Welfare Estimation 201: Understanding Life-Valuation Variability

Intro

For decades, the field of cost-benefit analysis has been troubled by an inability to understand and/or communicate an important conceptual point. I know this because, until a few weeks ago, my brain was infected by a confusion. I notice that almost everything written about the field seems to be infected with a similar confusion. EAs have resisted the confusion better than most, and they actually do the right thing by morally weighting all lives (of a certain age) equally, but their discussions of cause prioritization are still infected by subtle confusions from the literature that make it harder to do cause prioritization outside of certain narrow bounds. In this post I show how to resolve this. I apologize if anybody else wrote something like this before and I don't know about it, but I honestly did try to find someone saying this and failed.

I will start by presenting the solution/definition that resolves the confusion (which is technical and requires understanding the field or at least basic economic jargon) and then a specific plain-language rule, understandable by anybody, that emerges from the solution. Then the rest of the post will be spent on explaining the need for these changes, how they are related, why they are not already being used, and why it was not obvious in the first place.

The definition:

“The Value of a Statistical Life (VSL) in a country” should be understood very narrowly and specifically as “The exchange rate between lives and money when taking money away from, or giving money to, people in that country”. Be very careful to avoid any language that gives it more meaning, like “people’s preference for risk reduction”. 

The same is true of the value of a life-year, and all of its permutations and refinements, like QALYs, DALYs, WELBYs, etc. To keep this post shorter and focus on its central point, I will conflate lives, life years, and all of their refinements. Later on in the sequence I will go over when it is appropriate to use one or the other.

The implication:

When analyzing a program or policy that spends money to improve health or extend life, the value of a year of life should be based on who we are taking money from, not the beneficiaries of the program. 

This means that for the purposes of deciding where to spend a pool of donor money, we should use the same value of a life-year no matter where or when the life is saved. National governments should continue analyzing their own taxation and regulation policies using a specific value for their country.

An important caveat is that the poorer someone is, the more likely it is that they can purchase their own life-years more cheaply than we can. So, the poorer the potential recipients are, the more lives an intervention has to save in order to be more cost-effective than simply giving money to those people.

What is Right?

Let's start with a simple philosophical thought experiment. Suppose that you find a magic crystal, and when you touch it, it gives you a choice. One choice will cure 10 random Swiss people of lower back pain for a year, and the other choice will cure 10 random Somalians of lower back pain for a year. Which do you choose?

Almost all philosophical and moral theories would either say that you should be indifferent, or that you should preferentially help those who are worse off. There are only two outliers I can think of. One is a narrow type of utilitarianism which assumes that the utility of health will be greater to a rich person, and that it is appropriate to feed utility monsters. The other is consequentialism plus a confident belief in unequal second-order effects: a belief that assigns a high weight to something like art or technology or economic growth, and assumes that a Swiss person being healed will lead to more of this good thing.

Now let's make it easier. Suppose the choice is between 50 Somalians not getting back pain, versus 10 Swiss people. At this point, from practically every moral theory, it becomes quite clear that you should save the 50 poor people from the illness rather than the 10 rich people. You're doing more good for the world, and you're doing it for less privileged people who need it more, and as a general rule we should operate our society on the assumption that discretionary resources should help poor people rather than rich people.

We would be very suspicious of any form of analysis that says we should do something that helps 10 rich people rather than 50 poor people. Most ethicists would consider such a choice to be perverse, wrong, and evil. 

What is Being Done?

Before I claim that a whole field is doing something that seems stupid and evil, I should show that they are actually doing this, and that I’m not arguing against a strawman.

This guideline for cost-benefit analysis commissioned by the Gates Foundation is clearly meant to set standards in the field. And it probably will, for a decade or more. It is written by all of the big names in the field, and is the result of a long and extensive process of consensus-building. And, given who paid for the document and how it will be used, its purpose is to set the standards for analyzing and ranking programs and interventions in global health and development. Its methods will be used for deciding which activities, in which countries, should be funded out of a pool of donor money. Although it is written as an overall introduction to the field, it is not likely to be used by governments doing their own policy analysis using tax money collected from their own citizens.

On Pages 15 and 16 (of the pdf. Ignore the page numbering system on the bottom of the document pages), the document says (emphasis mine):

Ideally, the value of mortality risk reductions in low- and middle-income countries would be derived from multiple high-quality studies of the population affected by the policy… However, extrapolation from studies of other populations will likely be necessary in the near-term, given the paucity of studies conducted in these countries…. The analysis should include a standardized sensitivity analysis to facilitate comparison to other studies … Such analysis is particularly important when uncertainty in the value of mortality risk reductions substantially influences the estimates of net benefits or the rankings of the policy options. The sensitivity analysis should include alternative population-average VSL estimates for the target country… It should rely on gross national income (GNI) per capita

This is pretty clear. They argue that we should use a different value of saving a statistical life in different places. Specifically, the lives of poor people being affected by an aid policy are valued less, and the lives of rich people are valued more. The policies that have the highest net benefits, based on these valuations, should be chosen.

Using the methodology detailed in this document, using $1 million of Gates Foundation money to save a Swiss life will pass a cost-benefit test, whereas using $1 million of its money to save a Somali life will fail the test. This means that, if we had two completely identical programs, with identical costs and lives saved, the one in Switzerland would get funded and the one in Somalia would not. A policy that saved one Swiss life for each million spent could easily get reported as having higher net benefits than a policy that saved five Somali lives for each million spent, and would therefore be recommended (despite all the caveats about equity and the analysis just informing rather than deciding policy. In practice, what gets measured gets done).

If you want to accuse me of pulling one mangled quote out of context to make a point, well, you are partly right. But I promise that the behavior I am describing is standard in the field, and that if you read all 126 pages of the document, you would find that (although they never say so in a clear way) this is the clear implication of the overall method they recommend.

Why is this Being Done?

So, given that it is simple and correct to value all lives the same, why is everyone in the field valuing the lives of poor people less and using a methodology that drives resources towards rich people? In my experience, almost all of them are all good, moral people who want to do good for the world. How did they end up like this?

It is not because this methodology, the Value of a Statistical Life or VSL, is supposed to represent the economic value of a person’s wages, in a ‘seeing like a state’ sense. In the bad old days, people did use lifetime wages to estimate the value of a life, but the whole point of a VSL was to replace that with something better. 

There actually is a good reason. It was good enough to make me accept the practice of different valuations for over a decade.

Cost-benefit analysis evolved from policy analysts in specific governments trying to figure out how to use tax money (or regulatory compliance costs) to best benefit their own citizens. In this context, it makes sense for different governments to use different numbers, because the money they are spending can have a very different opportunity cost.

This change in the opportunity cost of tax money happens because, from a statistical point of view, taxation is not only theft, it is murder. People spend money to improve their own lives, in ways that increase their health and longevity. If we tax people, they have less money to spend on health and safety, and/or they take riskier jobs to make up the difference, so statistically some of them will die as a result. 

In the United States, the prevailing estimate is that every (roughly) $10 million of taxation will statistically kill someone. This value is based on looking at what people do when spending their own money. We look at what people will pay for cars with more safety features, or houses in healthier environments. We look at the difference in wages that people will require to take an otherwise-identical job that has a higher risk of death. And on average, Americans act in such a way that every $10 million they lose will, somewhere, lead to a dead body on the ground. 

Similarly, a regulation that destroys $10M of economic activity, or redirects it to regulatory compliance activities, will also, statistically, kill someone. This is because the things that were previously being made would have saved a life (or, assuming consumers are making reasonable trade-offs, it would have provided as much happiness or utility as saving a life).

So, the US government uses a $10M Value of Statistical Life. If a policy or regulation saves more than 1 life for each $10M it costs, it passes the cost-benefit test. If it saves fewer lives, it fails the test, because it probably killed more people than it saved.

But in a poor country, that $10 million of taxation will statistically kill a lot more people. That's because it's a lot easier for poor people to purchase improvements in health and life expectancy. They haven’t yet done some of the cheaper things to take care of their health that rich people take for granted, because they never had the money to. And it is much harder for poor people to earn extra money, and they will end up taking much bigger risks to do so.

So, collecting $1 million in tax from people in DRC (GNI per capita $1.1k) is a lot more murder than collecting $1 million in tax from Americans. Taking a million out of the American economy has a 10% chance of killing someone. Taking a million out of the DRC will probably kill several people. If the US government takes $1 million out of the US economy to save a life, it has caused much more good than harm. But if the DRC government takes $1 million out of the DRC economy to save a life, it has killed more of its citizens than it has saved.

So, if the DRC government were to do a cost-benefit analysis of a policy that saved lives, at the cost of taxes or regulations imposed on people in DRC, it should require that the policy save many more lives per dollar spent. In the terminology of cost-benefit analysis, this means ‘use a much lower VSL’ than the US government does. 

So, to review:

1) We observe that it is cheaper for poor people to improve their health, or reduce their risk of dying.

2) When governments are collecting tax money from their own citizens to invest in life-years, it makes sense for poor countries to require a better exchange rate, one that matches the exchange rate that their citizens are already paying.

3) Because of these important insights, the field developed a heuristic that the value of a statistical life should be different in different places. 

4) These different values were taken as given, even in the context of international allocations of donor money.

Also, a bit of linguistic confusion, this one less defensible, added to the problem. All of the methodology that looked at how people were spending their money to buy a lower risk of dying was identified as ‘revealed-preference’ methodology. This was to contrast it to stated-preference methodology, which is basically survey questions about how people would spend their money (and also produces similar values “if done right”). So, people started saying and thinking things like “By revealed preference, the VSL is lower in poorer countries” when they really should have said “Because people in poorer countries are more vulnerable, the amount of taxation that will statistically murder someone is lower.”

And this confusion, rightly so, generates moral anger at doing cost-benefit analysis. The process, when done badly, is a pseudoscientific justification for valuing the lives of rich people more and prioritizing health interventions that save them over interventions that save poorer people.

What is the Solution?

The framing of my analysis of the cost of taxation suggests the solution. What we're really doing is trading off lives (when collecting the money) for lives (when spending the money). We want to do the thing that increases the total amount of human flourishing. So instead of changing the VSL number based on where we're spending the money, we should change it based on where we're collecting the money. Since EA collects basically all of its money from people in the developed world, we use one standard value.

This is very clean and simple. When doing cause prioritization, EAs should count all human (and human-equivalent) lives, in all times and places, the same. We can ignore the confusion inherited from the literature. Now that I have explained why the old method exists, we can safely replace it in situations where it is not appropriate. 

Whenever any charity or international aid organization is thinking about spending a pool of money, they should follow the simple decision framework of buying the most life-years they can with that money. OpenPhil basically has a bar of a thousand times effectiveness, so they should have a simple global rule of paying for any program that saves lives for less than $10,000 a life (or for the equivalent number of disability adjusted life-years), no matter where or when the life is saved. 

This solution, when combined with the instruction in the 101 post to use the life-year as the basis of analysis, solves a lot of problems. Repeating the main point from that post:

When analyzing policies that have economic and health impacts in different places, use the life-year rather than the money as the fundamental unit of analysis.

In a sense, this is a very subtle change. Instead of saying “We value a DALY at two units of log income, OpenPhil should say, “We value two units of log income at a DALY”. (Personally I think that the value should be more like 4 units of log income, so that each DALY is worth about 1/40th of the VSL i.e. $250k, but that is an issue for another time.) They should assume that every DALY everywhere is worth the same, but that people can purchase their own DALYs more cheaply the poorer the country is, so we convert economic benefits into DALYs based on the income level in that country.

So for every calculation that EAs are currently doing, we don't need to change anything. But this solution allows us to expand the calculations to analyze cross-national economic effects in a sensible way, as I showed with the trade treaty example. And it will be especially useful in cause prioritization between global poverty relief and the more speculative parts of EA 

When looking at policies that give both life-years and economic benefits, we convert the economic benefits into life-years using an exchange rate where increasing the income of 200 people by 1% each is worth a life-year. (Linear combinations of this, for example boosting the income of 40 people by 5% each, are fine as long as we're not boosting income too much.) This is handy because measurements and outcome evaluations of quite a lot of interventions, like things that boost health and education, actually report increased income to recipients in percentage terms, so there's no reason to convert into a currency value and then back again.

Why was this not solved before?

So, why hasn’t anyone written a post like this before? It's one thing to say that I've noticed something that a small academic subfield, operating mostly on tradition and consensus, didn't notice. But it's an entirely different level of chutzpah to claim that I have an insight that both OpenPhil and GiveWell have failed to notice.

One answer is the EA world does implicitly realize this. All of the calculations have as a baseline a single moral value for saving lives or life-years anywhere in the world. But this is done in a convoluted way, which I am guessing is because they feel a need to justify their analysis with reference to an academic literature that is itself confused. So they do the right thing, while referencing a literature that implies they should be doing something different, which makes it confusing to actually work outside the narrow confines of the problems that the literature is meant to handle.

But also, the baseline for EA global poverty analysis is typically a cash transfer to poor people. So implicitly, an improvement in health is taking away money from poor people, because giving them money is the opportunity cost. So, if we are measuring the trade-off between life and health and comparing it to a hypothetical direct transfer in a poor country, we are doing something very similar to measuring the effects of taxing and spending in that country, which does require using a different VSL in that country. So, because the old method was partly right, there was no need to really confront it and think deeply about what was going on.