

−0.966

0.047

−20.36

Log likelihood AIC Relative likelihooda

−1,936.46 3,894.93 0.000

a

−589.01 1,202.02 1.000

−592.31 1,208.62 0.037

−595.00 1,214.00 0.003

The relative likelihood of model i is calculated as exp((AICmin −AICi )/2).

Table 5 Model Estimation Results for Non-motorists. Variables

Binary logit model

Mixed logit model IV ˇcost ∼-N(5 , 5 2 )

Mixed logit model V ˇcost ∼-logN(6 , 6 )

Coef.

Std. Err.

z

Coef.

Std. Err.

z

Coef.

Std. Err.

z

INCOME GENDER AGE1 AGE2 DELTACAU DELTAC Std. of DELTAC

0.462 0.743 −0.675 −0.411 −21,620.59 −0.007

0.060 0.110 0.144 0.178 1632.70 0.001

7.73 6.77 −4.69 −2.31 −13.24 −9.75

0.447 0.825 −1.080 −0.672 −17,946.77 −0.007 0.003

0.096 0.190 0.238 0.280 2573.23 0.002 0.007

4.68 4.35 −4.54 −2.4 −6.97 −3.66 4.13

0.573 0.975 −1.139 −0.735 −23,807.42 −4.823 1.852

0.174 0.269 0.310 0.327 4,432.95 0.236 0.201

3.30 3.63 −3.67 −2.24 −5.37 −20.40 9.22

Constant Log likelihood AIC Relative likelihooda

−0.966 −2,100.35 4,216.70 0.000

0.047

−18.12 −975.70988 1,967.42 1.000

variables were included in the model, including the variables about income, education, gender, age, drive age, occupation, whether the charged fees were used to improve private vehicle equipment, reduction in fatality rate, and change in travel cost. In terms of income, we got the expected result that people with higher income and education are more willing to pay for risk reduction. The higher educated people may pay more attention to traffic safety and had a better understanding about the potential effects of traffic safety countermeasures, thus are more willing to pay than the low educated people. The coefficient of gender is also positive, indicating that males are more likely to pay for risk reduction. In terms of age, the coefficient of AGE1 is positive while the coefficient of AGE2 is negative, indicating that motorists from 30 to 49 years old are more likely to pay for risk reduction while motorists over 50 years old are more prudent, as compared with those less than 30 years old. Also, motorists’ willingness to pay tend to decrease with an increase in their drive age, as these groups of people are often more experienced and skilled and they believe that the life threating events can be avoided by themselves. Private employers are more willing to pay for risk reduction than other occupation groups. Besides, motorists are more likely to pay for risk reduction if the charged fees are used to improve their private vehicle equipment. The result is intuitive, although this factor has seldom been mentioned in previous studies. Travelers’ willingness to pay for risk reduction also decreases with a decrease in fatality rate or an increase in travel cost.

−977.47549 1,970.95 0.171

The factors that significantly affect people’s willingness to pay for risk reduction are slightly different for non-motorists (see Table 5). In terms of income, gender, the change of fatality rate and the change of travel cost, the obtained results are consistent with those for motorists. As for the age, the coefficients of AGE1 and AGE2 are both negative, indicating that non-motorists over 30 years old are less likely to pay for risk reduction, as compared with those less than 30 years old. This is perhaps due to the reason that many people in the young group, although still unemployed, are more likely to obtain money from their family to pay for risk reduction. 4.2. Subjective value of statistical life With the model estimation results, the subjective value of statistical life can be obtained. As discussed above, the coefficients of DELTACAU and DELTAC may follow a random distribution. Thus, the subjective value of statistical life, which is estimated as the ratio of coefficients of DELTACAU and DELTAC, should also be a random parameter. VSL =

ˇcau ˇcost

where ˇcost ∼−Normal(0.009, 0.0062 ), ˇcau ∼−Normal(30,486.81, 15,987.662 ) for motorists; and ˇcost ∼−Normal(0.007, 0.0032 ), ˇcau = −17,946.77 for non-motorists.

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7

Table 6 VSL Values from the Reported Research (Millions of Dollars). Country

Study

Survey year

VSL in study year

Estimated VSL in 2014

Bangladesh Canada Chile Chile China China India Mongolia Poland Sweden Sweden Swedish Thailand U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S. U.S.

Mahmud (2008) Krupnick et al. (2002) Jara-Díaz et al. (2000) Iragüen and Ortúzar (2004) Krupnick et al. (2006) Krupnick et al. (2006) Bhattacharya et al. (2006) Hoffman et al. (2012) Giergiczny (2008) Svensson (2009) Persson et al. (2001) Andersson (2007) Vassanadumrondgee and Matsuoka (2005) Alberini et al. (2004) Blomquist et al. (2011) Corso et al. (2000) Corso et al. (2001) Evans and Schaur (2010) Evans and Smith (2008) Hersch and Viscusi (2010) Kniesner and Viscusi (2005) Kniesner et al. (2010) Kniesner et al. (2012) Leeth and Ruser (2003) Ludwig and Cook (2001) Scotton and Taylor (2016) Viscusi (2004) Viscusi and Hersch (2008)

2003 2002 1999 2002 2005 2005 2005 2010 2002 2009 2001 2001 2003 2004 2007 1999 2000 1998 2000 2003 1997 2001 2001 2000 2000 1997 1997 2000

0.003 0.92–2.14 4.348 0.162 0.214 0.378 0.042 0.378 0.79–2.41 4.20–7.30 2.840 3.17–4.89 1.555 0.70–1.54 1.57–14.08 2.34 ∼ 5.55 3.244 6.700 9.600 6.800 4.740 7.550 9.050 2.724 5.006 5.270 4.700 7.370

0.004 1.21–2.83 6.201 0.215 0.261 0.463 0.051 0.407 1.04–3.18 4.63–8.05 3.848 4.29–6.62 2.002 0.88–1.93 1.82–16.35 3.33–7.91 4.510 9.804 13.344 8.751 7.116 10.229 12.261 3.786 6.958 7.912 7.056 10.244

In this paper, the Monte Carlo (MC) method was used to obtain the distribution of VSL by using random sampling from probability descriptions of uncertain input variables to generate a probabilistic description of the results. The results indicated that VSL has a mean value of 3,729,493 RMB ($586,610) with a standard deviation of 2,181,592 RMB ($343,142) for motorists; and a mean of 3,281,283 RMB ($505,318) with a standard deviation of 2,376,975 RMB ($366,054) for non-motorists. Comparing the results with that of other countries, as shown in Table 6, it was found that the estimated VSL in this study was much lower than those in developed countries, but generally comparable with those in developing countries. 4.3. Social value of statistical life Considering that people with different income levels contribute different marginal proportions of salary to society as taxes, the collected data were categorized into five groups, including “INCOME0” (monthly income <3500 RMB), “INCOME1” (3,500 RMB ≤ monthly income <5,000 RMB), “INCOME2” (5,000 RMB ≤ monthly income < 8,000 RMB), “INCOME3” (8,000 RMB ≤ monthly income <12,500 RMB) and “INCOME4” (monthly income ≥12,500 RMB). Table 7 illustrates the current tax payment regulation as a percentage of income in China. The contribution of each income group to the social funds can be estimated using the following equation. income,i =

dTincome, i

 q

dTq

=

εi i



(16)

εi i

q

The results are shown in Table 8. The conversion factor from utility to monetary values () for each income group is estimated using the mixed logit model. According to Eq. (11), the social conversion factor s is estimated to be 0.00424 (utility/RMB). With the estimated coefficient for the parameter DELTACAU in the logit model, the social value of statistical life can be estimated as the ratio of ˇcau to s , which has a mean of 7,184,406 RMB ($1,130,032). As com-

pared with the subjective value of statistical life, the social value of statistical life seems to be much higher. This is due to the reason that the high income group contributes more tax to social investment, thus a higher weight () was assigned to the high income group in the estimation of the conversion factors from social utility to monetary values (s ), as shown in Eq. (11). 5. Summary and discussions This paper estimated the subjective and social value of statistical life through an empirical application in the city of Nanjing in China. Stated preference surveys were conducted to collect data regarding travelers’ willingness to pay under various hypothetical situations. Discrete choice models were established to estimate how various parameters influence travelers’ WTP. Considering the random tastes that exist among different respondents, this paper used mixed logit models to estimate the coefficients of various parameters for motorists and non-motorists, respectively. The results estimated using mixed logit models with random coefficients was compared to those estimated using binary logit models with fixed coefficients. It was found that the coefficients of discrete choice models differed greatly across different groups of people. The finding suggests that there exist complex interactions between travelers’ WTP and the various socioeconomic and demographic factors. The varying effects of various explanatory variables further support the use of random coefficient binary logit model for modeling the value of statistical life. According to model estimation results, VSL has a mean value of 3,729,493 RMB ($586,610) with a standard deviation of 2,181,592 RMB ($343,142) for motorists; and has a mean of 3,304,453 RMB ($519,756) with a standard deviation of 5,531,157 RMB ($869,993) for non-motorists. The estimated VSL in this study was much lower than those in developed countries, but generally comparable with those in developing countries. Using the tax system to illustrate the contribution of different income groups to social funds, the social value of statistical life were also calculated. Based on the estimated social value of statistical life, the social value of injuries can be calculated. As mentioned above, respon-

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8 Table 7 Tax Payments as a Percentage of Income in China.

1 2 3 4 5 6 7 8

Range of income (RMB)

Income that should pay taxes (RMB)

Tax payments as% of income that should pay taxes (RMB)

Paid taxes (RMB)

0–3,500 3,500–5,000 5,000–8,000 8,000–12,500 12,500–38,500 38,500–58,500 58,500–83,500 Over 83,500

0 0–1,500 1,500–4,500 4,500–9,000 9,000–35,000 35,000–55,000 55,000–80,000 80,000–

0% 3% 10% 20% 25% 30% 35% 45%

0 0–45 45–345 345–1,245 1,245–7,745 7,745–13,745 13,745–22,495 22,495–

Table 8 Income Distribution and Contribution of Each Income Group to Social Funds.

INCOME0 INCOME1 INCOME2 INCOME3 INCOME4 Total a b c d e f

εa (%)

kb (%)

c (%)

ε*

0.00 0.45 2.61 7.14 18.45

34.90 30.10 19.90 10.30 4.80 100.00

9.33 19.55 19.77 16.13 35.21 100.00

0.0000 0.0009 0.0052 0.0115 0.0650 0.0825

 d (%) 0.00 1.07 6.24 13.95 78.74 100.00

e

|ˇcau |

SVSLf (RMB)

0.02830 0.01388 0.00748 0.00514 0.00370 0.00424

30,487

7,184,406

ε represents average tax payments as% of income. k is the percent of population for each income group.

represents percent of GNP from each income group.  represents contribution to social funds.  is the conversion factors from utility to monetary values. SVSL = |ˇcau |/=30,487/0.00424 = 7,184,406 RMB.

Table 9 Social Value of Injury by AIS Level. AIS Level

Severity

Fraction

Mean (RMB)

AIS 1 AIS 2 AIS 3 AIS 4 AIS 5 AIS 6

Minor Moderate Serious Severe Critical Fatal

0.003 0.047 0.105 0.266 0.593 1

21,553 337,667 754,363 1,911,052 4,260,353 7,184,406

dents can hardly perceive the severity of crashes accurately, so that detailed willingness to pay estimates covering the entire range of potential disabilities are unobtainable. The value of injuries cannot be directly obtained from the coefficients of the utility function. Instead, an alternative standardized method was used in this paper to calculate the values of expected outcomes, scaled in proportion to VSL. Injuries with different severities are rated on a scale of quality-adjusted life years, which represent the alternative of life years in perfect health, as shown in the six Abbreviated Injury Scale (AIS) levels in Table 9 (U.S. Department of Transportation, 2015). These scores can be applied to VSL to assign each injury class a value corresponding to a fraction of a fatality. The values range from 21,553 RMB for a minor injury to 7,184,406 RMB for a fatality. The estimated values can be directly used in the cost-benefit analysis of safety related projects in China. Acknowledgements This research was sponsored by the National Natural Science Foundation of China (Grant nos. 51238008 and 51322810), the Natural Science Foundation of Jiangsu Province (BK20150747) and the Fundamental Research Funds for the Central Universities (NJ20160016). References Alberini, A., Cropper, M., Krupnick, A., Simon, N., 2004. Does the value of a statistical life vary with age and health status? Evidence from the United States and Canada. J. Environ. Econ. Manage. 48 (1), 769–792.

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