The value of life (4)

 How Much Is a Human Life Worth? A Systematic Review

The distinction between a statistical life and a human life is crucial. Generally, economic research and policy evaluation aims at eliciting the VSL. A common misconception is that the VSL expresses the value for which an individual would trade their life. It does not. The VSL identifies how people value a smallreduction in mortality risk. For instance, if each individual is willing to pay $1 to reduce the risk of dying by 1 in 1000 000, then a population of 1 million individuals would be willing to pay $1 million to save 1 statistical life – the VSL is $1 million. Even though valuation tasks in surveys/experiments are generally framed as a change in the participant’s own mortality risk, the objective is to elicit the VSL because it is unlikely that the participant’s life will be saved owing to the intervention considered. 

Closely related to the concept of a VSL, the value of a statistical life-year (VSLY) represents the value of one additional year of life. One of the benefits of using VSLY estimates instead of VSL estimates is that the age of individuals benefiting from an intervention is taken into account when performing an  economic evaluation. As such, a higher value would be placed on the life of a child than the life of an elderly person owing to the difference in remaining life expectancy.

Unfortunately, VSLY are currently not available, you'll find VSL in this table:

 

Table 3. Median of the midpoint of reported value of a statistical life (VSL) estimates in included studies.

Sector	Overall (no. studies)	Developed countries (∗no. studies)	Developing countries (∗no. studies)	Stated-preference studies (∗no. studies)	Revealed-preference studies (∗no. studies)	Human capital approach (∗no. studies)
Environment	$1 062 630 (6)	$5 146 850 (2)	$680 489 (4)	$1 381 201 (5)	NA (0)	$744 058 (1)
Health	$6 770 534 (33)	$8 989 328 (21)	$580 663 (12)	$6 770 534 (33)	NA (0)	NA (0)
Labor market	$8 740 231 (35)	$11 784 289 (22)	$1 430 105 (13)	NA (0)	$8 740 231 (35)	NA (0)
Safety	$3 010 740 (9)	$7 075 108 (5)	$409 110 (4)	$3 010 740 (7)	$2 942 773 (2)	NA (0)
Transportation safety	$5 335 248 (41)	$7 075 108 (28)	$403 798 (13)	$5 335 248 (37)	$5 383 706 (4)	NA (0)
All sectors	$5 716 830 (116)	$8 342 027 (73)	$858 599 (42)	$5 185 402 (74)	$7 940 006 (41)	$744 058 (1)

NA indicates not available.

∗

No. studies indicates the number of studies on which the calculations for the median of the midpoint estimates are based. The number of studies considering all sectors is not necessarily equal to the sum of studies across the single sectors owing to some studies reporting VSL estimates for multiple sectors.

Covid and the Value of Statistical Life

 COVID-19 and Uncertainties in the Value Per Statistical Life

Do the Benefits of COVID‐19 Policies Exceed the Costs? Exploring Uncertainties in the Age–VSL Relationship

For an individual, VSL can be derived by dividing WTP by the risk reduction. A population-average VSL of $10 million indicates that the typical individual is willing to pay $1,000 to decrease the chance of dying in a given year by 1 in 10,000. Individual WTP also can be summed across individuals expected to accrue the risk reduction. If 10,000 people will experience a 1 in 10,000 risk reduction and are each willing to pay $1,000 for the risk change, the total value is $10 million (10,000 times $1,000), and one less person would be expected to die that year as calculated by 10,000 times 1/10,000.

But

Individual WTP, then, is the fundamental measure—the $1,000 in this case. The conversion to a $10 million VSL is simply for convenience. 

 In a recent study with Ryan Sullivan and Jason F. Shogren, I compare the effects of three approaches often used to adjust for age: an invariant population-average VSL; a constant value per statistical life-year (VSLY); and a VSL that follows an inverse-U pattern, peaking in middle age. We find that when applied to the U.S. age distribution of COVID-19 deaths, these approaches result in average VSL estimates of $10.6 million, $4.5 million, and $8.5 million. The differences in these values is substantial enough to alter the conclusions of frequently cited analyses of social distancing.

 Table II. VSL by Age Group (in 2019 millions of dollars)

Age Group	Invariant VSL	Constant VSLY	Inverse‐U Relationship
Under 1 year	$10.63	$13.88	$5.38
1–4 years	$10.63	$13.74	$5.38
5–14 years	$10.63	$13.37	$5.38
15–24 years	$10.63	$12.64	$5.38
25–34 years	$10.63	$11.76	$8.50
35–44 years	$10.63	$10.63	$10.63
45–54 years	$10.63	$9.19	$10.72
55–64 years	$10.63	$7.54	$8.15
65–74 years	$10.63	$5.68	$8.15
75–84 years	$10.63	$3.72	$8.15
85 years and over	$10.63	$2.03	$8.15

 Table III. COVID‐19 Age‐Weighted Value (in 2019 millions of dollars)

	Invariant VSL	Constant VSLY	Inverse‐U Relationship
Total value, all COVID‐19 deaths	$937.6 billion	$394.8 billion	$773.4 billion
Average VSL, weighted by COVID‐19 deaths by age	$10.63 million	$4.47 million	$8.31 million

Table IV. Effect of Alternative Approaches on Analytic Results

		————————————————‐Benefits————————————‐————
		Lives	Original	Invariant	Constant	Inverse‐U
	Costs	Saved	Approach	VSL	VSLY	Relationship
Thunström et al. (2020)	$7.2 trillion	1.24 million	$12.4 trillion	$13.16 trillion	$5.54 trillion	$10.30 trillion
Greenstone and Nigam (2020)	N/A	1.76 million	$7.94 trillion	$18.72 trillion	$7.88 trillion	$14.64 trillion
Acemoglu et al. (2020)	$2.15 trillion	8.7 million	N/A	$92.44 trillion	$38.93 trillion	$72.31 trillion

Does this make sense? It seems quite high. If we value identified life more than a statistical life, can you imagine the final figure?

Whether the social distancing policy considered by Thunström et al. (2020) yields net benefits varies depending on the valuation approach. The authors use an invariant VSL but apply a somewhat lower value than we use in our analysis ($10 million rather than $10.63 million). However, both our invariant VSL and inverse‐U approaches lead to positive net benefits. Under our invariant approach, the benefits increase by almost $800 billion due to differences between the VSL estimates. Benefits decrease when using the inverse‐U approach, but not by a large enough amount to drop below estimated costs. Under the constant VSLY approach, benefits decrease by a substantial amount and the policy no longer appears cost‐beneficial.

While Greenstone and Nigam (2020) do not include a cost estimate in their calculations, the effects of our three approaches on their featured benefit estimates are significant. The benefit estimates more than double when applying the invariant VSL approach rather than their age‐adjusted approach. Interestingly, their estimates are very similar ($7.94 vs. $7.88 trillion) to the results using our constant VSLY method, while applying our inverse‐U estimates almost doubles the value in comparison to their inverse‐U approach. This result reflects the relative steepness of their curve at older ages as well as our assumption that values level off at older ages under the inverse‐U approach. As noted earlier, the additional sensitivity analyses reported by the authors also show siginificant variation in the results.

Acemoglu et al. (2020) have by far the largest estimates of lives saved across the three social distancing studies, which naturally increases the benefit values. Under all three approaches, we find that benefits exceed costs by an order of magnitude. However, Acemoglu et al. (2020) find that approaches other than the scenario reflected in Table IV are more cost‐effective, particularly if they target higher risk, older age groups.

Anyway, let's search a little bit more on that. Let's take the press. I don't think that this helps to take policy decisions in the current pandemic. It's just recreational research.

PS. The price of freedom is 103€ per day in my country (cost of non being free by mistake). Explained here.

Hockney

Statistical vs. identifiable lives

Do We Really Value Identified Lives More Highly Than Statistical Lives?

The recent Ebola evacuated case exemplifies the concept created by Shelling a long time ago, the difference of how a society allocates resources according to 2 different rules:

In 1968, in a paper about valuing ways to reduce the risk of death, Thomas Schelling1 distinguished between “identified lives” and “statistical lives.” Identified lives are the miners trapped in a mine or the child with a terminal disease—specific people who need help now. Statistical lives are those people, unidentifiable before the fact and often after as well, who will be saved by a new safety regulation, public health program, or environmental standard. Schelling observed that people seem to be willing to pay more to save an identified life: “Let a six-year-old girl with brown hair need thousands of dollars for an operation that will prolong her life until Christmas, and the post office will be swamped with nickels and dimes to save her. But let it be reported that without a sales tax the hospital facilities of Massachusetts will deteriorate and cause a barely perceptible increase in preventable deaths—not many will drop a tear or reach for their checkbooks.

Really such a case goes beyond Shelling insight because of uncertainty and unavailability of effective treatment. Bioethics field has argued over what they called "rule of rescue", a different perspective of the same issue. In this respect, NICE statement helps to understand both views:

When there are limited resources for healthcare, applying the ‘rule of rescue’ may mean that other people will not be able to have the care or treatment they need. NICE recognises that when it is making its decisions it should consider the needs of present and future patients of the NHS who are anonymous and who do not necessarily have people to argue their case on their behalf. NICE considers that the principles provided in this document are appropriate to resolve the tension between the needs of an individual patient and the needs of present and future users of the NHS. The Institute has not therefore adopted an additional ‘rule of rescue.

The article by Louise B. Rusell reflects precisely the theoretical and practical controversy and ends with this paragraph:

Adjustments and controversies aside, the evidence provided by VSL estimates suggests that people’s willingness to pay for statistical lives may be consistent with their willingness to pay for identified lives. The apparent existence of 2 different decision rules may have been no more than an artifact of the economic method for valuing statistical lives in use at the time the distinction was proposed. Now that economists’ methods more fully reflect “the interests, preferences and attitudes to risk of those who are likely to be affected by the decisions,” their estimates of the value of a statistical life support the idea that there just may be a single rule: Identified and unidentified lives may be equally valuable. This is good news for decision makers who use cost-benefit and cost-effectiveness analysis to inform decisions.

The theoretical suggestion sounds good, nowadays the political decision making reality goes in the opposite way, at least close.

PS. A must read post on GCS blog about the same topic.

PS. Ebolanomics, the economics of ebola at the New Yorker. Nothing new, prizes instead of patents to promote R&D, a good idea with difficult implementation.

PS. How much would you pay for a quality adjusted life year?

Walt  Khun.  From Tita Cervera  St. Feliu exhibition

Health spending in late life

Predictive modeling of U.S. health care spending in late life

In US, it is said that a quarter of public expenditure for the elderly (Medicare) is spent in the last 12 months of life. Really what happens is that the last year is only close to 10% of the whole lifetime health spending. Anyway, a new article in Science highlights commmon misunderstandings on such figure and disentangles the fundamentals.

These common interpretations of end-of-life spending flirt with a statistical fallacy: Those who endup dying are not the same as those who were sure to die. Ex post, spending could appear concentrated on the dead, simply because we spend more on sicker individuals who have higher mortality—even if we never spent money on those certain to die within the year. Empirically, this suggests using predicted mortality, rather than ex post mortality, to assess end of-life spending.

Less than 5% of spending is accounted for by individuals with predicted mortality above 50%. The simple fact that we spend more on the sick—both on those who recover and those who die—accounts for 30 to 50% of the concentration of spending on the dead. 

Crucial conclusion:

In sum, although spending on the ex post dead is very high, we find there are only a few individuals for whom, ex ante, death is near certain. Moreover, a substantial component of the concentration of spending at the end of life is mechanically driven by the fact that those who end up dying are sicker, and spending, naturally, is higher for sicker individuals. Of course, we do not— and cannot—rule out individual cases where treatment is performed on an individal for whom death is near certain. But our findings indicate that such individuals are not a meaningful share of decedents. These findings suggest that a focus on end-of life spending is not, by itself, a useful way to identify wasteful spending. Instead, researchers must focus on quality of care for very sick patients.

Good article.

PS Eight years ago I made this presentation on estimates of costs of late life. The summary in this post (in catalan)

Club des Belugas - Never think twice

Pandemic economic reasoning

 ECONOMICS IN ONE VIRUS. AN INTRODUCTION TO ECONOMIC REASONING THROUGH COVID-19

The outline of the book:

1. WHAT DOES IT MEAN TO BE ECONOMICALLY “WORSE OFF” DURING A PANDEMIC?

An introduction to economic welfare

2. SHOULD I BE FREE TO RISK INFECTING YOUR GRANDMA WITH A DEADLY VIRUS?

An introduction to externalities

3. DID WE CLOSE DOWN THE ECONOMY?

An introduction to public and private action

4. HOW MUCH WOULD YOU SPEND TO SAVE MY LIFE?

An introduction to the value of a statistical life

5. WHEN IS A LOCKDOWN CURE WORSE THAN THE DISEASE?

An introduction to cost-benefit analysis

6. WHY WAS I BANNED FROM GOING FISHING?

An introduction to thinking on the margin

7. WHAT GOOD IS A PANDEMIC PLAN WITH SO MANY UNKNOWNS?

An introduction to uncertainty and the knowledge problem

8. WHY DID PROTESTS AND MARCHES NOT LEAD TO OBVIOUS SPIKES IN COVID-19 CASES?

An introduction to endogeneity

9. WHY COULDN’T I GET A COVID-19 TEST BACK IN FEBRUARY AND MARCH 2020?

An introduction to regulatory tradeoffs

10. WHY WAS THERE NO HAND SANITIZER IN MY PHARMACY FOR MONTHS?

An introduction to the price mechanism

11. DOES THE PANDEMIC SHOW THAT WE NEED MORE U.S.-BASED MANUFACTURING?

An introduction to trade and specialization

12. WHY IS THAT GUY IN THE MASK GETTING SO CLOSE?

An introduction to moral hazard

13. WHY DID AIRLINES GET A SPECIAL BAILOUT BUT NOT MY INDUSTRY?

An introduction to public choice economics

14. WHY DIDN’T MY WORKERS WANT TO BE REHIRED?

An introduction to incentives

15. WHY WEREN’T WE WELL PREPARED FOR THE PANDEMIC?

An introduction to political incentives

16. CAN WE REALLY JUST TURN AN ECONOMY OFF AND BACK ON AGAIN?

An introduction to the nature of an economy

CONCLUSION: WHAT IS ECONOMICS GOOD FOR?

And a message on cost-benefit:

Cost-benefit analysis is a useful economic technique for considering whether a project improves societal welfare and to compare the societal net benefits of different projects. To do cost-benefit analysis well, we must account for all the direct and indirect impacts of the proposed policy on societal welfare, account for externalities, and ensure that we compare like-with-like in both timeframe and measurement. When it comes to COVID-19, cost-benefit analysis can, in theory, be used to examine the efficacy of lockdowns. However, there are huge uncertainties that make it hard to weigh up the precise costs and benefits of those policies. Even if the societal benefits do appear to exceed the costs on reasonable assumptions, that doesn’t mean the exact contours of the lockdown are “optimal policy.” In an ideal world, we’d find the policy mix that minimizes the overall societal costs of the pandemic.

This ideal world doesn't exist. 

Economic evaluation of vaccination

 Evaluating Vaccination Programs That Prevent Diseases With Potentially Catastrophic Health Outcomes: How Can We Capture the Value of Risk Reduction?

Why QALYs doesn't fit for CEA of vaccination?

In the last 5 years, guidelines have been developed for performing cost-effectiveness analyses (CEAs) for the economic evaluation of vaccination programs against infectious diseases. However, these cost-effectiveness guidelines do not provide specific guidance for including the value of reducing the risk of rare but potentially catastrophic health outcomes, such as mortality or long-term sequelae. Alternative economic evaluation methods, including extended CEA, the impact inventory, cost-benefit analyses, willingness to pay or the value of a statistical life, to capture the value of this risk reduction could provide more complete estimates of the value of vaccination programs for diseases with potentially catastrophic health and nonhealth outcomes. In this commentary, using invasive meningococcal disease as an example, we describe these alternative approaches along with examples to illustrate how the benefits of vaccination in reducing risk of catastrophic health outcomes can be valued. These benefits are not usually captured in CEAs that only include population benefits estimated as the quality adjusted life-years gained and reduced costs from avoided cases.

 

In Memoriam of Thomas Schelling

Thomas Schelling: Game Theory, Cold War, Coordination, Leadership, Tipping, Focal point...

Eleven years ago, Thomas Schelling was awarded with the Nobel Prize, 4 days ago he died. It is not often that one man has such a profound impact on the world and the field of public policy. In this blog I have devoted some posts to him: Statistical life vs. identifiable life, Els pirates dels medicaments s'escapoleixen, Validesa i utilitat de les proves genòmiques.  Basically, all of them were related to his main contribution: The Strategy of conflict, a must read book for all people interested in negotiation. Today, the best thing you can do is to read Josep M. Colomer and his post on Schelling, it fits perfectly with his contribution and message, excellent post.

 Cubism and war. Picasso Museum exhibition in Barcelona

The welfare state as a social insurance mechanism

 Probable Justice. Risk, Insurance, and the Welfare State

This book is a review of the role of social insurance, from mutual insurance to the development of current welfare policies. Too often we forget that we have our public coverage of risk as the efficient solution for an intractable issue at individual level.

Key take-aways from last chapter:

I have advanced three principal claims about probability theory and its relationship to welfare thinking. The first is that mathematical probability is frequently, if not inherently, normative in its character. We saw that the very project of quantifying probabilities grew out of a moral and legal question, namely the need to apportion fair shares in an interrupted game of chance. Each subsequent account of probability has in turn both reflected and furthered the practical aims of its exponents. This should not be  surprising, given that the discipline is at its core an attempt to guide good judgment and quantify equality, both of which are normative efforts, closely linked to views about the ends of human action and justice broadly understood.

The second claim, which follows from the first, is that theorists of mathematical probability have long tried to reconcile individual choice with some account of the common good. Not long after the  founding of the discipline, probabilists began to recognize a potential disconnect between personal prudence, or common sense, and contractual fairness as defined by their calculations. Many subsequent contributions to the theory attempted to resolve this problem in its various forms. Each account had a different character and resulted in different proposals. Yet they shared the promise of harmonizing individual judgments with aggregate regularities, which respectively correspond to the two sides of probability itself.

Finally, I have argued that the answers to this problem that emerged in connection with probability theory, from roughly the end of the eighteenth century through the twentieth, played a crucial role in the development of the modern welfare state. Statistical insurance was the first practice in which philosophers of probability sought, and in their view found, the means to reconcile individual benefit with a common good. The application of insurance principles on a social scale therefore promised to extend such harmony well beyond isolated associations to the polity as a whole. Insurance would refl ect the free choices of individuals while simultaneously securing social order. It would give each citizen her due while promoting the aggregate benefit. And it would distribute resources on the basis of both personal responsibility and equal vulnerability or need, accommodating the two principles without clearly favoring either one.

And a reflection, 

Any book about social insurance must address, at least briefly, the most pressing political controversies surrounding the welfare state today: namely, the problem of finance and the question of personal responsibility. If at one point the rubric of insurance invoked an image of fi scal restraint, promising to limit what the state distributes to the amount that it collects in contributions, the welfare state has come to be identifi ed among critics with out- of- control spending and government debt. And if mutual insurance was originally touted as a reflection of prudence and a means to propertied independence, it is now commonly associated with what economists refer to as moral hazard, meaning the  encouragement of risky and expensive behaviors, as well as dependence on the state. It is true that, in most advanced welfare states, social expenditures increased over the course of the twentieth century, not only in absolute terms but also as a percentage of gross domestic product. Some scholars have explained this phenomenon as a product of Wagner’s Law, which predicts that the share of government spending relative to GDP will increase with rising incomes.  As citizens grow wealthier and live longer, this argument goes, they will increasingly seek out the kind of quality- of- life improvements provided by the risk- pooling and consumption- smoothing functions of the welfare state, including healthcare,  pensions, and education.