# Should public policies save lives or add years of life?

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Should public spending to reduce mortality take age into account? For example, following an intense heat wave or a violent epidemic, should the death of children, adults or elderly people be avoided first?

In other words, for a given budget should we seek to save the greatest number of lives possible, without making any age distinction among them, or save the greatest number of years of life possible by favoring the population that benefits from a longer life expectancy because you are younger?

An article by François Lévêque, Professor of Economics, Mines Paris, and Emile Quinet, Professor Emeritus Ecole des Ponts-ParisTech and Associate Member of Paris School of Economics, École des Ponts ParisTech (ENPC) – Published on The Conversation

The question is hotly debated among economists. It takes the form of a choice of using the value of a uniform human life or the value of a year of human life, two notions that can be compared with public expenditure to assess their relevance and compare them. We recommend counting according to the years of life gained – therefore according to age – when hazards primarily affect the elderly. As in the case of heat waves or Covid-19. It should be remembered that in France 86% of deaths from the 2003 heat wave and 83% of deaths from the SARS-CoV-2 epidemic affected people aged 70 and over.

## What is the “statistical value of a life”?

Before arguing this choice, we must return to some basic notions and principles of economic calculation. In order to better allocate public expenditure to save people, applied economics needs figures. To decide which actions to take against road accidents or against smoking, it is necessary to compare their costs with the benefits in terms of human lives saved. And since the cost is expressed in euros, the benefits must also be expressed in euros.

We thus arrive at the consecrated notion of “statistical value of a life”. Please note, this is not the price of a life: since the end of slavery, there is no longer a market, and therefore no price for human lives. It is not more than a value of *there* life, let alone *there* value *there* life. This is a statistical value on two counts. First, it reflects the reduction in an individual risk of death resulting from a public policy. As such, it should not be confused with a value of human lives. Second, it concerns an unidentified individual.

Imagine a society of 100,000 individuals considering funding a public security project. Suppose that everyone is ready to pay 100 euros on average to reduce the probability of death from 3/100,000 to 1/100,000, or 2 fewer deaths for the whole of this society. We will deduce a “statistical value of a life” of 5 million euros (100,000×100/2). Or, in a much better but longer formulation, “the cost of avoiding an additional anonymous death” of 5 million euros.

This statistical approach is an instrument to help public decision-making aimed at reducing the risk of mortality and doing so as intelligently as possible. The State cannot devote its budget exclusively to saving human lives. It is important to estimate whether it is advisable to spend a little more to prevent cardiovascular diseases than to treat them, to fight against alcohol and heroin, or even to reduce road accidents and plane. The challenge is to save as many lives as possible with a given budget.

Of course, death cannot be avoided forever. Intuitively, the value of an individual to delay his death depends on the time gained – a year is better than a week – and on age – a year older at 40 is better than a year of more than 80 years old. Hence the second notion, that of “statistical value of a year of life”, to designate the loss of one year of life less.

## Three million euros on average for an additional life saved

One of the widely used methods for estimating these values consists of asking individuals themselves what they are willing to pay for a reduction in risk. The reported amounts are then aggregated and the averages calculated.

The most comprehensive inventory of studies on the value of a human life saved is that produced by the Organization for Economic Co-operation and Development (OECD) in 2012. It covers some 1,000 academic studies on the subject; it classifies them according to the type of risk taken into account (transport, health, environment), according to the type of surveys (questionnaire administered face to face, by telephone, by e-mail exchanges, etc.), according to the method (contingent analysis in which the interviewee is asked how much money he is willing to spend for a reduction of X in his risk of death over the next year; or the conjoint analysis where the interviewee is asked his choice between two situations which are proposed to him and which differ by the risk and by the sum of money which he must pay). This census resulted in a statistical average value of a life of 3,000,000 euros for the whole of the OECD.

Alongside these numerous estimates of the statistical value of a life, those relating to the year of life are rarer. Let us cite as an example a study, involving more than a thousand people questioned in 2010 in several European countries, which resulted in an amount of 40,000 euros for the value of one year of life. The question concerned their willingness to pay for a gain in life expectancy of 3 months or 6 months according to a more or less ambitious pollution reduction scenario.

Behind this type of results, it is necessary to imagine protocols as precise as they are complex (in particular to explain the difficult notions of risk and probability) and sets of questions tested with rigor and formulated with care. It should also be noted that the values obtained in the responses are dispersed among the individuals subjected to the same survey.

Higher for wealthier individuals, for example. Ditto for the average values obtained from one survey to another according to the protocols chosen and the questions asked. They are higher for a health program than for a road improvement project. To take account of theoretical progress and the proliferation of applied work, the values officially recommended or adopted by the administrations evolve over time.

In France, the statistical value of a life has thus gone from the first reference in 1970 to the most recent in 2013 from just under 300,000 euros today to just over three million today. today. One of the authors of this article moreover directed the reflections and work which led in 2013 to the choice of this amount as well as the amount of 160,000 euros for the statistical value of the year of life. The report that justifies these values specifies that it is useful to use the year of life lost to complete the analyzes and calculations when “the question of age arises”. However, it does not recommend using only this value in this case. It is now necessary to decide this neither yes nor no.

## Fair innings

Why do we propose to opt for a value taking into account the age?

Let us first examine the consequences of such a choice. As the elderly have fewer years to live ahead of them, the transition from accounting by value of a life lost to accounting by year of life lost leads to the selection of proportionally fewer projects to reduce the risk of mortality in their favor . For example, in the choice between a project which avoids deaths from heat waves and a project which avoids deaths from road accidents and therefore benefits a population that is more balanced in age, the first will be economically more advantageous, all things being equal elsewhere.

The choice of one value or another thus arises from a concern for intergenerational justice, either that of favoring the older generations or that of favoring the younger generations.

Privileging the latter and not the opposite is based on the idea that everyone would have a similar lifespan equal to the life expectancy of their age group. Anyone who died earlier would suffer an injustice that the community should prevent. This principle is defended by an English health economist, Alan Harold Williams. He was inspired by the reflections of a fellow philosopher. In reference to the national sport of England, it bears the name of argument of the *Fair innings*the latter term designating an innings of the game of cricket for the batsman’s team.

He posits that the avoidance of deaths of people who have passed or are approaching old age is not acceptable if it can only be obtained by costing lives to those who are far from it. Such a situation appears when the company has set itself a constrained budget for expenditure on health and civil security. More broadly, the argument of *Fair innings* agrees with the idea of a legitimate reduction of inequalities in lifespan between individuals.

Let us observe that this principle is not without pictorial references. For example through the popular formulation of “bonus years” to qualify those beyond life expectancy. Or even in the Bible specifying that “The days of our years amount to 70 years” and suggesting that those who live longer need not take pride in it because they have nothing to do with it.

## Inverted U curve

Therefore, what value of the cost of one less year of life avoided should be chosen?

A first way consists in determining it from the “statistical value of a life” by cutting it up. For a 40-year-old individual with a life expectancy of 78 years, the value of a slice of a year of life is equal to the « statistical value of a life » divided by 38 (ie, 78 – 40 ). But to take into account over time the trade-off between consuming today or tomorrow, it is necessary to update the number of years of life in the denominator. This is the approach followed in the report cited above which results in the amount of 160,000 euros by taking a discount rate of 3%.

This way of doing things is very convenient because we have a much greater number of works which directly determine the statistical value of “a life” rather than “a year of life”. One of its main weaknesses is that the result is very sensitive to the discount rate while it has not been observed. It is the result of a choice by experts and this choice therefore involves an element of arbitrariness.

A second method is still based on the « statistical value of a life » but considers that it is not independent of age. Many surveys and models suggest that this is indeed the case. They show that the value of a life as a function of age roughly takes the shape of an inverted U. It increases rapidly during the young years, stabilizes in adulthood and decreases more or less quickly during old age. The precise shape of the inverted U and therefore the value of a year of life according to age, which is therefore no longer constant unlike the first method, however differs greatly according to the studies.

A third way consists in identifying, through questions with individuals, how their statement on the value of additional years of life varies according to their age. However, there are extremely few works in France or elsewhere proceeding in this way.

Until such direct surveys develop or other research advances, we suggest employing one of the other two methods. But we recommend that the presentation of the results to evaluate such and such public expenditure be accompanied by a study of sensitivity to the discount rate and curves of reversed U chosen.

Let us conclude with two observations which are in line with current debates and reflections on the end of life. First, the weighting of lives saved by the number of years of life gained must naturally take into account the quality of life during these years gained. This is another well-stocked section of economic research that extends those mentioned here. It has developed in particular in the health sector. Second, our proposal needs to be discussed and debated beyond the subject matter experts and the administration. This is not a technocratic choice. Citizens must be involved and deliberate.

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