Consistent estimation of the value of statistical life

Conventional estimators of the value of statistical life are biased. People differ in risk from each of many health threats, ability to reduce these risks, willingness to pay to reduce risk, and other utility parameters—creating a problem of multi-dimensional heterogeneity existing single-equation methods cannot handle. Herein we propose a general method of moments (GMM) approach that uses functional relationships between underlying parameters and observed data to estimate a person's willingness to pay for mortality risk reduction. This approach yields a consistent estimate of the value of statistical life. We use simulations to show that the GMM estimate of the value of statistical life performs well even when combining data from different sources that are sampled at different, low frequencies.     

Using job changes to evaluate the bias of value of a statistical life estimates

This paper presents a new approach to obtaining unbiased estimates of the value of a statistical life (VSL) with labor market data. Investigating job changes, we combine the advantages of recent panel studies, allowing us to control for unobserved heterogeneity of workers, and conventional cross-sectional estimations, which are less affected by measurement error. We find a VSL of 6.1 million euros from pooled cross-sectional estimation, 1.5 million euros from the first-differences panel model and 2.0 million euros from the job-changer specification. Thus, ignoring individual heterogeneity causes overestimates of the VSL, whereas the attenuation bias in panel data models leads to underestimates of the VSL. Our results are less biased than former results and can be used to perform cost–benefit analyses of public projects aimed at reducing fatality risks, e.g., in the domains of environmental, health, or traffic policy.     

Exploring heterogeneity in the value of a statistical life: Cause of death v. risk perceptions

Most current environmental policy analyses use Value of a Statistical Life (VSL) figures inferred from workplace safety and traffic accident contexts to compute the benefits of environmental programs that avoid premature deaths. There is considerable debate about the appropriateness of this practice, in part because the effect of cause of death may be partly confounded with latency, initial risks, and competing risks. Preference for reducing risks can be also affected by individual-assessed risk attributes that are rarely controlled in valuation studies. This paper explores reasons for differences in preferences for mortality risk reductions (if any), and establishes the magnitude of the effects of such risk attributes as compared to other sources of VSL heterogeneity. In our conjoint choice experiments, cause of death, the size of the risk reduction, and latency, the “price” of the risk reduction and the mode of delivery of the risk reduction are explicit attributes of the alternatives to be examined by the respondent. Our statistical models also control for actual and perceived exposure to risks, initial risks, risk attributes such as dread, and sensitivity to and controllability of specific risks. We find that there is significant heterogeneity in the valuation of mortality risks and thus in the VSL. The VSL increases with dread, exposure to risk, and the respondents' assessments of the baseline risks. It is higher when the risk reduction is delivered by a public program, and increases with the effectiveness rating assigned by the respondent to the mode of the risk reduction. Even when we control explicitly for all of these factors, the cause of death per se accounts for a large portion of the VSL. All else the same, the fact that the cause of the death is “cancer” results in a VSL that is about one million euro above the amount predicted by dread, exposure and other risk perception variables. The VSL in the road safety context is about one million euro less than what is predicted by dread, exposure, or beliefs compared to VSL for the respiratory risk context. The effect of cause of death is thus as large as the effect of other sources of VSL heterogeneity. Our respondents do not seem to discount future risks.     

The age-dependent value of time: a life cycle analysis

A life cycle framework is developed to examine how the value of time (VOT) changes as one ages. We consider two risk-sharing schemes, the Tonti scheme under which wealth is actuarially insured, and the Robinson Crusoe scheme under which insurance institution is entirely absent. For the first time in the literature, we characterize the condition, in terms of key parameters for valuating VOT, under which VOT may increase, decline, or even display more complicated profiles, as one ages. Our analysis reveals the crucial role played by the relative magnitude of the market interest rate to other parameters (including the parameter of time preference, the age-specific mortality and the wage growth rate) in determining the age profile of VOT, and the difference in VOT that is caused by the insurance scheme.      

Recognizing progeny in the value of life

This note generalizes the value of life to incorporate the preferences for descendants of a dynastically altruistic decision-maker. It derives the value of progeny and shows how it depends on the Benthamite vs. Millian nature of dynastic altruism.     

The statistical significance of a change in concentration

This note examines statistical tests for the significance of a change in the logvariance measure of concentration between two points in time. The note points out flaws in two existing tests, proposes a correct test, and provides an empirical example.     

The discount rate and the value of remaining years of life

We back out an estimate of a personal discount rate of between 3 and 4 percent for a person with a life expectancy of 74 years who dies at age 30 or 40 and has a value of statistical life of $6.3 million. We employ the Makeham “model” of life expectancy and Murphy-Topel “values of life years” in our calculations.     

A note on ‘trying to value a life’

Broome's alleged paradox that application of the usual compensation test to the valuation of life would produce an infinite monetary value is shown to be false because it is based on illegitimate generalisation from a special case in which no effective compensation is possible. In the general case, relevant to public sector project appraisal, such compensation is possible, and finite values are to be expected, judging by people's ordinary behaviour.     

The Political Economics of Tax Reform in Chile

This paper explores the political economy at the time of the 2012 tax reform, which paved the way for a radical tax increase in 2014. Both were an explicit response to demands to improve public education. As opposed to the 2014 reform, the 2012 tax adjustment was an unplanned decision made in the wake of a pact of long-term fiscal stability during the government's last year in office and was partially negotiated with student associations and pressure groups. We hypothesise that the existing institutions were not strong enough to meet emerging social demands through formal channels. We will show evidence for the hypothesis that the government's incorporation of students’ demands in its agenda was mainly a response to the role of the media, the fact that it is not difficult for students to organise themselves and express their demands, the support of students’ families and the ruling government's fear of missing out on a second term in office.     

Shadow prices,consistency and the value of life

This paper examines the consequences of inconsistent shadow pricing. The principal example of such inconsistency is the value of life/safety. Second-best shadow pricing policy is shown to depend upon how public sector budgets are allocated and the principle that public sector decision-makers should agree to a consistent shadow price is shown to require information unlikely to be available. A weaker consistency principle requiring minimal information is then developed.     

The statistical measurement of discrimination

This note argues that measures of discrimination should compare the whole distribution of the logarithm of earnings when there is discrimination with the whole distribution when there is no discrimination. It derives a form for the density of the distribution when there is no discrimination and discusses how this might be estimated.     

The value of information in a simple duopoly model

This paper is concerned with the evaluation of information in a duopoly model in which the cost functions are subject to uncertainty. It explores how changes in information about the costs available to either firm affects the welfare of both firms along with the welfare of consumers. By comparing the ten possible types of information structures, it is shown that information may be detrimental, that improved information for one firm may or may not benefit the other firm and/or the consumer, and that it may be more desirable for a firm to gather information about the rival's cost rather than its own. All of these “irregular” results depend on the values of the variances of the costs and their correlation coefficient.     

The value of public information in a Cournot duopoly

We derive alternative sufficient conditions for the value of public information to be either positive or negative in a Cournot duopoly where firms technology exhibits constant returns to scale.