Does GDP Growth Mislead Us About Quality of Life?
Reading Trammell & Jones on Measuring Living Standards
0:00Seth: Would you rather be a middle-class person today, or the king of China 2,000 years ago? He has the strong intuition — I don’t want to put words in his mouth, but I think he’d agree with this — that you’d rather be an upper-middle-class American today than the king of China 2,000 years ago. I don’t know if I have that intuition. I can think of a lot of really fun things I could do if I was king of China. Welcome to Justified Posteriors, the podcast that updates its beliefs about the economics of AI and technology. I’m Seth Benzell, whose utility from your listenership grows at a rate completely unmeasured by traditional economic analysis, coming to you from the beautiful recording studio of Boston University in gloomy Boston, Massachusetts.
Andrey: And I’m Andrey Fradkin, surprisingly also coming to you from Boston University in — it’s actually not that gloomy — Boston, Massachusetts. Welcome, Seth, to Boston. We’re going to be talking about quite an important and interesting paper today. Do you want to introduce the paper?
Seth: The title of the paper is “When GDP Misleads: Inferring Living Standards from the Value of a Statistical Life,” from friends of the show Phil Trammell and Chad Jones. And what could be more important than how good is life? On a scale of one to ten, how good is life, Andrey?
Andrey: Eleven.
Seth: Oh, beautiful. When I’m with you, Andrey, it’s always an eleven.
Andrey: So, as context for this paper: although the words “AI” do not show up in the paper, it is very much about AI, and we’ll get into it.
Seth: And by two co-authors who are very AI-brained.
Andrey: Yeah. And I should mention, I’ve talked with both Phil and Chad about this paper. They always like to bring it up in these sorts of discussions, so we’re very excited to be digging into it. As usual, let’s get to our priors.
Priors: Is GDP per Capita a Good Proxy for Welfare? 2:12
Seth: So the whole premise of this paper is we’re going to think about a new way of trying to measure how much better life has gotten. And a first question you might ask is, “Professor Fradkin, don’t we already know how good life is? It’s called GDP per capita, and we measure that pretty well.” The essay is going to give us some arguments about why it may not be such a good measure. But let me start off by asking you: has real GDP per capita done a good job being a proxy for welfare? Is it maybe an overestimate, underestimate? And how do you think about how that might change in the age of AI?
Andrey: Real GDP per capita is a number that we measure every year —
Seth: Hell of a number. They measure it every quarter, dude.
Andrey: — and it varies a lot across countries. But just looking at that one number doesn’t tell us how much better life has gotten over time. It’s just a snapshot. I don’t think there’s an obvious way to map a given GDP per capita to welfare or utility or something else broadly. But the argument that has been made is that differences in GDP per capita are capturing something that’s very relevant to how good life is across places.
Seth: Sure — index whatever year you want to one. Fair enough.
Andrey: The point is that it only matters for comparisons, not in terms of the raw number.
Seth: You’re not 70,000 units happy this year?
Andrey: Exactly, that’s what I’m trying to say. So then we have to think about the change in GDP per capita. And as economists, as a profession, we’ve gone all around the world to policymakers everywhere saying how great of a measure this is. All these other things you might care about that are not captured in GDP — well, if you squint at it, they’re super correlated with GDP.
Seth: Give us some examples.
Andrey: Life expectancy —
Seth: That’s good.
Andrey: — measures of life satisfaction.
Seth: Cool. Education.
Andrey: Yeah, education. Well, is that good or bad?
Seth: You’ve seen what education did to this guy.
Andrey: Too much education. So many good things are correlated with GDP per capita, and it’s something that we can compute across countries as well, and that allows us to think about who’s doing well and who’s not. One of the key debates on Twitter recently has been how much poorer is Europe than the United States? And if you look at the statistics, it’s pretty clear that Europe has substantially become poorer than the US, because it hasn’t grown as much as the US over the past decade and a half or so. People were skeptical of that, but I think their arguments were not so great. So I do think that GDP per capita is a very useful metric. Now, that said, it is not a perfect metric, and in some sense it wasn’t designed to measure how much welfare people have.
Seth: This is an early-twentieth-century thing that’s trying to think about the industrial capacity of a nation — how many tanks could different countries crank out if the time called for it.
5:29Andrey: Yeah. So it’s useful to think about GDP per capita growth and the numbers involved. One number I pulled up was GDP per capita growth in China from — I think 1962, or 1952 — to today. And that number, depending on which time series you use, is over 50. It can be as high as 72. So: has life gotten 72 times better in China from 1952 to today? It’s a very interesting question, isn’t it? Because life was pretty bad in China at the time. People were dying of starvation. There was political repression.
Seth: But this is not an economic history podcast.
Andrey: No, no. But I’m just saying, all these things affect welfare in a way that GDP per capita is only very loosely connected to.
Seth: And maybe we’ll talk about this more in the limitations of this measure in a second, but you might imagine two kinds of concerns. One concern is diminishing returns to consumption — once you get enough corn that you’re not starving to death, does doubling the amount of corn make you worse off? And then there’s this other issue, which is growth in varieties, which maybe this real GDP adjustment is supposed to do something to talk about quality improvements, but maybe we don’t think it does a perfect job.
Andrey: You’re kind of getting into the paper already.
Seth: Fair enough. So give me your prior.
Over or Under? China, the US, and Pinball Machines 7:08
Andrey: Is GDP per capita a good proxy for welfare? That’s hard to have a prior on, because I don’t know what “good” means. But we do have more precise questions. Has it or underestimated the growth in welfare in the past? And my point was, in China, it’s probably overestimated the growth in welfare.
Seth: You don’t think Chinese lives have gotten 83 times better?
Andrey: 72 times.
Seth: 72 times better.
Andrey: I think they’ve gotten so much better, but 72 times is truly a staggering amount. But at the levels that we’re seeing in the US — maybe I think it’s underestimated.
Seth: I can also give you the 1980 numbers. The 1980 number: we’ve had 116% real GDP per capita growth. Does that feel like an or an underestimate?
Andrey: That feels like an overestimate, honestly.
Seth: Life isn’t twice as good as it was in 1980. They already had pinball machines. Cocaine. Basic heart surgery.
Andrey: So I think a lot of this hinges on things that you want more of as you get wealthier. It could be new goods — we have smartphones now, which are pretty great, despite the naysayers. And then medical advances. But even in the ‘80s we had antibiotics and other things, and while medicine has drastically improved, average life expectancy has not improved that much. One way to think about it is: if life expectancy doubled from the 1980s, that would be a pretty good argument that things are twice as good.
Seth: That’d be a pretty good way to get there.
Andrey: What do you think?
Seth: Great question, Andrey. I would say since 1980, 116% does seem too big — as does 543% since 1940. So I’m thinking about the US in particular. And for me, the biggest factor there is diminishing marginal returns from consumption. Even setting aside these complications around new products, new healthcare, that would tend to go in the other direction. The major effect is: if you go from not having enough protein in your diet to having enough protein, that gets you a lot of the way towards satisficing. As we think about moving towards the AI age, I think there’s more of a reason to think that we’re going to start underestimating. The way I would put it is: pretty confident we’ve overestimated in the past. Moving forward, there’s more of a concern that GDP per capita might underestimate, if we have tremendous growth in variety but it doesn’t show up in terms of more stuff — it shows up mostly in terms of better, more pleasant digital experiences, or medical enhancements that enhance your quality of life, but maybe people aren’t working as long. I would think it’s going to be less of an overestimate in the future.
Variety Growth, the Eudaimonia Button, and Putting Numbers On It 10:09
Andrey: Haven’t we had a lot of variety expansion since the 1980s? We’ve had the internationalization of trade, all the digital things that we’ve gotten — there’s so many different websites to read.
Seth: We got Fallout: New Vegas.
Andrey: We have podcasts. They didn’t exist. That’s a new product.
Seth: We have radio shows. We have Prairie Home Companion.
Andrey: What are these new varieties that we’re missing out on?
Seth: Well, dear listener — if you knew the new variety, you’d have it already.
Andrey: We’ve read a lot of science fiction, right? It’s not crazy to imagine new things.
Seth: Nozick’s experience machine, dude.
Andrey: Well, this is kind of the crux of it, isn’t it? If we had a happy button, and we just pressed the happy button, then we’d be happy the entire time versus only some of the time.
Seth: It’s a eudaimonia button. You also get complete human flourishing. It’s not just happiness.
Andrey: Great. Perfect. So in that world, I do agree with you that we might be underestimating welfare gains. But given the argument that we’ve made, I do think it’s still going to overestimate welfare gains.
Seth: All right. Do we want to put a probability on the probability with which it will overestimate in the AI age? Give me a number, percentage chance.
Andrey: 95%.
Seth: 95%. I still think on balance it will overestimate — it’ll just overestimate less. I’ll come in at, let’s say, 80%. All right. And now I’m going to ask you an even harder question, Andrey: how much has life gotten better since 1940, or since 1980? You can take either one.
Andrey: Maybe ‘86, since that’s when I was born.
Seth: Okay. Since 1986, since that halcyon year.
Andrey: That’s a hard question. And in the US — I wasn’t born in the US, dude.
Seth: Well, how much worse has it gotten in Belarus, dude?
Andrey: It’s still gotten better in Belarus. I can imagine maybe 25% better?
Seth: 25% better. Okay. I’ll report — this is not the complex analysis that’s done in the paper we read, but maybe to ground my prediction: one analysis they do in the paper is they just take the change in life expectancy and multiply that by, basically, the logarithm of consumption per capita. One reason you might do that is that a common way of adjusting for decreasing marginal returns is to put it into some sort of production function, and a logarithmic utility function is a very common one. There’s various reasons you might like that one. And so if you plug those two growth rates in, you get an improvement in life goodness of 41% since 1980 in the US. And to me, that seems like it’s in the right order of magnitude.
Andrey: I think that’s in the right order of magnitude.
Seth: Okay. So, Phil — we go into this paper feeling like the state of the art does a pretty good job. I guess we’re going to be really curious to see what his innovations add.
The Paper’s Setup: Food and String Quartets 13:25
Seth: So, Andrey, the first part of this paper is laying out an argument why GDP per capita might not do such a great job. Tell me about that.
Andrey: At a high level, they give us a very simple example where things don’t quite work out as you’d expect. The setting is you have two goods. Let’s say you have food, and you have string orchestras.
Seth: Or services. Anything you can think of that starts with an S that has low productivity growth.
Andrey: I don’t actually enjoy string orchestras. I’m not sophisticated enough. But let’s say you have two goods. What they do is they say there is productivity growth in food, and that productivity growth means that over time you’re getting more and more food per capita. If food was the only thing in the economy, then the growth rate of the economy and the growth rate of GDP per capita would just be in terms of food. So if that growth rate is 5% per year, then our GDP growth would be 5% per year.
Seth: Seems fine. What’s wrong with that?
Andrey: Let’s say in addition to that, string orchestras are invented, and they have a productivity growth of only 1%. Because of people’s preferences, people have diminishing marginal utility from consuming both food and orchestras.
Seth: Speak for yourself. Bring me to that all-you-can-eat buffet, dude — I’ll explode.
Andrey: That means that once this new good gets created, people are going to shift more and more of their consumption into this new good. And so when you measure GDP growth per capita, it’s going to be a spend-weighted average of a 5% growth rate of food and a 1% growth rate of string quartets. As a result, we’re going to have GDP per capita growth that’s substantially less than 5% when this new good is invented. But this is counterintuitive, since people are much better off — they now have two goods that they consume instead of one. They could have consumed as much food as they wanted, but they’ve chosen not to. So this creation of a new good results in a change in how we think about GDP per capita. It is an example where welfare and GDP per capita don’t move in the same direction.
Seth: Right. So they diverge. Inventing the new thing makes us better off, clearly, but it also clearly slows GDP growth. Whoa — paradox, my mind explodes.
Andrey: And to be clear, this is a well-known feature — though I think underappreciated, as they argue — of GDP per capita and these sorts of calculations.
Seth: And it’s a big challenge. The real challenge is that at the moment it’s invented, the price of the string quartet goes from infinity to non-infinity. It’s that moment of invention that’s the real challenge in adjusting for new varieties.
16:37Andrey: Just to take a step back — we haven’t even talked about adjusting for new varieties. But it’s related to adjusting for improvements in the quality of something. Going back to the smartphone: the smartphone does a bunch of things that other products were doing, like calculators back in the day, that people would pay a lot for. And then how do you create a composite smartphone out of previous things? Is that even possible?
Satiation, and Would You Rather Be the King of China? 17:08
Seth: One other detail I want to pull out of this example: there’s a problem even before the invention of the string quartets. If you think people get satisfied with the amount of food — if once you have your 2,000 calories a day you’re done — and we just keep doubling the amount of food, you’re going to start evolving this infinite divergence between welfare, which is stuck, and GDP per capita, which goes off to infinity.
Andrey: In fact, the previous Chad Jones paper we discussed on this podcast made this exact point.
Seth: Right. One aside I want to make — hopefully this is not too much of a divergence — is that when talking to Phil personally about the value that comes from AI, he’s really of the camp that wants to emphasize that value over time comes from growth of varieties rather than growth in abundance. So the thought experiment he gave me, and this is one I’ve been thinking about a lot: would you rather be a middle-class person today, or the king of China 2,000 years ago? And he has the strong intuition — I don’t want to put words in his mouth, but I think he’d agree with this — that you’d rather be an upper-middle-class American today than the king of China 2,000 years ago. I don’t know if I have that intuition. I can think of a lot of really fun things I could do if I was king of China.
Andrey: Yeah, I wouldn’t want to be the king of China.
Seth: Because it’s too stressful?
Andrey: Well, there’s that part of it too — you might get killed at any moment. But also, I just don’t enjoy bossing people around. Just not my style.
Seth: Listen, when I see all the fun they got up to in those palaces — you guys will know what I would choose. Maybe I’ll leave those details up to your imagination.
Andrey: I thought you were going to say — and sorry, Phil, for this side discussion — that Phil’s bull case on AI is that we’re going to create a lot more beings that are capable of having utility. And so then welfare goes up, and it goes up because we have these transhumanist beings that have infinite utility. Not each instance of it is getting infinite utility, but all of them have very high utilities, and we’re creating so many of them that that’s the bull case.
Seth: Well, he’s a total utilitarian. I think that’s a whole other argument, and something that really doesn’t show up in this paper at all, because we’re going to be focused on this one representative agent guy. So we’re not really going to be thinking about distributional questions, or summing over lots of people.
The Clever Idea: The Value of a Statistical Life 19:44
Seth: Maybe I can lay out what they show as the resolution of this challenge. This is their innovative idea, and I really do want to say this is a very, very clever idea. It’s a very Phil-and-Chad idea, because they take the economic theory very literally in a way that is both wonderful and can feel a little bit out of left field — but when you appreciate it, has some real deliciousness to it. This is a delicious little bit of theory, because it comes out really simple. Once you see it, you’re like, “Oh yeah, that is how you could calculate that” — but apparently nobody’s made this point before. So what they point out is: believe it or not, people have this nominal measure of how valuable being alive is, and maybe we can do some funny calculations around this. It’s this thing called a value of a statistical life. What’s a value of a statistical life? You may have run into this if you think about policy analyses where people ask questions like, “How much should I spend on this road in order to prevent one car accident every year?” You can imagine other settings where you would need a number like this.
Andrey: Yeah, like environmental-related things.
Seth: Environmental is perfect.
Andrey: Pollution causes some marginal amount of deaths. Climate change as well.
Seth: And so there’s this number. One obvious question is: presumably, if life is better, that number should be bigger. You should be willing to pay more to preserve a life that’s a good life. All right — let’s take this number really literally. That’ll be maybe one question we can come back to at the end: how literally we want to take this number. Apparently, according to the US Department of Transportation — do you know what that number is today, Andrey?
Andrey: Fourteen?
Seth: Fourteen and a half million dollars is the value of a human life. So, now you know. [Correction: Jones & Trammell cite $13.7 million for 2024 from US DOT guidance — not $14.5 million.]
Andrey: In America.
Seth: In America, in 2024. So we’re going to be talking about everything through 2024. So what’s the challenge here? The challenge is: fourteen and a half million what? So we’re back to this issue of needing a real deflator, a real way of converting fourteen and a half million whats into utils, into goodness. That’s the overall logic. But maybe the level doesn’t tell us anything. So the next step in the logic is that maybe we can start thinking about the change in that number telling us something. And they have this really interesting paper that we’ll talk about later, that looks at different US policy proposals over time and measures the change in this value of a statistical life over time. So we’ve now got this number, which is the change in a value of a statistical life over time. Maybe the answer is as simple as: the growth in this nominal value of a statistical life is equal to the growth in lifetime utility. And that’s basically the answer.
There’s going to be an important adjustment, but that’s the high-level answer. So what is that adjustment? Now you might worry: there’s growth in the nominal value of a statistical life, and there’s this growth in lifetime utility, but we’re still back to the question of what the deflator should be. Because you can imagine there’s hyperinflation. In Weimar Germany, the value of a statistical life goes to a gazillion Deutsche Marks. Did life really get that much better? So you need some sort of deflator. How do they get this deflator? They observe that your total lifetime goodness — your total lifetime utility — should be equal to your value of your statistical life, and they say the right deflation measure is the marginal utility of consumption. Because that tells you how good a dollar is, so that’s the right deflator. And then you’ve got this problem: what’s the marginal utility of consumption? That’s also a number we don’t have a good way of getting at. But, Andrey, if you’ve taken intermediate microeconomics, you know we do know something about the change in the marginal utility of consumption, from our good friend the Euler equation.
The Deflator Problem and the Euler Equation 24:12
Andrey: I’m confused by your calling it microeconomics rather than macroeconomics.
Seth: Listen, I always obey the Euler condition when I spend my money. I don’t know about you.
Andrey: Oof. So, the famous Euler condition. It’s this magical equation in macroeconomics that essentially is the equilibrium relationship between interest rates and how much you save and how much you consume today. In a simple model, it’s a very simple formula. It is only true under very many, very restrictive conditions.
Seth: So what are the caveats here? First of all, even in the simplified model, you need people to not be at a boundary — they need to be saving some of their money, they need to not be saving 100% or saving zero. But conditional on you being a fully rational guy, you’re not saving 100%, you’re not saving zero. In the background here, this is a representative agent who doesn’t age. They just have a constant probability of dying in every year. So set that aside too. In that case, imagine what would be the case if you cared the same amount about consuming today as consuming tomorrow, and there was no interest rate. As long as you have some diminishing marginal returns from consumption, you’d want to consume the same amount in every period. So in the simplified intertemporal Euler, you save the amount of money such that you eat the same every day of your life. There’s two adjustments to that. The first is the personal discount rate. What’s that, Andrey?
Andrey: Well, it’s an interesting question. You don’t value consumption tomorrow as much as you value it today. But the question is why. It is empirically a true thing, I think, that people do not, and so economists have estimated what this discount rate is. But I’ve always interpreted at least part of the discount rate as being about mortality risk — you don’t care as much about consumption fifty years from now because you might be dead fifty years from now.
Seth: This isn’t that.
Andrey: This is very much not that. But I think putting it in there while trying to measure the value of statistical life — I’m wondering if there was potentially a double counting going on there.
Seth: Yes. So one challenge here is we’ve got to think about what this discount rate is as separate from mortality risk. It’s like, if you knew for sure — let’s say, to simplify, you’re going to live forever — how much more would you care about consuming today versus consuming tomorrow? So that’s the first one. And then there’s another reason you might want to consume tomorrow instead of consuming today, which is —
Andrey: The interest rate.
Seth: The positive interest rate.
Andrey: You get the big bucks from putting money in your savings account. Or even in the stock market.
27:17Seth: Exactly. So as we mentioned before, if there was no time preference, you would want to consume everything that you got equally on every day. If you had $1,000 in lifetime income and you lived for ten years, you’d want to consume $100 every year. But we’ve got these two time factors pushing in different directions: you value today more than tomorrow, but you also want to save for the future because you get this interest rate. So we combine the intertemporal Euler with our previous observation that the value of a statistical life times the marginal utility of consumption should tell you something about your lifetime utility. And we take logarithms, and we take the first derivative, and we get a magic, simple equation. The way that they write this down is: the change in the value of being alive is equal to the change in the value of a statistical life, plus your personal discount rate, minus the interest rate. That way is a little confusing, so let me say it a slightly different way, which I think is more intuitive.
I’ll put the preference things on one side and the nominal things on the other side. So you might equivalently say that the growth in lifetime utility, minus your personal discount rate, is equal to the growth in the nominal value of a human life, minus the interest rate. And that’s a nominal interest rate — theoretically, we can go out there and measure it in the world. And now we’ve got an equation we can bring to the data. Andrey, aren’t you so glad to learn how much life has gotten better with this easy, simple equation?
Why Andrey Doesn’t Buy It 28:59
Andrey: It is a very, very, very simple equation.
Seth: It’s a beautiful result. Let’s call it that. Let’s be honest.
Andrey: It is very clever. I’m sure we’ll come back to this a little bit, but when I go back to thinking about why I didn’t become a macroeconomist — how dissatisfied I was with the Euler equation had to be in the top three.
Seth: Wow. The intertemporal Euler is getting some intertemporal shade.
Andrey: It is just not how people make decisions.
Seth: You don’t try to smooth out your consumption over time?
Andrey: Not in this way.
Seth: I think about the interest rate when I decide whether I want to spend today or tomorrow.
Andrey: I don’t think most people do. I think the evidence suggests that many people do not. And even when they do save, it’s not according to this equation. One of the implications of these Euler equations is, for example, the result of Ricardian equivalence.
Seth: I tax you today, and you know I’m going to spend on you in the future, so you don’t change your behavior at all.
Andrey: Yes — which is so provably false as to invalidate this entire approach.
Seth: Well, it might be wrong because the Euler equation’s wrong, or it might be because the representative agent Euler equation is wrong and there’s heterogeneity.
Andrey: My understanding in this literature is that for a decent subset of people — for an important enough subset of people — the Euler equation does not seem to be correct. But there is a distributional thing as well, which is that you can’t aggregate unless you’re in an absurdist model.
Seth: Unless you’re a macroeconomist.
Andrey: Unless you’re a macroeconomist, you can’t aggregate a bunch of individual people’s Euler equations into a linear functional form in this way.
Seth: Don’t tell Chad that while he’s cooking, dude.
Andrey: I have told Chad this. I literally have. I’m sure I’m not the first person who’s made this point. I view a lot of Chad’s papers as being thought experiments, so this is one. And to be clear, I do think they’re making an obvious point — that the value of statistical life should be related to welfare. That I’m buying. But in this way, I’m not buying.
Seth: To me, the beauty of the equation is how, when we line everything up perfectly, we get the welfare terms on the left-hand side and the nominal terms on the right-hand side. Just the beauty of the idea that we can learn about people’s true love and value of life from measuring these statistical aggregates, in a way that’s more sophisticated than “GDP go up” — I think it’s a cool insight. I think there’s going to be huge application issues. I think there’s going to be huge issues about who gets to decide what, and why the VSL is what it is. But I think that this analysis, if you could somehow do it at the individual level, would be a great starting point.
How VSL Is Actually Measured 31:49
Andrey: It would be much more plausible at the individual level. But even there, we then have to dig into how value of statistical life is actually measured. Taking a step back — how is value of statistical life measured? Is this a good time to discuss that?
Seth: Let’s bring it up in one second. I just want to make the point that at the individual level, you could imagine people making insurance or healthcare decisions that would allow you to infer the same number, which is: how much money am I willing to pay to reduce my cost of death a certain amount? I don’t think it’s so heroic to imagine that you could do this at the individual level.
Andrey: I think it’s extraordinarily heroic. But you’re proposing just different identification strategies for value of statistical life.
Seth: So how do they do it?
Andrey: Costa and Kahn run a regression where they regress the wage of a person on a bunch of things, and one of them is the likelihood that you will die on the job. And there are certain jobs that entail a higher likelihood of death, like if you’re a coal miner or something like that.
Seth: And this is a 2004 paper. It’s a little bit out of date.
Andrey: Yeah, it’s a 2004 paper. It doesn’t really matter — I don’t think any value of statistical life paper is very good. It’s just economists being clever, and it’s fine. But there’s an implicit assumption there that people who are making these decisions — for example, to be a coal miner — are rationally weighing, in a very specific statistical sense, their probability of death on the job when they’re picking their wage, and that the market clears in a way that reflects that. And then you can have better measurements that would be much harder to get over time. One of the advantages of Costa and Kahn is that they’re able to do this for a very broad set of data. But if you’re focusing on very microeconomic decisions, or maybe even with survey data, that might be more plausible. This approach seems very problematic to me. Another reason it seems problematic is that the identification of this number is coming, presumably, from jobs that have a very high probability of death on the job.
Seth: And these attract the irrational.
Andrey: These attract the irrational. These attract people with unusual sorts of preferences. So what these numbers’ relationship is to the reality of this hypothetical number that people don’t even want to think about — to me, it’s very far.
Seth: Do you like better the 2024 fourteen-and-a-half-million highway safety number? Is that a better number or a worse number?
Andrey: It’s just made up. It’s just made up.
Seth: This is the Doctor Manhattan meme.
Andrey: Fourteen and a half mil — why not? I don’t know what to make of that.
Seth: So what other numbers do we need to plug in order to make this analysis?
Andrey: We need a discount rate, and we need the interest rate. The discount rate — there are standard ones you can use.
Seth: They choose 1%, uncited. “We use 1%,” period. It’s one-sentence paragraphs.
35:22Andrey: For interest rates, they use the T-bill plus some convenience yield. The numbers are sensitive to the interest rate. Now, if you take the Euler equation seriously, then the interest rate should be whatever interest rate people have risk-free access to, plus some other stuff. But if people were making decisions according to the Euler equation — what are they putting in that Euler?
Seth: If the one representative human was making decisions according to the Euler equation, and they had access to this interest rate, and they had this discount rate, and they had this value of a statistical life. Sure.
Andrey: And we measured them correctly over time.
The Results: 2.3% a Year — and a Decline After 1980 35:53
Seth: What are the results?
Andrey: So the results — oh, let me put on my glasses.
Seth: Oh, shoot. Oh, shit. Shit’s getting real.
Andrey: So the results are that welfare has gone up by 2.3 —
Seth: 2.3 percent per year, on average.
Andrey: Percent per year, yeah.
Seth: Since 1940.
Andrey: Since 1940, exactly — with the biggest gains coming in 1940 to 1950, which is an interesting thing to think about. Why could that be? I don’t know.
Seth: If you think about what goes into this measure, mechanically it comes from the fact that the interest rate is going up. The interest rate going up makes welfare look good, because to make VSL stay the same, it means that welfare had to have gone up.
Andrey: The value of statistical life went up a lot between 1940 and 1950.
Seth: Yeah, so the value of statistical life is going up a lot. And then maybe the other headline number is from 1980 to 2024.
Andrey: Where it’s actually going down.
Seth: So actually, life got worse since 1980.
Andrey: Life got worse. Woo.
Seth: Life peaked in 1984. What can I say?
Andrey: You and George Orwell.
Seth: So it’s a high enough interest rate, while value of statistical life does not grow as much. Man — big if true, life got 0.5% worse per year since 1980.
Andrey: The other thing is: 2.3% growth in welfare — how does that compare to GDP per capita growth?
Seth: Over the same period, it’s actually in the ballpark, isn’t it?
Andrey: So one thing to naturally go to is: when calculating utility in the kind of dumb way, where we literally take the GDP growth and we say that utility is log of C, log of consumption — then GDP per capita growth just mechanically, drastically understates — sorry, overstates — welfare growth.
Seth: Right, just because you have to double in order to have a linear increase.
Andrey: Yes. But here, welfare is growing at that rate and there’s no additional logging involved. So as a result, that means welfare has grown a lot more using this measure of calculating things than using the other measure.
Seth: So just to report those numbers: since 1940, according to this baseline projection, they see lifetime utility going up by 6.9x. Whereas the measure that I kind of prefer since 1940, which they also report — life expectancy times a log utility function over consumption — goes up by 2.4x since 1940. Could you convince me that life is two and a half times better than 1940? Probably faster than you can convince me that it’s seven times better.
For Whom? Representative Agents and Whose Life 39:27
Andrey: For whom?
Seth: Maybe we should start thinking about caveats now, and about refinements. If somebody said, “Seth, invent your own social welfare function and tell me how much total welfare has changed for the average person in the United States since 1940” — probably where that analysis would have to start is: how much desperate poverty have you eliminated? How many people were horribly impoverished? How many people had messed-up tuberculosis? How many people faced racism that’s been addressed in some ways today? You wouldn’t really think about the average person. You’d be trying to think about the 10th and 20th percentile people.
Andrey: That’s right.
Seth: What other sort of — at the high level, we talked about this being an analysis that has a single representative agent. We think there’s all sorts of heterogeneity that also matters at the theoretical level, because you imagine that people over the course of their life cycles are making savings decisions based on that.
Andrey: So this is actually one of the key caveats here: the distribution of demographics has changed a lot over time, and it’s completely unclear from Costa and Kahn how that should play into the statistical value of life. Because presumably your willingness to take a death risk when you’re 60 is very different than when you’re 15 — by the way, for many different reasons. Some of them rational and some of them irrational.
Seth: Exactly. What is a value — whose statistical life, if you will? Does the 1% time discount rate bother you? I guess that’s a related issue.
Andrey: I haven’t thought through how I would try to — I haven’t read this literature, on what share of the discount rate is due to death risk. Another version of it is the Parfit risk: that you in the future are a different person, and so you don’t —
Seth: Right, I don’t want to give that guy money. He might donate to a political party I don’t like.
Andrey: Yeah — maybe according to Parfit, why would you care about yourself in 100 years? You’re a totally different person.
Seth: Exactly. Future Tuesday indifference. On Tuesday, I don’t care what happens to Tuesday Seth. Another way to put it, I would say, is that even if it’s an empirical regularity that people treat consumption in the future as not as good as consumption today, it’s unclear from a social welfare perspective whether we need to adopt that view.
Posteriors 42:07
Andrey: So do we want to go to our posterior?
Seth: We’ll proceed to our posteriors.
Andrey: Honestly, I enjoyed reading through this paper. It’s very simple. To me, it really highlights the importance of thinking about new goods, and whether AI changes what new goods we get.
Seth: Which is funny. If Phil’s bull case on AI creating welfare is lots of agents that we just multiply, that’s almost like a linear technology in GDP — in which case all these adjustments don’t matter, because it’s just more GDP equals more welfare, one for one.
Andrey: Well, I think we wouldn’t traditionally count non-humans in GDP.
Seth: Yeah, but come on. We’re enlightened beings. We accept all sentient life here on this podcast, Andrey.
Andrey: Be careful. We might become even more effective altruists than we currently are.
Seth: We love our EA fans.
Andrey: So it was useful to think about. But ultimately, my pessimism on our ability to measure value of statistical life, and my pessimism on the Euler equation, means that I have not updated. It was good to think through how much welfare could have increased over this time period — so there’s a good scaffolding for that — but I don’t believe this method at all.
Seth: And one thing we should point out is that they do a bunch of robustness analyses, where they try different interest rates —
Andrey: And it matters a ton.
Seth: — and it goes from “life got 100% worse” to “life has gotten 1,000 times better.” To give you one example of a confidence interval: just changing the interest rate you discount by 1% in either direction changes the percentage increase in welfare from 1940 to 2020 from 16.1x to 3x. And that’s just from changing one of the parameters by one percentage point.
Andrey: So, not a lot of updates. What about you?
Seth: Not a lot of updates. How do I want to think about this? Ultimately, this is a theoretical exercise that I guess I’m a little bit more optimistic about. You could go out and try to measure these at the individual level a little bit more seriously. I think that when somebody shows — or a society shows — this is how much more we’re willing to put in to keep you alive, we should be able to learn something about welfare from that. So I do think this is inspiring as a direction. But for our actual numerical intuitions about how much life has gotten better or worse — yeah, I’m still in the same place. GDP per capita has overestimated welfare in the past. Maybe we’ll overestimate it a little bit less in the AI age; 80% chance it will. Haven’t really moved from that. And my initial estimates about how much welfare has changed since 1940 or 1980 haven’t changed. But maybe I’m just a little bit more optimistic about the method.
45:10Andrey: Okay, cool. Well, thanks for joining us for another episode of Justified Posteriors. Please let us know if you enjoyed this episode, or any other topics you’d like us to cover, and make sure to like, comment, and subscribe.
Seth: And always keep your posteriors justified.