VALUE OF STATISTICAL LIFE
K.R. SHANMUGAM
DISSEMINATION PAPER - 27
Centre of Excellence in Environmental Economics (Sponsored by Ministry of Environment and Forests, Government of India)
MADRAS SCHOOL OF ECONOMICS DECEMBER 2013
DISSEMINATION PAPER SERIES The Centre of Excellence in Environmental Economics was asked by the Ministry of Environment and Forests to explain the concepts of environmental economics to non-economists through a series of short dissemination papers. The authors welcome feedback on the papers from readers. The following Twenty Seven dissemination papers have been posted on the Centre Website (http://coe.mse.ac.in). No. Title Author 1. Environmental Externalities Dr.U.Sankar 2. Vehicular Pollution Control Dr.Vinish Kathuria 3. Environmental Accounting Dr.G.S.Haripriya 4. Public Disclosures Using Information to reduce pollution Dr. Vinish Kathuria 5. Hedonic price method A Concept Note Dr. Haripriya Gundimeda 6. Contingent Valuation Method Dr. Haripriya Gundimeda 7. Environmental Health Dr. Zareena Begum I 8. Precautionary Principle Dr. K.S. Kavi Kumar 9. Ecosystem Services - A concept note Dr. Vinish Kathuria 10. Climate Change and Adaptation Dr. K.S. Kavi Kumar 11. Social Discount Rate, Intergenerational Equity and Climate Change Dr. U.Sankar 12. Plastics and Environment Dr. Zareena Begum I 13. Clean Development Mechanism Dr. K.S.Kavi Kumar 14. Sustainable Development Dr. K.S.Kavi Kumar 15. Cost Benefit Analysis and Environment Dr. K.S.Kavi Kumar 16. Carbon Trading Dr. K.S.Kavi Kumar 17. Ecological Footprint Dr. Ramprasad Sengupta 18. Choice Experiments Dr. Sukanya Das 19. Solid Waste Management Dr. Zareena Begum I 20. Common Property Resources and Collective Action A Short Review Pranab Mukhopadhyay 21. Green Economy Dr. K.S. Kavi Kumar 22. Economics of Natural Resources Rabindra N. Bhattacharya 23. Travel Cost Method For Environmental Valuation Dr. Sukanya Das 24. Trade and Environment Badri Narayanan 25. Environment and Development Dr. K.S. Kavi Kumar 26. The Economics of Biodiversity Suneetha M S 27. Value of Statistical Life K.R. Shanmugam Hard copies may be obtained from: Member-Secretary Centre of Excellence in Environmental Economics Madras School of Economics Gandhi Mandapam Road, Chennai 600 025 Email :
[email protected] Use of any part of this publication should be duly acknowledged
VALUE OF STATISTICAL LIFE
K.R. Shanmugam Director, Madras School of Economics
[email protected]
DISSEMINATION PAPER – 27
December 2013
Center of Excellence in Environmental Economics (Sponsored by Ministry of Environment and Forests, Government of India)
Madras School of Economics
VALUE OF STATISTICAL LIFE 1. Introduction Valuing life is one of the most sensitive and controversial areas in economics. Much of the controversy arises from a misunderstanding of what is meant by this concept/terminology. The aim of this dissemination paper is to provide a non-technical introduction to the concept of value of life, its measurement, and its usage in evaluating life saving public programs. Section 2 conceptualizes the value of life and highlights its policy usage. Section 3 briefly reviews the popular hedonic approach for measuring it. Section 4 discusses how the insurance benefits affect the value of life estimation. Section 5 deals with the heterogeneity of value of life. Section 6 reviews other approaches adopted in the literature to measure the value of life and the final section compares the value of life estimates of different studies and concludes the paper. 2. The Value of Statistical Life: The Concept and its Policy Usage The value of statistical life (VSL) or the hedonic value of life is the trade-off between money and very small risk of death. This measure is the most prevalent benefit assessment approach used by Government agencies when valuing changes in risk. In the case of labor market, it is the wage-fatality trade-off revealed by workers‟ decision about how much extra pay or wage compensation the workers require for accepting jobs that pose additional risks.1 The VSL concept is based on the standard willingness to pay (WTP) principles from the public finance literature. While many non-economists continue to attack the entire concept of monetizing risks to life, these implicit trade-offs are reflective of how people themselves value the risks and respect consumer sovereignty in much the same way as do prices in other economic markets (Viscusi, 2008a). Before conceptualizing the value of life, it is useful to distinguish this optimal deterrence amount from the amount that is optimal from the insurance standpoint. People buy optimal insurance because it is preferable to continue to 1
In the case of automobiles, the trade-off implied by seat-belt usage decisions infers a value of life (Dreyfus and Viscusi, 1995).
1
transfer money to the post accident state until the marginal utility of money in the ill health state equals the marginal utility of money in the healthy state. In the case of property, this rule is perfectly valid. But in the case of severe health outcomes (like fatalities), making a lower level after a fatality is desirable from an insurance viewpoint. The reason is that severe health outcomes like fatalities affect individual‟s utility function that decreases both the level and marginal utility for any given level of income. For such severe health outcomes, the optimal deterrence amount will exceed the optimal level of compensation (Viscusi, 2008b). The economic measure for the optimal deterrence is the trade-off between money and very small risks of death. Since risk regulation policies will prevent some expected number of adverse health outcomes, these effects are usually probabilistic. Therefore, the appropriate concept for policy evaluation is what value we should place on small reductions in the probabilities of these outcomes for large number of affected individuals and not how much we value for preventing certain adverse health effects. This distinction is critical for at least two reasons: (i) Society‟s attitude toward saving identified lives is quite different from the attitude toward saving statistical lives. Society‟s value on an identified life is likely to be substantially higher than the implicit valuations of life and health status of individuals who cannot be identified, such as the prospective beneficiaries from improved flood control program or traffic signal, and (ii) Individual‟s relative valuation of risk reduction is likely to be greater for small changes in the risk. Since an individual‟s willingness to pay (WTP) per unit of risk reduction decreases with his/her wealth, he/she will be willing to spend relatively more for initial than for subsequent reductions of risk as his/her wealth become depleted with each successive purchase of a decrease in risk. When extrapolated, this relationship indicates that the individual will spend less per unit of risk to prevent certain death and injury than to bring about small changes in these risk levels (Viscusi, 2008b) Thus, for our case, the VSL is the tradeoff between money and small risks of death. Another distinction is that it is not the value of an individual life with the present value of his or her future earnings. Of course, such measures have 2
prominence in personal injury litigation, as they serve as a principal reference point for the financial loss that a family has incurred after a wrongful death to a family member. However, the economic approach to valuing life is quite different and more legitimate than an accounting procedure based on one‟s income (Viscusi, 2008a). Let us now conceptualize the value of life by asking the question: how much would you willing to pay to eliminate a one time only risk of death of 1/1,000? Suppose each of 1000 people is willing to pay Rs. 1000 to eliminate this risk. This means that to avert the one expected death, it would be possible to raise Rs. 1000 per person x 1000 people or Rs. 1 million. The VSL is consequently Rs. 1 million.2 Alternatively we can calculate it by dividing the WTP amount by the probability reduction: Rs. 1000/(1/1000) = Rs. 1 million. What the VSL captures here is the society‟s rate of trade-off between money and very small risks of death. In the market context, the above trade-off is the same as what firms will make between cost and safety improvements. Looking across different dimensions of choice a consumer will seek similar trade-offs if options available are continuous. Thus, if improvements in safety are achievable for Rs. 1 million per statistical life by purchasing a safer car as opposed to Rs. 2 million per statistical life by removing the asbestos from one‟s basement, it is preferable to spend one‟s life saving money on the more cost effective option that has a lower cost per life saved. People will do this subject to a budget constraint. But the key result is that the marginal efficacy of safety enhancing expenditures will be the same across domains of choice. Likewise for Governments, if improvements in safety can be obtained for, say $ 1 million per statistical life in project A (installing a traffic signal) as opposed to $ 5 million (constructing a metal road) and $ 10 million (constructing a bridge) per statistical life in project B and project C respectively, then it is desirable to spend on the most cost effective option (i.e., project A) that has the lowest cost per life saved. In reality, there is no such
2
Because it is not possible ex ante to identify the person whose life will be saved, this prevented mortality is considered a statistical life (Aldy and Viscusi, 2007).
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comparable market process at work. As a result, the Governments (like the USA) use the value-of-life estimates from the market in making their deliberations concerning risk reduction policies. Rather than impose the preferences of Government officials on risk reduction efforts, the guiding principle is democratic in nature as the revealed preferences of the citizenry are the guide (Viscusi, 2000). While the VSL literature began to be established in the late 1970s and early 1980s, policymakers long viewed the idea of placing a value on human life as being immoral so instead they used the human capital measure based on earnings losses. This practice continued until the debate in the Reagan administration in USA over the proposed Occupational Safety and Health Administration (OSHA) hazard communication regulation. The OSHA proposed an expensive regulation that for the first time would require hazard warning labels for dangerous chemicals in the workplace. The U.S Office of the Management and Budget (OMB) asked to submit a benefit cost analysis. When the OSHA used the estimates of cost of death, which was the human capital measure for lost earnings and medical expenses, costs exceeded benefits and the proposed regulation was rejected. Later, when the VSL was used, benefits exceeded the costs and the regulation was issued. After that many agencies not only in USA but also in other developed nations have adopted the VSL procedure. Now this has become the standard for assessing the benefits of risk and environmental regulations (Viscusi, 2008a). As the most of the programs for environmental safety reduce the risk to death/health, and given public nature of reductions in environmental risk, the program contributing to a small reduction in risk could contribute large health benefits to the society. These benefits have to be estimated as the sum of the WTP for reduced risk to all affected people. In a free market, prices paid by people represent their WTP for goods and services. Prices paid for preventing health and death risks cannot directly be obtained. However, there are instances where WTP of people for these services could be measured indirectly by analyzing the prices observable in the market of certain goods that are either complements or substitutes to the environmental risk reduction. For example, when people purchase smoke detectors (or seat 4
belts) for their homes (automobiles), they are making a judgment that the reduction in risk of death and other losses associated with fire (traffic accidents) is worth at least as much as the cost of the smoke detector (seat belt). In the literature, the revealed preference methods of environmental valuation such as hedonic prices, travel cost, and household health production function are developed by exploiting the possible relationship between an individual‟s demand for environmental risk reduction and certain goods with observable market prices. In the case of hedonic pricing method of valuation, there are more than one hundred studies analyzing housing markets and labor markets for estimating WTP of people for environmental risk reduction. The hedonic property price model considers that demands for houses and environmental quality are complements while the hedonic wage model considers that the environmental risk at work place and wages are substitutes. The following section explains the hedonic wage model of valuing risks to human life and health. 3. Hedonic Approach of Measuring the VSL Economic Foundations Adam Smith‟s theory of compensating differentials forms the basis of the hedonic approach. He suggests that: “The whole of the advantages and disadvantages of the different employments of labor and stock must, in the same neighborhood, be either perfectly equal or continually tending to equality…The wages of labor vary with ease or hardship, the honorableness or dishonorableness of employment”. “If non pecuniary advantages and disadvantages of different employments are unequal then the pecuniary rewards must be unequal in the opposite direction to preserve the equality of total advantages”. Smith (1776) lists five principal compensating non-pecuniary characteristics of employment: (i) agreeableness or disagreeableness of employment, (ii) difficulty and expense of learning, (iii) constancy or inconstancy of employment, (iv) degree of trust required and (v) probability or improbability of success. These have inspired the development of two applied economic models, namely (i) the human capital model and (ii) the hedonic wage model. 5
While the former considers the length of training (formal schooling and informal training) as the principal compensating wage differentials while the latter focuses on quality variations in both worker and job attributes as an explanation for wage differences. The hedonic approach treats jobs as bundles of characteristics such as working condition, and levels of risk of accidental injury. Employees are described by the amount they require as compensation for different risk levels while firms (employers) are characterized by the amount they are willing to offer workers to accept different risk levels. An acceptable match occurs when the preferred choice of an employee and that of an employer are mutually consistent. Thus, the actual wage embodies a series of hedonic prices for various job attributes including accidental risk and other prices for worker characteristics. Suppose that there are m such indicators of worker‟s personal and job attributes other than job risk level (p), denoted by a vector c = (c1, c2, …, cm). Let w represent the schedule of annual earnings. Then, w (p, c) reflects the market equalizing differential function. Controlling for other aspects of the job would provide an estimate of the wage premium that workers receive for job risk. Thus the theory considers both sides of the market and examines equilibrium risk choices and either wage levels or price levels associated with these choices. The firm‟s demand for labor decreases with the total cost of employing a worker. As providing greater workplace safety is costly to the firm, it must pay a lower wage to offset the cost of providing safe work environment in order to maintain the given level of profits along the iso-profit or wage-risk offer curve. Figure 1 shows wage offer curves for two firms, with wage as an increasing function of risk, OC1 for firm 1 and OC2 for firm 2. The labor supply is characterized subject to several mild restrictions on preferences. With a von Neumann-Morgenstern expected utility approach with state dependent utility functions, u (w) represent the utility of a healthy worker at wage w and v (w) represent the utility of an injured person at wage w. Worker‟s compensation after an accident is a function of the worker‟s wage. We assume that the relationship between worker‟s compensation and wage is subsumed into the functional form of v (w) and that workers prefer health to 6
injury, (i.e., u (w) > v(w)) and that marginal utility of income is positive (i.e., u (w) > 0 and v (w) > 0). For any given risk level, workers prefer the wage risk combination from the market offer curve with the highest wage level. The outer envelop of these curves is the market opportunities locus w (p). That is, workers choose from potential wage-risk combinations along market opportunities locus w (p) to maximize the expected utility. In figure 1, the tangency between the constant expected locus EU1 of worker 1 and firm 1‟s offer curve OC1 represents his optimal job risk choice. Worker 2 maximizes his expected utility when EU2 is tangent to OC2. Eu2
Wage Eu1
w (p)
w1 (p2) OC2
w2 (p2)
Eu3 Eu2 OC1
w* (p)
w1 (p1) w3 (p2)
OC2
Eu1 OC1
p2
p1
Figure 1. Wage-Risk Trade-off 7
Risk
All wage-risk combinations associated with a given worker‟s constant expected utility locus must satisfy: Z = (1-p) u (w) + p v (w) and the wage-risk trade-off along this curve is: dw Z p u ( w) v( w) 0 dp Zw (1 p) u ' ( w) p v ' ( w)
so that the required wage rate is increasing in the risk level. The estimated dw dp
is a local measure of the wag-risk trade-off for marginal changes in risk. This estimated slope is both the worker‟s marginal willingness to accept risk (WTA) and his marginal WTP for more safety and the firm‟s marginal cost of more safety and its marginal cost reduction from an incremental increase in risk. That is, it reflects the marginal supply as well as the marginal demand price of risk. It is noted that the estimated wage-risk trade-off curve w (p) does not imply how a particular employee is compensated for non-marginal changes in risk. In figure 1, worker 2 has revealed a WTA risk p2 at wage w2 along EU2. If risk exposure to employee 1 changes from p1 to p2, he will require a higher compensation to keep his utility constant. Thus, with large changes in risk, a worker‟s wage-risk trade-off will not be the same because the relevant tradeoff must be made along the worker‟s expected utility locus not the estimated market wage-risk trade-off (Viscusi and Aldy, 2003). Since each point on the hedonic wage function w (p) represents the slope of the expected utility curve, this function is used to estimate the welfare effect of a marginal change in job risk. If all employees have homogenous preferences, then there will be only one expected utility curve, and the observable points on the w(p) will represent the constant expected utility locus. Likewise, if all firms are homogenous, w(p) will approximate the firm‟s offer curve. Ideally, one needs to estimate the constant expected utility curve in order to estimate the WTP/WTA for risk reduction. However, most studies use the hedonic function as it is the locus of tangencies that is observable in the labor market data.
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Econometric Specification of the Hedonic Wage Function Thaler and Rosen (1976) carried out the first empirical study to estimate the value of life using the hedonic wage approach. Currently we have a hand full of studies to provide life value estimates for developed as well as developing countries. Basically, these empirical studies specify some sort of wage equation as given below: wi = + 1 pi + 2 qi + k k Xki + i
(1)
where wi is the worker‟s wage rate, X is a vector of worker‟s personal characteristics variables (such as age or job experience, education, union and marital status, and caste or racial indicators) as well as job characteristics variables (which include indicators for supervisory status, job security, irregular work hours, pleasant worksite etc.,).3 pi and qi represent the probability of work related fatal and non fatal injury risks faced by worker i (in some studies the risk variables p and q are allowed to interact with other X variables), and i is the regular random error term reflecting unmeasured factors influencing worker‟s wage rate. (a constant term), 1, 2, and k are parameters to be estimated using the regression method. As the theory is silent on whether the wage equation is linear or log linear (semi-log),4 Moore and Viscusi (1988a) suggest the use of the flexible functional form given by Box-Cox transformation in order to choose the right specification with greatest explanatory power as:
wi 1
1pi + 2qi + k k X ki + i
3
(2)
Inclusion of these non-pecuniary job characteristics control for a variety of job attributes, and reduce the bias in the estimated coefficient of the job risk variable. Further they provide an additional test of the validity of the theory. 4 Another issue raised against the the theory is that most attractive job in the economy also pays more. To resolve the apparent paradox, Viscusi (1978) suggests the wealth effect. He argues that a rich person will prefer to work in safe job and earn more. Studies such as Viscusi (1978), Garen (1988) and Shanmugam (2001) estimate a risk equation in which the wealth variable enters as an explanatory variable and show that the wealth variable gets a negative and significant parameter.
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This approach assumes that a exists such that the model is normally distributed, homoscedastic, and linear in the regressors. The functional form is dictated by this parameter , which is estimated as the value that maximizes the log-likelihood function. The case where →0 represents the semi-log form, while the case where →1 represents linear functional form. The flexible form under the Box-Cox transformation can test the appropriateness of these two restrictions on the form of the model. Studies such as Moore and Viscusi (1988a) and Shanmugam (1996/7) employed this procedure. Using the maximum likelihood methods, these studies reject both specifications based on a likelihood ratio test. However, they find that the semi-log form generates results closer to those found with the unrestricted flexible form. The wage-risk trade-off based on the Box-Cox transformation can be computed by totally differentiating (2) with respect to wage and risk (p or q) and rearranging the terms as:
ˆ ˆ dw dw 11 and 21 dp w dq w
(3)
If the dependent variable is in log form, the wage-risk premium can be computed by:
dw ˆ dw ˆ 1.w and 2 .w . dp dq
(4)
Most of the existing studies on the topic employ the semi-log form due to the famous Mincerian earning function model. If p is the average probability of job related fatal risks per 1 lakh workers and w is the hourly wage rate, then the estimated regression yields a measure of the average value of a statistical life as: VSL ˆ1.w x 2000 x100000
(5)
This equation normalizes the VSL to an annual basis by the assumption of a 2000 hour work-year and by accounting for the units of the fatality risk variable. 10
Since the market opportunity locus reflects both workers‟ preferences over wage and risk and firms‟ preferences over costs and safety, an ideal measure of on–the-job risk should reflect both the workers‟ perception and the firms‟ perception of the risk. Few studies such as Viscusi (1979) Gerking et al. (1988), Liu et al. (1997) and Shanmugam (2000) have used workers‟ subjective preferences regarding risk. As on date, no study has compiled data on firms‟ perception. The subjective measure utilizes a danger perception dummy indicator that takes value 1 if the worker believes that his job exposes him to dangerous or unhealthy conditions and 0 otherwise. However, majority of the studies have constructed an objective index of job risk such as probability of fatal or non-fatal risk for workers by industry or by occupation from the secondary sources. Several papers on US labor market in 1970s and early 1980s used actuarial data (Thaler and Rosen, 1976 and Arnold and Nichols, 1983). These studies used a job-related risk measure based on data collected by the Society of Actuaries for 37 occupations in 1967. Almost all recent studies on US labor market have used fatal and injury risk data collected by the US Department of Labor Bureau of Statistics. Studies such as Butler (1983) and Causineau et al. (1992) have used Canada‟s workers‟ compensation records to construct risk measures. Kneisner and Leeth (1991) used the Yearbook of Labor Statistics for Japan and Industrial Accidental Data for Australia. Marin and Psacharopoulos (1982) and Sandy and Elliott (1996) employ the data provided by the Office of Population Census and Survey (UK). Shanmugam (1996/7, 2000, 2001) and Madheswaran (2007) have used the risk data from the Office of the Chief Inspector of Factories in Chennai. Liu et al. (1997) used Labor Insurance Agency Data for Taiwan5. 4. Role of Insurance Benefits Since the employer can compensate the workers for employment risks either through wage premium (i.e., ex ante compensation) or insurance benefits (i.e., ex post compensation), the failure to control the ex post compensation would 5
A well known problem with the use of average of aggregate industry data on risk to measure individual risk is that workers in different jobs in the same industry face same probability of risk. Further, the objective measure does not necessarily reflect the worker‟s belief about the risk of his employment.
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cause a bias in the estimation of the wage-risk trade-off of workers. An issue in this regard is whether an additive effect of workers insurance benefit on wages or an interactive effect with job risks is incorporated in the estimable wage equation. Viscusi and Moore (1987) argue that insurance benefit affects wages only at positive risk levels. At zero risk, no risk occurs and so no benefits. Therefore making an interactive model is theoretically appropriate. With this suggestion, the hedonic wage equation in (1) will take form:
ln wi 1pi + 2qi + k k Xki + WCi .qi + i
(6)
where WCi is the workers compensation benefits payable for a job injury suffered by worker i. Other studies adopted this procedure include Ruser (1985) and Shanmugam (1999). 5. Heterogeneity of the VSL The VSL is not a natural constant (Viscusi, 2010). Individuals‟ money risk trade-off vary across the population, and also vary over time for particular individuals as their age and economic circumstances change. This issue is illustrated in figure 1. Suppose that some worker group (say non union members, black or SC/ST community, etc.) faces the lower and flatter wage offer curve w*(p). Worker 3 chooses risk p2 for which his constant expected utility locus EU3 is tangent to the market offer curve. This worker will have a lower VSL than the VSL of worker 2 who faces the same risk but has different market opportunities. Hersch and Viscusi (2009) used fatality risks based on industry, immigrant status and age and found that Mexican workers face grater risk than native US workers and receive less risk compensation. They argue that the source of labor market segmentation appears to be due to differences in language skills. Shanmugam (1998) estimated different compensation amounts for union and non-union members using self-selection bias correction method; Viscusi (2003) estimated different wage-risk trade-offs for black and white workers; Viscusi (2004) estimated different wage-risk trade-off for workers in different industry/occupations. Shanmugam (2005) used the random coefficients model to estimate the individual specific VSL of Indian workers. Kneisner et al. 12
(2010) examines the heterogeneity of labor market estimates of VSL using quantile regression estimates of panel wage equations. It has been argued for long that a young worker faces a more substantial loss from a given fatality risk than an old worker. Thus, there may be age-related differences in proclivity toward risk-taking. Studies like Thaler and Rosen (1976), Viscusi (1979) and Shanmugam (1996/7) address this issue by including the death risk-age interaction term. However, this approach does not rightly capture the changes in the life expectancy with age or the role of discounting with respect to the years of life at risk. Professors Viscusi and Moore have developed three alternative methodologies to address these issues, namely discounted expected life years (DELY) approach (Moore and Viscusi, 1988b and Shanmugam, 2006), the Markov decision (MD) model (Viscusi and Moore, 1989) and the life cycle (LC) model (Moore and Viscusi, 1990 and Shanmugam, 2011). The DELY approach includes the expected discounted life years lost (ELYL) variable (instead of job risk) in the hedonic model to estimate the impact of changes in expected remaining lifetime on wages. Future health risks are discounted at a rate of time preference, r so that the ELYL of a worker with T years of remaining life who chooses the risk level p is:
ELYL px T0 1 e rT dT p x 1 e rT r , where r is the parameter
(and not a variable collected from the sample workers). r is an estimate of workers‟ implicit rate of discount that workers reveal through their choices of job risks and is computed as part of estimation process. The discounted duration of life at risk is also known as the quantity adjusted death risk and is useful to calculate the quantity-adjusted value of life. The quantity adjusted value of life differs from the conventional estimates of the value of life in that the trade off is not between wages and death risk probabilities but between wages and death risks that have been weighted by the discounted number of potential years of life lost. Consideration of duration of life lost makes it possible to estimate the Value of a Statistical Life Year (VSLY). The VSL is considered as the present value of all the VSLY levels 13
throughout the remainder of the person‟s life. If people lived forever then VSL will equal the discounted present value of an infinite steam of constantly valued annual VSLY levels (Aldy and Viscusi, 2007) . With a finite life expectancy we need to account for the fact that the stream of VSLY amounts is not infinite, as VSL will not include the VSLY values after the person‟s expected future life time. Thus, there is a deduction for a finite lifespan so that: VSL
VSLY 1 VSLY r (1 r )T r
(7)
Alternatively, it is possible to solve this equation for VSLY as a function of the estimated rate of discount, r leading to: VSLY r (VSL) / [1 (1 r )T
(8)
Although this model is simple to estimate, its structure has no formal theoretical basis. However, the MD and LC models have formal theoretical basis. In the former, worker selects the optimal job risks from the wage offer curve where this risk affects the probability of death in each period. In selecting their optimal occupational risks, workers determine their life expectancy. The latter model recognizes that there is a probability in each period that the consumption stream may be terminated. Thus, the wage responses to the variation in life years at risk provide the direct estimates of the discount rate that workers apply to their future utility in all these models. Using the discounted expected life years lost approach and the Markov decision approach, Moore and Viscusi (1988) and Moore and Viscusi (1990) found that the estimated rate of time preference was 11 per cent for US workers. Adopting life cycle approach, Viscusi and Moore (1989) found that the real discount rate for US workers was 2 per cent. In the Indian context, Shanmugam (2006) estimated the implicit discount rate (ranging 7.6 – 9.7 per cent) for workers using the DELY approach. Utilizing the LC model,
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Shanmugam (2011) estimated the real discount rate that varies across regions ranging 2.4-5.1 percent. 6. Other Approaches of Valuing Life Other approaches for valuing life include: human capital approach, insurance approach, court awards and compensation approach and portfolio approach. (i) Human Capital Approach It seeks an objective measure of the value of life (see, Fromm, 1971). There are two variants of this approach. The first (Gross output) method values life in terms of discounted present value of a person‟s expected future earnings (L1). If the earnings and the probability of survival until year i are Ei and pi respectively, r is the discount rate and n-is the livelihood of a person, then L1 is:
L1 i n
pi Ei (1 r )1 n
(9)
As this method neglects the fact that dead people do not consume, the second (Net output) method considers that a life saved is valued (L2) at the expected value of its human capital less the expected value of anticipated future consumption, Ci (see Ridker, 1967):
L2 i n
pi ( Ei Ci ) (1 r )1 n
(10)
(ii) Insurance Approach This approach values life on the basis of individual life insurance decisions. It values the loss of life on the implied assumption of a straight line relationship between the probability of a person being killed and the sum he would pay to cover the risk. A major limitation of this approach is that it measures only a person‟s willing to compensate others following death rather than he value set on his own life (see Eisner and Strotz, 1961).
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(iii) Court Awards and Compensation Method In some circumstances, after one‟s death the court awards the heirs an amount of money, say Z as restitution from a party felt to be responsible for the fatality. The courts use several factors to choose this Z amount. In almost all cases, this represents a value taken from a descriptive process. In this approach, the emphasis is on compensating victims for monetary losses, principally foregone wage and medical expenses rather than for pain and suffering (see Atiyah, 1982). (iv) Portfolio Approach In this approach, the probability of death to each person affected is compared with portfolio of risks from the same or other sources to which the individuals are already exposed. That is, it compares changes in mortality risk with the entire portfolio of risks assumed by the society (see Starr, 1969). 7. Concluding Remarks In this dissemination paper, we have provided a non-technical introduction to the concept of value of statistical life. Then we have explained the hedonic approach of measuring it, and other related issues of measuring it. We have also briefly reviewed other approaches of valuing life. Now we can compare the VSL estimated by different but selective empirical studies. Table 1 summarizes past (selected) studies on value of life and injury. The estimated life values vary dramatically among these studies. Dillingham (1985) argues that values vary either due to specification errors or the errors in variable problem. Viscusi and Aldy (2003) listed almost all the major studies and found that the range of value per statistical life was $3.8–$9.0 million range, when converted into year 2000 dollars in the United States. In the developing countries like India and Taiwan, the values are less relative to values in advanced countries. In India, the VSL ranges between US $ 1.0 – 1.5 million and for Taiwan it ranges from $0.2 million to $0. 9 million in 2000 US dollar.
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Table 1 Summary of Labor Market Studies on the Value of Life and Injury Study (year)
Sample
Baranzini and Ferro
Swiss Labour Force Survey,
Luzzi (2001)
1995, Swiss Wages
Source of Risk Variable Swiss National Accident Insurance Company, 1991–1995
Value of life ($million) $6.3, $8.6
Value of Injury
Structure Survey, 1994 Cousineau et al. (1992)
Labor Canada Survey, Canada, 1979
Quebec Compensation Board
$4.6
$38,104
Garen (1988)
Panel Study of Income Dynamics (PSID), USA, 1981-82
Bureau of labor Statistics (BLS)
$17.3
$26,953
Herzog and Schlottman (1990)
U. S. Census, 1970
BLS
$11.7
-
Kniesner and Leeth (1991)
2 digit manufacture Data, Japan, 1984;
Year book of Labor statistics; Industrial Accident Data; and National Traumatic Occupation Fatality Survey (NTOS)
$9.7 $4.2 $0.7
$60,624
2 digit manufacture data, Australia, 1984; and Current Population Survey, USA, 1978.
17
Study (year) Kim and Fishback (1999)
Sample
Ministry of Labor‟s Report on Monthly Labor Survey and
Source of Risk Variable Ministry of Labor‟s Analysis for Industrial Accidents
Value of life ($million) $0.8
Value of Injury
$99,431– $114,663
Survey on Basic Statistics for the Wage Structures, South Korea Leigh and Folsom (1984)
PSID, 1974 and Quality of Employment Survey, USA, 1977
BLS
$10.1– $13.3
Liu et al. (1997)
Taiwan Labor Force Survey , 1982 to 1986
$0.2–$0.9
Marin and Psacharopoulos (1982)
Population Census and Surveys, U.K., 1977
Labor Insurance Agency, Taiwan Occupational Mortality Tables
$4.2
-
Moore and Viscusi (1988)
PSID 1982
$9.7
-
Shanmugam (1996/7)
Author‟s survey of
BLS and NTOS Administrative Report of Factories Act 1987–1990
blue collar manufacturing workers, Madras, India 1990
18
$1.2, $1.5
Study (year) Shanmugam (2000)
Siebert and Wei (1998) Thaler and Rosen (1976)
Viscusi (1981)
Sample
Source of Risk Variable
Value of life ($million) $1.0, $1.4
Value of Injury
Author‟s survey of blue collar manufacturing workers, Madras, India 1990 Hong Kong Census 1991
Administrative Report of Factories Act 1987–1990
Labour Department
$1.7
Survey of Economic Opportunity, USA PSID, USA, 1976
Society of Actuaries
$1.0
-
BLS
$8.3
$59,238
$150– $560
(Values of life and injury are in 2000 US dollars; All values are taken from Viscusi and Aldy (2003)).
19
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Madheswaran, S. 2007, “Measuring the Value of Statistical Life: Estimating Compensating Wage Differentials among Workers in India”, Social Indicators Research 84: 83-96. Marin, Alan and George Psacharopoulos 1982, “The Reward for Risk in the Labor Market: Evidence from the United Kingdom and a Reconciliation with Other Studies”, Journal of Political Economy 90(4): 827-53. Moore , Michael J and W.Kip Viscusi, 1988a, “Doubling the Estimated Value of Life: Results using New Occupational Fatality Data, Journal of Policy Analysis and Management 7: 479-90. Moore, Michael J. and W.Kip Viscusi. 1988b, "The Quantity-Adjusted Value of Life", Economic Inquiry 26, 369-88. Moore, Michael J. and W. Kip Viscusi. 1990, "Discounting Environmental Health Risks: New Evidence and Policy Implications", Journal of Environmental Economics and Management 18, 381-401. Ridker, R.G. 1967, “The Economic Cost of Air Pollution”, Praeger. Ruser John W. 1985, “Worker‟s Compensation Benefits and Compensating Wage Differentials”, BLS Working Paper No. 153. Sandy, R. and R.F. Elliott 1996, “Union and Risk: Their Impact on the Level of Compensation for Fatal Risk” Economica 63: 291-309. Shanmugam, K.R. 1996/7, “The Value of Life: Estimates from Indian Labor Market”, Indian Economic Journal 44 (4): 105-14. Shanmugam, K.R. 1998, “The Impact of Unions on the Compensation for Job Risks”, Artha Vijnana, Vol XL, No.3: 271-84. Shanmugam, K.R. 1999, “Insurance Benefits, Wage Premiums and the Value of Injury Risks”, Manpower Journal 35(1): 1-11. Shanmugam, K.R. 2000, “Valuations of Life and Injury Risks: Empirical Evidence from India”, Environmental and Resource Economics 16: 379-89. 22
Shanmugam, K. R. 2001, "Self Selection Bias in the Estimates of Compensating Differentials for Job Risks in India", Journal of Risk and Uncertainty 22, 263-75. Shanmugam, K.R. 2005, “Individual Specific Value Of Life And Injury Risk: The Random Co-efficient Approach,” Conference Proceedings, „International Conference on Environment and Development: Developing Countries Perspectives”, Jawaharlal Nehru Uuniveristy, New Delhi, April 7-8, Shanmugam, K. R. 2006, "Rate of Time Preference and the Quantity Adjusted Value of Life in India ", Environment and Development Economics 11, 569-83. Shanmugam, K.R. 2011, “Discount Rate for Health Benefits and the Value of Life in India”, Economics Research International, Vol. 2011, Article ID191425 Siebert,W.S. and X.Wei. (1998), “Wage Compensation for Job Risks: The Case of Hong Kong,” Asian Economic Journal 12(2), 171–181. Smith, Adam. 1776, “The Wealth of Nations”, Reprint Ed., New York: Modern Library. Starr, C. 1969. “Social Benefit Versus Technological Risks”, Science 165: 1232-38. Thaler, Richard and S. Rosen. 1976, "The Value of Saving a Life: Evidence from the Market," in Nestor E. Terlecky. (eds.), Household Production and Consumption, NBER, 265-98. Viscusi, W.Kip. 1978, Wealth Effects and Earnings Premiums for Job Hazards”, Review of Economics and Statistics 60: 408-18. Viscusi, W Kip. 1979, "Employment Hazards: An Investigation of Market Performance", Cambridge: Harvard University Press.
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Viscusi, W.Kip. 1981, “Occupational Safety and Health Regulation: Its Impact on Policy Alternatives”, in Research in Public Policy Analysis and Management (ed. J.Crecine), JAI Press: 281-99. Viscusi, W Kip. 1993, "The Value of Risks to Life and Health," Journal of Economic Literature 31 (4), 1912-46. Viscusi, W Kip. 2000, “Misuses and Proper Uses of Hedonic Value of Life in Legal Context”, Journal of Forensic Economics 13(2): 111-25. Viscusi, W Kip 2003, “Racial Differences in Labor Market Values of a Statistical Life”, Journal of Risk and Uncertainty 27 (3): 239-56. Viscusi, W Kip. 2004, “The Value of Life: Estimates with risks by Occupation and Industry”, Economic Inquiry 42(1): 29-48. Viscusi, W. Kip. 2008a, “How to Value Life”, Journal of Economic Finance 32:311-23. Viscusi, W.Kip. 2008b, “Value of Life”, in The New Palgrave Dictionary of Economics (ed. Steven N. Durlauf and Lawrence E. Blume), Palgrave Macmillan. Viscusi, W Kip. 2010, “The Heterogeneity of the Value of Life: Introduction and Overview”, Journal of Risk and Uncertainty 40(1):1-13. Viscusi, W Kip and Joshep E. Aldy. 2003, "The Value of a Statistical Life: A Critical Review of Market Estimates Throughout the World", The Journal of Risk and Uncertainty 27: 5-76. Viscusi, W.Kip and Michael J.Moore 1987. “Workers‟ Compensation: Wage Effects, Benefit Inadequacies, and the Value of Health Losses”, The Review of Economics and Statistics 69: 249-61. Viscusi, W Kip and Michael J. Moore. 1989, "Rate of Time Preference and Valuations of the Duration of Life", The Journal of Public Economics 38, 297-317.
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