The Benefits of Reducing Gun Violence: Evidence from Contingent-Valuation Survey Data

This article presents an estimate of the benefits of reducing crime using the contingent-valuation (CV) method. We focus on gun violence, a crime of growing policy concern in America. Our data come from a national survey in which we ask respondents referendum-type questions that elicit their willingness-to-pay (WTP) to reduce gun violence by 30%. We estimate that the public's WTP to reduce gun assaults by 30% equals $24.5 billion, or around $1.2 million per injury. Our estimate implies a statistical value of life that is quite consistent with those derived from other methods.     

Living Healthy and Living Long: Valuing the Nonpecuniary Loss from Disability and Death

This analysis uses three valuation approaches—risk–risk tradeoff, paired risk–dollar comparison, and utility function estimation—to estimate the nonpecuniary cost associated with disability in late life. In addition, we obtain an estimate of the value of life using a paired risk–dollar comparison. The data were obtained from interviews with 548 persons using an iterative computerized questionnaire. Respondents reported a median value of life of $12 million. They were willing-to-pay .7–1.4 million to avoid disability in late life or approximately $47–$95 thousand for each year of disability over age 62. The results were robust to the valuation technique employed.     

The Value of a Statistical Life and the Coefficient of Relative Risk Aversion

Individuals’ risk preferences are estimated and employed in a variety of settings, notably including choices in financial, labor, and product markets. Recent work, especially in financial economics, provides estimates of individuals’ coefficients of relative risk aversion (R’s) in excess of one, and often significantly higher. However, it can be shown that high R’s imply equally high values for the income elasticity of the value of a statistical life. Yet estimates of this elasticity, derived from labor and product markets, are in the range of 0.5 to 0.6. Furthermore, it turns out that even an R below one is difficult to reconcile with these elasticity estimates. Thus, there appears to be an important (additional) anomaly involving individuals’ risk-taking behavior in different market settings.JEL Classification: D80, G11, G12, I10, J17     

The Simplest Dynamic General-Equilibrium Model of an Open Economy

This paper presents the simplest possible general-equilibrium model of an open economy in which producer and consumer decisions are both intra- and intertemporally consistent. Consumers maximize the present value of the utility of consumption; producers maximize the present value of profits. The model solves for the set of intertemporally consistent prices. The parsimonious structure of the model is achieved by dividing the economy into two producing sectors—exports and domestic goods—and two consumed goods—imports and domestic goods. As a result, there is only one endogenous price per period to be solved for (the price of the domestic good), although “structural” questions, such as the evolution of the real exchange rate, can be posed with the model. Furthermore, with this structural breakdown, the model can be calibrated with national accounts data only. In the paper, we show how to calibrate such a model (including specification of an adjustment-cost function, to avoid “bang-bang” behavior) and use the model to examine various questions where intertemporal issues are important, including terms-of-trade shocks and tariff reform.     

The Value of a Statistical Life: A Critical Review of Market Estimates Throughout the World

A substantial literature over the past thirty years has evaluated tradeoffs between money and fatality risks. These values in turn serve as estimates of the value of a statistical life. This article reviews more than 60 studies of mortality risk premiums from ten countries and approximately 40 studies that present estimates of injury risk premiums. This critical review examines a variety of econometric issues, the role of unionization in risk premiums, and the effects of age on the value of a statistical life. Our meta-analysis indicates an income elasticity of the value of a statistical life from about 0.5 to 0.6. The paper also presents a detailed discussion of policy applications of these value of a statistical life estimates and related issues, including risk-risk analysis.     

Individual and Household Values of Mortality Reductions with Intrahousehold Bargaining

I derive alternative measures of maximum willingness to pay (WTP) and value of statistical life (VSL) for selfish members of two-person households who bargain efficiently over consumption of individual and household goods. There is then no systematic bias in letting one member conduct the valuation on behalf of the household. Public-good VSL may exceed private-good VSL when each member attaches (selfish) preferences to survival of the spouse, and to any income from a surviving spouse in period 2. When period 2 is a retirement period and household members’ incomes are fixed, interview surveys tend to overvalue VSL due to ignored negative effects of own survival on private of public pension budgets.JEL Classification: I12, G22, J17     

Did We Overestimate the Value of Health?

Adam Smith's idea that wage differences reveal preferences for risk rests on strong theoretical foundations. This paper argues, however, that the dominant approach to identify compensating wage differentials—regressing individual wages on aggregate measures of risk—may lead to arbitrary estimates of these risk differentials. In a dataset with information on both, the incidence of illnesses or injuries across firms and industries, I calculate an implicit value of one injury or illness of about (1990) USD 18,800 pursuing the dominant approach. In contrast, regressing wages on the incidence of risk across firms produces a value of one injury or illness of about USD 11,300.     

The effect of residence in enclaves on civic concern: An initial exploration

Will those residing in urban enclaves—enclosed socially homogenous residential communities protected by private security—have a lower level of civic concern as compared to those who do not reside in such enclaves? Reich's (1991) work suggests that this is to be expected. To conduct an empirical test, two random samples were drawn from two areas of New York City, one a residential enclave—Battery Park City—the other a non-enclave—Chelsea. The analysis establishes that those who do not live in the enclave have a statistically significant higher level of civic concern. Sample respondent years of education, age, income, gender, and career (arts/business) differences were employed as control variables; after having introduced each control variable independently, the main research hypothesis was sustained.     

Helping a Victim or Helping the Victim: Altruism and Identifiability

Although it has been claimed that people care more about identifiable than statistical victims, demonstrating this identifiable victim effect has proven difficult because identification usually provides information about a victim, and people may respond to the information rather than to identification per se. We show that a very weak form of identifiability—determining the victim without providing any personalizing information—increases caring. In the first, laboratory study, subjects were more willing to compensate others who lost money when the losers had already been determined than when they were about to be. In the second, field study, people contributed more to a charity when their contributions would benefit a family that had already been selected from a list than when told that the family would be selected from the same list.     

Aspects of a new world development strategy II: Factors affecting the long-term prospects of developing nations

This paper explores some quantitative dimensions of the interdependence of rich and poor regions in the context of the United Nations World Model. It extends the original work on that model in three ways: (1) by updating some of the key parameters and exogenous variables in the light of recent data; (2) by developing a “control” solution to be used as a point of reference in policy simulations; and (3) by exploring the sensitivities of each of two groups of regions— developed and developing—to changes in one another's growth rates. Goals of closing the income gap between developed and developing regions and of increasing income levels in the latter are discussed.     

Discounting and the evaluation of lifesaving programs

The evaluation of lifesaving programs whose benefits extend into the future involves two discounting issues. The intragenerational discounting problem is how to express, in age-j dollars, reductions in an individual's conditional probability of dying at some future age k. Having discounted future lifesaving benefits to the beginning of each individual's life, one is faced with the problem of discounting these benefits to the present—the intergenerational discounting problem. We discuss both problems from the perspectives of cost-benefit and costeffectiveness analyses. These principles are then applied to lifesaving programs that involve a latency period.The authors are, respectively, Associate Professor of Economics, Univesity of Maryland and Senior Fellow, Resources for the Future; and Senior Fellow and Vice President, Resources for the Future. We thank the National Science Foundation for their support under grant DIR-8711083.     

On the evaluation of solution concepts

It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.     

On the Definition and Age-Dependency of the Value of a Statistical Life

The value of preventing a fatality or (saving) a statistical life is an important question in health economics as well as environmental economics. This paper adds new insights to several of the issues discussed in the literature. It is shown that the conventional way of measuring the value of a statistical life yields a biased estimate, in general. The major exception is the case where the estimate can be based on an infinitely short drop in the hazard rate. This is so in both life cycle models with and without actuarially fair annuities. Moreover, the claim that there are strong theoretical reasons for believing that the value of statistical life declines with age is shown to be wrong.     

Public Perceptions of Risk and Preference-Based Values of Safety

This article reports the results of two studies aimed at estimating preference-based values of safety in three contexts—namely rail, domestic fires and fires in public places—relative to the corresponding value for roads using matching (or equivalence) questions. In addition, both studies included a variety of questions intended to shed light on respondents' perceptions of risk and attitudes to safety in the various contexts. While the two studies were, to all intents and purposes, identical in the procedure that they employed, the essential difference between them was that the first study took place in late 1998, whereas the second study was carried out in early 2000 in the aftermath of a major rail accident at Ladbroke Grove near London's Paddington station which occurred in October 1999 and in which 29 passengers and 2 train drivers died. In addition, the second study sample was deliberately weighted to contain an above-average proportion of regular rail users. These studies demonstrated how certain factors which have been shown to affect people's perception of risk (see Slovic, P. (1992). In S. Krimsky and D. Golding (eds.), Social Theories of Risk, Westport, CT: Praeger, pp. 117–152) also affected our respondents' priorities over safety programs. The results also showed however, that the impact of these perceptions upon the trade-offs between preventing deaths in different hazard contexts was a good deal less pronounced than has been suggested by the value differentials that are currently implicit—and in some cases, explicit—in public policy making.     

Risk Perceptions and Value of a Statistical Life for Air Pollution and Traffic Accidents: Evidence from Bangkok,Thailand

This paper presents results of two contingent valuation surveys conducted in Bangkok measuring individuals’ willingness to pay (WTP) to reduce mortality risk arising from two risk contexts: air pollution traffic accidents Results from the risk perception survey disclose that respondents view the two risks differently. WTP to reduce air pollution risk is influenced by degrees of dread, severity, controllability and personal exposure, while WTP to reduce traffic accident risk is influenced by perceived immediate occurrence. Nevertheless, the value of a statistical life (VSL) for both air pollution and traffic accidents are comparable (US$0.74 to $1.32 million and US$0.87 to $1.48 million, respectively). This indicates that the risk perception factor alone has little impact on the VSL, a finding similar to previous studies using program choice indifferences.JEL Classification: I18, D61, J17, J28     

Health-health analysis: A new way to evaluate health and safety regulation

Regulations to promote health and safety that are exceptionally costly relative to the expected health benefits may actually worsen health and safety, since compliance reduces other spending, including private spending on health and safety. Past studies relating income and mortality give estimates of the income loss that induces one death — a value that we call willingness-to-spend (WTS)-to be around 9 to9 to 12 million. Such estimates help identify regulations that do not improve health and safety, and moreover, fail benefit-cost comparisons. WTS is a multiple of the willingness to pay to avert a statistical death. International data yield estimates of WTS and willingness-to-pay in different countries.The views of the authors do not necessarily reflect the views of the Office of Information and Regulatory Affairs or OMB. Thanks are due to Ivy Broder, Kenneth S. Chapman, Govind Hariharan, and W. Kip Viscusi for helpful comments. Some of this material is included in theRegulatory Program of the United States Government, April 1, 1992, March 31, 1993, of the Executive Office of the President.     

A test of generalized expected utility theory

In two experiments we test Machina's Hypothesis II (fanning-out). In each experiment we analyze patterns of responses to hypothetical lottery choice questions within a Marschak-Machina triangle. One set of questions involves lotteries on the border of the triangle, an the other set of questions involves lotteries in the interior of the triangle (off the border). Our results show that a large proportion of the observed patterns in the on-border treatment support Hypothesis II, with a considerable amount of fanning-out behavior observed. The patterns observed in the off-border treatment are significantly different from those in the on-border treatment. Hypothesis II performs well in the off-border treatment because expected utility theory itself, which satisfies the restrictions of Hypothesis II, performs well.This is an expanded version of a paper originally prepared for presentation at the Fifth International Conference on the Foundation and Applications of Utility, Risk, and Decision Theories, held June 9–13, 1990 at Duke University, Durham, NC. We acknowledge helpful comments made by participants at that conference, especially those of Mark Machina.     

Self Selection Bias in the Estimates of Compensating Differentials for Job Risks in India

This study contributes to the hedonic wage literature in developing countries by estimating the collective willingness to pay of a statistical life/injury, using an original data set from the Indian labor market. As self-selection by workers results in biased estimates of the wage premium for job risks, the study uses a modified selectivity bias correction technique. Empirical results indicate substantial heterogeneity in returns to risk. The estimated value of life without selectivity bias is Rs. 56 million (US $3 million), which is substantially larger than the value with selection bias. The estimates provided by the study can aid policy makers, international agencies and other researchers in evaluating health projects in India and other developing countries.     

Racial Differences in Labor Market Values of a Statistical Life

This article constructs measures of job fatality rates for black and white workers using information on job-related fatalities from 1992–1997. The fatality rates for black employees are somewhat greater than those for whites. Each of these groups receives significant compensating wage differentials for fatality risks, controlling for nonfatal risks and expected workers' compensation benefits. The implicit value of a statistical life is lower for black workers than for whites. These results in conjunction with evidence that blacks receive less annual compensation for fatality risks than do whites imply that black and white workers face different market offer curves that are flatter for blacks than for whites.     

Policy modelling of the trade-off between agricultural development and land degradation—the Sudan case

The agricultural policy model of the trade-off between agricultural growth and land degradation that we have developed, with Sudan as an application, shares common features with the computable general equilibrium (CGE) models. The model is used to address two questions. First, what are the future prospects of a green gross domestic product (GDP), are there reasons for alarm or not, and to what extent? Secondly, which among the four policies of price incentives, property rights, poverty reduction, and human capital are more effective than the others? We show that the prospects of natural resource-friendly agricultural development in Sudan—a rising green GDP—are not promising in the medium run, but that, indeed, there is a range of effective policies and choices that could reduce the trade-off between economic growth and land degradation.