[author]蒂姆·哈福德

[content]

托马斯.谢林与 “统计学意义上的生命价值”

 

 

*蒂姆·哈福德（Tim Harford）

英国《金融时报》的经济学专栏作家

 

 

编者按

 

2020年4月3日“金融时报”发表从“统计学意义上的生命价值”看当前防控新冠疫情的如下文章。该文作者Tim Harford追溯了2005年诺贝尔经济学奖得主托马斯.谢林1968年首次提出这个概念的背景。1948年正式成立的兰德公司从美国国防部接受的第一个研究项目是用运筹学设计对苏联的核轰炸方案。但兰德设计出的方案被国防部拒绝了。原因是国防部很多官员是飞行员出身，不能接受兰德公司方案中把飞行员的“生命价值”设定为零。从1948年到1968年的20年间，兰德公司的研究人员对飞行员的“生命价值”多次重新估算，例如从飞行员培训成本定为27万美元，但从飞行员紧急跳伞的弹出系统设计成本来倒推，飞行员的“生命价值”在100万和900万美元之间 （ Tim Harford此文又基于“统计学意义上生命价值概念的冷战起源”一文，参见：

https://www.aeaweb.org/articles?id=10.1257/jep.28.4.213）

 

托马斯.谢林1968年“你救的生命可能是你自己的”(“The Life You Save May Be Your Own”)一文（见谢林文集“选择与后果”）的革命性意义在于指出兰德公司“生命价值”概念的错误。谢林认为，研究人员和政策制定者没有能力和权利判定其他人的“生命价值”，而应该在“社会成本-收益”分析中以当事人（如飞行员）本身的风险偏好为基础。1963年，谢林指导一位前飞行员Jack Carlson写作博士论文。

Carlson发现（通过访谈和从实际行为倒推），飞行员在和平时期愿意多承担0.00232%的死亡风险以换取增加2280美元的年收入。Carlson没有进一步用2280除以0.00232%得出491万美元的飞行员自身的“生命价值”估计。但5年后的1968年，谢林深化了Carlson这一观察，提出了基于当事人自身的“统计学意义上的生命价值”概念。目前，很多国家的政府在公共政策制定中必须进行“社会成本-收益分析”，都要运用谢林的“统计学意义上的生命价值”概念。例如，美国环境署把“统计学意义上的生命价值”定为1000万美元（https://www.epa.gov/environmental-economics/mortality-risk-valuation#whatvalue）。

 

Tim Harford此文据此估算，花费10万美元去防止新冠肺炎感染一个人，从“社会成本-收益分析”的角度是值得的。“实验主义治理”公号第195期曾介绍“谢林图示”对于研究社会合作机制的重要作用，希望本期公号有助于读者进一步了解谢林思想在当前全球抗疫斗争中的意义。如果读者想对“社会成本-收益分析”中的“统计学意义上的生命价值”进行深入研究，可参考哈佛大学法学院桑斯坦教授2018年出版的 “成本收益革命“一书第三章。

 

 

 

 

 

How do we value a statistical life? 

It is clear that we should be willing to pay huge costs to save lives from Covid-19

 

TIM HARFORD

https://www.ft.com/content/e00120a2-74cd-11ea-ad98-044200cb277f

 

The coronavirus lockdown is saving lives but destroying livelihoods. Is it worth it? I’ve been accused of ignoring its costs. For an economist, this is fighting talk. Love us or hate us, thinking about uncomfortable trade-offs is what we economists do. 

Three points should be obvious. First, we need an exit strategy from the lockdowns — a better strategy than President Donald Trump’s, “One day it’s like a miracle, it will disappear.” Expanding emergency capacity, discovering better treatments, testing for infection and testing for antibodies could all be part of the solution, along with a vaccine in the longer term. 

 

Second, the economic costs of any lockdown need to be compared with the costs of alternative policies, rather than the unachievable benchmark of a world in which the virus had never existed. 

 

Third, the worth of a human life is not up for discussion. This week I lost a mentor of unlimited kindness. As I write these words I hear that a beloved family member is also reaching the end of her remarkable journey. Their lives, like the life of any individual, were priceless.  

 

Yet no matter how much we want to turn our gaze away from the question, it hangs there insistently: is this all worth it? 

 

We spend money to save lives all the time — by building fire stations, imposing safety regulations and subsidising medical research. There is always a point at which we decide we have spent enough. We don’t like to think about that, but better to think than to act thoughtlessly. So what are we willing to sacrifice, economically, to save a life? 

 

A 1950 study for the US Air Force ducked this question, recommending a suicidal military strategy that valued pilots’ lives at precisely zero. Other early attempts valued lives by the loss of earnings that an early death would cause — effectively making retired people worthless, and the death of a child costly only if the child could not be replaced by a new baby. 

 

The late Thomas Schelling, a Nobel Prize-winning economist, mocked these errors as he imagined the death of a family breadwinner like himself: “His family will miss him, and it will miss his earnings. We do not know which of the two in the end it will miss most, and if he died recently this is a disagreeable time to inquire.” 

 

There must be a better way to weigh the choices that must be weighed. But how? 

 

Schelling suggested focusing not on the value of life, but on the value of averting deaths — of reducing risks. A life may be priceless, but our actions tell us that a statistical life is not. 

The engineer Ronald Howard has proposed a convenient unit, the “micromort” — a one-in-a-million risk of death. Implicitly, we constantly weigh up small risks of death and decide if they are worth it. Despite inconsistencies and blind spots in our behaviour, we value reducing risks to our own lives very highly, but not infinitely so. 

 

We vote for governments that hold our lives in similarly high regard. For example, the US Environmental Protection Agency values a statistical life at $10m in today’s money, or $10 per micromort averted. I have seen lower numbers, and higher. 

 

I am giving most of my figures as conveniently round numbers — there is too much uncertainty about Covid-19 to be more precise. But if we presume that 1 per cent of infections are fatal, then it is a 10,000 micromort condition. Being infected is 100 times more dangerous than giving birth, or as perilous as travelling two and a half times around the world on a motorbike. For an elderly or vulnerable person, it is much more risky than that. At the EPA’s $10 per micromort, it would be worth spending $100,000 to prevent a single infection with Covid-19. 

 

You don’t need a complex epidemiological model to predict that if we take no serious steps to halt the spread of the virus, more than half the world is likely to contract it. That suggests 2m US deaths and 500,000 in Britain — assuming, again, a 1 per cent fatality rate.  

 

If an economic lockdown in the US saves most of these lives, and costs less than $20tn, then it would seem to be value for money. (By way of comparison, each 20 per cent loss of gross domestic product for a quarter represents a cost of about $1tn.) One could quibble with every step of this calculation. Perhaps some of those who die were so ill that they would have died of other causes within days. Perhaps Covid-19 is not quite so dangerous. Yet it is clear that with so many lives at stake, we should be willing to pay huge costs to protect them. 

 

We must remember something else: the risk of being wrong. We will inevitably make mistakes. The measures we take to contain coronavirus might do more damage to people’s livelihoods than necessary. Or we might allow the virus too much leeway, needlessly ending lives. In a spreading pandemic, the second mistake is much harder to repair than the first. 

 

Fighting this virus demands economic sacrifices: not without limit; and not without end. But if not now, then when?

转载自 实验主义治理 公众号