Skip to content

Who are you gonna believe, me or your lying eyes?

This post is by Phil Price, not Andrew.

A commenter on an earlier post quoted Terence Kealey, who said this in an interview in Scientific American in 2003:

“But the really fascinating example is the States, because it’s so stunningly abrupt. Until 1940 it was American government policy not to fund science. Then, bang, the American government goes from funding something like $20 million of basic science to $3,000 million, over the space of 10 or 15 years. I mean, it’s an unbelievable increase, which continues all the way to the present day. And underlying rates of economic growth in the States simply do not change. So these two historical bits of evidence are very, very powerful…”

One thing any reader of this blog should know by now, if you didn’t learn it long ago, is that you should not take any claim at face value, no matter how strongly and authoritatively it is made. Back In The Day (pre-Internet), checking this kind of thing was not always so easy. A lot of people, myself included, would have a copy of the Statistical Abstract of the United States, and an almanac or two, and a new atlas and an old atlas, and a CRC datebook, and a bunch of other references…but honestly usually we just had to go through life not knowing whether a claim like this was true or not.

But now it’s a lot easier to check this sort of thing, and in this case it’s especially easy because another blog commenter provided a reference:

So I look at that page, and sure enough there’s a nice graph of US GDP per capita as a function of time…and the growth rate is NOT, in fact, the same after 1940 as before!

US per capita GDP from late 1800s to 2011, in 2011 dollars; y axis is logarithmic

I have done no quantitative calculations at all, all I’ve done is look at the plot, but it’s obvious that the slope is higher after 1940 than before. Maybe the best thing to do is to leave out the Great Depression and WWII, and just look at the period before 1930 and after 1950, or you can just look at pre and post 1940 if you want…no matter how you slice it, the slope is higher after WWII. I’m not saying the change is huge — if you continued the pre-WWII slope until 2011, you’d be within a factor of 2 of the data — but there’s no doubt that there’s a change.

I pointed out to the commenter who provided the link that the slope is higher after WWII, and he said, in essence, no it isn’t: economists agree that the slope is the same before and after. So who am I gonna believe, economists or my lying eyes?

I have no idea about the topic that started the conversation, which is whether government investment in science pays off economically. The increase in slope after WWII could be due to all kinds of things (for instance, women and blacks were allowed to enter the workforce in ways and numbers not previously available).  I’m not making any claims about that topic. I just think it’s funny that someone claims that the “fact” that a number is unchanged is “very, very powerful” evidence of something…and in fact the number did change!

This post is by Phil.


  1. Divalent says:

    And why couldn’t science funding be one of the things that allowed GDP growth to continue? (vs leveling off.) And anything else that is common and obviously economically important now, but wasn’t long ago? Motor vehicles. Interstate highways. Telephones. Satellites. Plastics. Microelectronics and computers. Etc. Etc. Etc.

    • Joshua says:

      > And anything else that is common and obviously economically important now, but wasn’t long ago?

      Not to mention, direction of causality. Presumably, a slower-growing economy could mean less money available to spend on science.

    • Reverse Nostradamus says:

      What I was thinking was what would be the economic importance of e.g. plastics or telephones if those hadn’t been invented?

      • confused says:

        To be fair (and I do support science funding!) I think the argument is that those things weren’t developed using government funding. (Both plastics and telephones do predate 1940, though I don’t know how much of the vast diversity of current plastic types was developed using government funding).

  2. Jim says:

    I am not familiar with Maddison dataset that this graph uses, and I don’t have time to research in depth, but my initial response to these exercises is to not to jump to conclusions. The measurement of economic statistics went through a revolution in the 1940s.

    Without first understanding the quality of the data used in this case to stitch the series together before and after the breakpoint, I hesitate to make any strong conclusion.

    • Phil says:

      Me too! I’m just pointing out that one thing that these data do NOT show is that the rate of increase of GDP per capita is the same after WWII as it was before. The supposed constancy of that number is, according to Terence Kealey, “very strong evidence” for a particular proposition. But the data presented to bolster the claim do not in fact show that the rate is constant.

      It’s (yet another) illustration of why it’s important to go back to the data and not simply take people’s word for things, even for simple statements of ‘fact’ …the fact here being that this particular dataset supposedly shows a constant slope, which, in fact, it does not. Kealey (or anyone else) can certainly say that the data are no good, or that the slope changed but for some other reason, etc.; but one thing they can’t say (or at least shouldn’t say) is that this dataset indicates that the rate is constant.

  3. James Annan says:

    This seems a fairly trivial gotcha, in the absence of any discussion of the magnitude (significance?) of the change. Of course the trends in two distinct real-valued time series will not be identically the same to 16 significant digits, and it does not seem plausible that the blog author believed that this was meant. Therefore, the debate hinges on whether the difference exceeds some threshold. Is it obvious that it does? Hard to tell.

    • Brent Hutto says:

      Sure looks like a small difference in slope to me.

      If I were verbally describing that graph, I’d probably say the slope has remained nearly constant for more than a century with the exception of the 1930’s and early 1940’s.

      Not much of a gotcha based on visual inspection of the graph. Looks like a prime candidate for one of those overfitted change-point models this blog detests.

    • Yes, it comes down to the magnitude. Clearly the magnitude of the change is enough here that by eye you can see that there’s a hinge at around 1940 and after that we have enough higher growth that by 2000 the GDP/capita is maybe 40k/person and without the increase in rate it would have been maybe 30k/person (just eyeballing).

      I think most people in 2000 wouldn’t have called $10k per person trivial, so the change is non-trivial.

    • Phil says:

      James, nobody (sane) is talking about 16 significant digits. The slopes before and after 1945 (or any date around then) are easily seen to be different. By the time you get to 2000 or 2010, you get a noticeably different value for per capita GDP if you take the pre-1945 slope vs what actually happened. “Noticeably different” meaning something like $8-10K different — I pretty much agree with Daniel Lakeland’s eyeballing — or roughly $3 trillion in GDP out of about $13 billion at the time.

      I don’t think this is anything like negligible in the context of the discussion about whether the government is getting its money’s worth. I’m not talking about whether two things are “identically the same to 16 significant digits.”

      I am absolutely NOT claiming that the government is getting its money’s worth, as I said in the post. But if someone claims that “underlying rates of economic growth in the States simply do not change”, when in fact the change is easily seen on a graph and leads to a $3 trillion difference in outcomes, I think the burden is on them to explain why they think the change is too small to matter.

  4. J79J says:

    GDP is a very coarse, controversial economic assessment and a very odd place to first turn to regarding the original issue raised here.

    Ultimately, GDP measures nothing more than how many dollars were “spent” in the national economy on arbitrarily selected goods and services.

    Government “spending” is a major factor in the GDP total, even if the government spent it building 10,000 Hula-Hoop factories.

    • Phil says:

      I don’t disagree! I’m not the one arguing that GDP per capita is the way to judge the value of scientific research (or of anything else).

      But if someone _does_ choose to hang his hat on “per capita GDP growth” as the metric that matters, they shouldn’t claim that it’s constant when it isn’t.

  5. Peter Gerdes says:

    You should give more context for that quote. If the point of the quote was that the US increased science funding way faster than they increased in wealth then the change in slope at 1940 is trivially small and irrelevant.

    OTOH if the point of the quote is to suggest that science funding had no effect on rate of growth then the change in the graph isn’t so small as to be insignificant for that claim (implicitly, the relevance to that discussion is whether it was worth 3 billion a year so even a tiny change matters).

    • Phil says:

      Peter, good point.

      Kealey’s argument is that government funding of science has not resulted in increased GDP per capita, and has therefore been wasted. I think he would agree that there is some not-terribly-large multiplier A such that, if government science funding of $X per capita results in an increase of GDP per capita of at least $X*A, then it’s worth it. For the sake of this argument, the increase in the growth rate of GDP does not have to be very large at all. I guess I figured that was obviously what Kealey was arguing, but I probably only thought it was obvious because I read a lot more than that one paragraph.

      • Zhou Fang says:

        Hang on. Kealey’s argument doesn’t make sense. If government funding of science has been wasted, it should not lead to a *consistent rate of GDP growth*. It should have presented a fiscal drag and reduced growth. Even if you accept that the growth rate is unchanged, the conclusion would be that the government is getting *exactly* its money’s worth, no more, no less.

        • Joshua says:

          The entire causality argument is so weak…I’m surprised people are taking it seriously. Hmmm. Or maybe not.

          Seems to me there is not particular reason to assume a causal mechanism. There are an infinite number of potentially causal factors that would influence GDP growth. And as I said above – there’s no particular reason to assume either direction of causality even if we do assume an particularly explanatory causal relationship.

          As a justification, there could be all kinds of reasons to support spending on science other than GDP growth, basic stuff such as increased longevity, nutrition, health, quality of life, etc.

          This seems to me like basic “correlation doesn’t equal causation” stuff…it’s amazing that smart and knowledgeable people, who work all the time in analyzing causality, are engaged as if the causal mechanisms would be clearly implied by an association.

        • I think it’s worse than that… The growth rate is an exponential growth rate. Whereas science expenditure is what? Constant in time (in real dollars?) or itself growing exponentially? And if growing exponentially, at what rate?

          Presumably if science expenditure is say 5% of GDP and grows at say 1.2%/yr and because of that GDP overall grows at 1.99%/yr instead of 1.69%/yr then in the 10th year we’re spending .05*1.012^10 = .056 (of base year GDP) in order to make an extra (1.199/1.169)^10 = 1.288 (of base year GDP)

          which is a HUGE win

          • Steve says:

            +1 Exactly, let’s take a historical example to hammer home the point. One of the projects, that the U.S. government funded was something called the Manhattan project. During the course of that project John von Newman conceived of the first programmable computer, which they built. How much of our economic growth can be attributed to that one invention? You can have an enormous amount of failed science projects before you would drag down the growth associated with a few success like the programmable computer, the satellite, GPS, the internet, etc. By the way 20% of our energy in the U.S. comes from nuclear power, which was, of course, the main point of the Manhattan Project.

            • I really think the attribution of the additional growth rate to science funding is very tricky. But I totally agree with you that science funding is a “long tailed” thing, where the average has almost nothing to do with the typical outcomes. Most science may well be within epsilon of zero with some things plus and some minus… but every so often this system will throw off something like GPS and make shipping a bazillion tons of freight around the entire planet say 10% more efficient, or software defined radio protocols that allow us to use radio spectrum 1000x more efficiently.

              I hope eventually we do get some kind of fusion reactor. I hope we eventually get some cheap organic molecule that converts sunlight to electricity even at low efficiency, but very low cost… so that solar panels that produce a kW cost $20…

              But in the end, my real point was people aren’t even comparing things that are comparable. If you want to talk about comparing science expenditure (dollars / yr) to GDP growth rate (1/year) through time… then you need to look at something that compares science expenditure to GDP through time, something like:

              limit t-> inf: (d/dt GDP+) / (d/dt GDP-)

              where GDP+ is the GDP with the science expenditure, and GDP- is the counterfactual without.

              • confused says:

                Long tailed… exactly.

                And also long payoff times. Transistors were invented in 1947 for example, Bakelite (first synthetic plastic) in 1907, etc. But it took ages for electronics and plastics to really change the world.

                (If fusion does happen, though, I’m not sure it will come from the government projects… things like the NIF seem very unlikely to produce anything practical. They’re more physics projects.)

            • Bob76 says:

              Well, just to be picky. Maybe JvN’s thoughts on computer organization were both (1) original and (2) funded by the Manhattan Project. Even so, the computer would have been invented about the same time. JvN’s famous report was funded by the Army as part of the EDVAC project. JvN knew Turing at Princeton. That was after Turing published his description of a theoretical computer that could operate on a program that was stored in the same memory as the data (key concept in the Von Neumann architecture). So, JvN’s ideas were influential but progress on the computer was well underway when he wrote his report. See also Harvard-Aiken Mark I, Colossus, etc.

              Arguably, the MIT Radiation Lab and the Harvard Radio Research Lab (radar and radar countermeasures respectively) had an enormous stimulating impact on the post-war electronics industry. The head of the HRRL was Fredrick Terman—later known as one of the founders of Silicon Valley.

              For some interesting perspective on this, see Chapter 6b is a good short version.

              • Steve says:

                Turing’s work was also funded. Look, I agree with Daniel that attributing economic growth to scientific funding is extremely tricky. But, if you are going to try you have to acknowledge the extreme fat tailed nature of the payoffs. Also, the idea of a universal computer goes back at least to Leibniz. I thomltrying to claim that something would have happened even if the timeline were different is even speculative than figuring out the return on science funding. The truth is WWII happened and the US and Britain hired a bunch of theoretical physicists and mathematicians who changed the world. It could have happened another way, but it didn’t.

  6. I don’t understand this post. (Or, if I understand it, I disagree with it!) Isn’t a key aspect of thinking properly about statistics, implicit in every (correct) criticism of null hypothesis significance testing, that it is silly to ask if things are “the same” or “different.” Everything is of course different from everything else. Is the rate of increase of GDP per capita after 1940 different than than the value before? Of course; it is impossible for them to be the same to infinite precision. It is meaningless to argue about whether this rate is constant or not, without stating what you (Phil) and your opponent mean by “same” or “different,” which neither of you have done. (And the burden of this certainly falls on Phil.)

    You may reply that it is “obvious” what same or different means, but as the above comments note, it is not. I’d say the slopes are pretty much the same, to the precision that anyone would care about them.

    One could, of course, compare the difference in slopes to the uncertainties in the slopes. This is often a great, practical way to assess whether things are similar or not. Doing this will show that the change pre/post 1940 is large compared to the slope uncertainty, so the values are “different.” (With the assumption, of course, that the uncertainty in the slope completely captures the uncertainty in the data — doubtful for old data.)

    Or one could compare pre/post differences in slope across countries, which I would guess would show that the US change is small compared to others, so the pre/post US values are “the same.” (I tried this for the Netherlands; pretty radically different.).

    Anyway, this is fruitless.

    • Phil says:

      Raghu, I disagree. See my comment to James Annan, above. I’m not quibbling about whether two numbers are identical to 16 decimal places, I’m talking about differences that are easily big enough to be relevant to the topic under discussion.

      • “…easily big enough to be relevant to the topic under discussion” is not self-evident from the graph. You’re comparing what’s “obvious” from eyeballing the graph to what *you* think is a relevant magnitude for the topic under discussion. You may be right that it’s relevant; you may be wrong; neither is obvious.

        • Phil says:


          You’re right that I should have given some more context for the relevant scales, a point Peter Gerdes made above. By the time I wrote the post I had read the comments on the earlier blog posts about this, plus the Scientific American interview with Kealey, plus the Nintil post from which I took the graph, so it was ‘obvious’ to me what the relevant scale is. But clearly not obvious to everyone.

          As for what scale of is relevant here, that scale is set by the size of government expenditures on science. If the government is spending $300 per person per year on science (a number I just made up), Kealey thinks that is wasted unless there is a resulting increase in GDP per capita that has a net present value of something more than $300. For the sake of argument I’m willing to accept GDP per capita as a metric, so then the question is, is the change in the growth rate of GDP per capita so flat that its flatness is a “very, very powerful” argument that government funding of science does not affect the growth rate of GDP per capita on this sort of scale. So I look at the plot and am surprised to see that the GDP per capita in 2005 appears (to me, based on the plot) to be 30-50% higher than it would have been if the pre-1945 growth rate had held all the way through to that time. I don’t actually know what the government investment in science has been, and I also am skeptical that all or even most of the increased slope is due to government investment in science, so I make no claims that that difference proves anything about the question. But it is clear (to me, anyway) that the difference is easily large enough that it’s wrong to say that there has been no increase. Kealey says “underlying rates of economic growth in the States simply do not change”, and it is not a pedantic argument to point out that that isn’t true. I’m not talking about a difference between 2% growth and 1.995% growth, more like a difference between 2% growth and 1.9% growth. On the scale of the question, that’s very relevant.

  7. jim says:

    GDP growth is clearly bang on the line from 1918 onward sans depression/WWII. Prior to that there are longer periods with flatter or steeper slopes, but 2% is a reasonable eyeball. Whatever the case, we don’t have to eyeball because the rate has been calculated: Here’s a quote from the author (link).:

    “As per Maddison’s GDP data, RGDP per capita growth in the US has been 1.76% on average since 1800. Taking the time series from 1870 would yield 1.95% instead. ”

    Here’s another quote from the author:

    “in the spirit of Donald Knuth I’m launching the “Prove me wrong, earn money!” rewards program. It covers everything I’ve published since 2017-01-01 and onwards.”

    There’s even a fee schedule:

    Minor argument, doesn’t affect conclusion 4$
    Major point, invalidates a section’s main point 20$
    Fundamental error, entire article is wrong 200$

    So Phil, give it a go! Ask the author to calculate the 1870-1940 GDP per capita and let us know the result.

    • Phil says:

      I don’t think the plot invalidates anything in that Nintil blog post. The author of that post doesn’t make any strong quantitative statements; certainly nothing as strong as Kealey’s claim that the per capita economic growth rate doesn’t change with time. Indeed, he shows plots of ‘productivity’ growth rate as a function of time and it clearly is not constant. His argument — I assume it’s a “he” but maybe not — is that the growth rate is _approximately_ constant, not that there are no practically significant deviations at all.

      Kealey’s argument, on the other hand, is that government funding of science doesn’t do anything good at all as far as GDP per capita is concerned. Even if we accept Kealey’s metric of ‘GDP per capita’ as the right way to evaluate worthiness, It really wouldn’t take much additional growth to make government investment worthwhile. When Kealey claims there is _definitely_ not enough of an increase in slope — the slope is so flat that this is “very, very powerful” evidence against a positive effect — that is an extremely strong claim. In fact there is an increase in growth rate, although very slight…but still, exponential growth being what it is, it’s enough to have a very substantial effect over time. Per capita GDP in 2005 was something like 30%-40% higher than it would have been if the pre-1945 growth rate had applied for the entire post-1945 period. In the context of Kealey’s argument, that’s a long way from “unchanged.”

    • I’m tempted to grab the data:

      and do the regression to get the coefficients using GLM in Julia but honestly it’s probably not a good use of my time. Though I need the practice with munging data in Julia… but it comes in one of my least favorite forms: xlsx files, ugh.

      The easiest way would be to simply print the graph, and then lay a ruler along the pre-1930 data and the post 1950 data and just read off how big a change it was…

      It’s clear that by 2000 there was 20-30% higher GDP/capita compared to if the pre 1930 trend were extended linearly. This is sufficiently large that I think it matters for the question at hand. That’s basically enough. Phil is clearly right about that. On the other hand, just proving that there is a difference in trend-line doesn’t do anything in terms of proving one way or another whether investment in science by the government was responsible for this increased growth.

      • Ok. I admit, I went and did the Julia thing… here’s before vs after:

        julia> fitbefore = lm(@formula(log(USA) ~ year),gdpdat[(gdpdat.year . 1870),:])

        :(log(USA)) ~ 1 + year

        Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95%
        (Intercept) -23.3714 0.752535 -31.06 <1e-36 -24.8783 -21.8645
        year 0.0169035 0.000396055 42.68
        julia> fitafter

        :(log(USA)) ~ 1 + year

        Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95%
        (Intercept) -29.1885 0.624191 -46.76 <1e-50 -30.4354 -27.9415
        year 0.019929 0.000314677 63.33

        So after 1950 growth rate is 1.93 percent, between 1870 and 1930 growth rate is 1.69 so the difference is about 0.3% which is about 18% increase over the pre war rate.

  8. Yuling says:

    Curve fitting is hard. The one who created this graph could argue he knew the annual GPD numbers were not on a straight line a priori. Indeed he could even compute the R^2, and that would be a very large number in this graph, large enough to seemly make it convincing that it is a good fit. On the other hand, there are many degrees of freedoms here. Should I leave WWII and great depression at all? Or should I subtract their shock from the next few years as those represented a decompensated growth? Should I adjust multiple compassions when I have already used the graph to pick 1940s as a change point? Should I trust early GDP and GDP deflator?

    That said, given a statically deceasing population growth rate, it is impossible to have a both constant GDP growth rate and a constant GDP per capita growth rate. You should ask the economist to pick one to support.

    • Phil says:

      Yuling, you’re right. I, for one, am not arguing that these numbers mean anything in particular. But Kealey is. Specifically, he is arguing that the growth rate did not change after 1940, which he claims is “very, very powerful” evidence for his argument. But the growth rate did change, from (via Daniel Lakeland) 1.69% to 1.93%. People can argue about whether that’s a big difference or a modest difference, and I suppose someone could even argue that it’s a small difference, but I don’t think a reasonable person could say it’s a negligible difference.

      Interesting point about GDP vs GDP per capita, thanks for pointing that out!

  9. Dimitris says:

    The original argument does not provide the funding of basic science *per capita*. We can therefore assume that the “legal” inference would be about change in GDP and NOT in GDP per capita. I think that in what he calls “underlying rates of economic growth” you cannot find a “per capita”.
    Actually, there are 2 more graphs back in one for population growth which displays a change of slope at the same point as GDP per capita. And the second one is GDP, which is remarkably constant — and we don’t know why.
    Now, GDP = GDP per capita * population, so the perceived kink in the per capita graph is simply due to baby boomers saying hello. The unexplained bit of info is that although the population changed abruptly, although tech funding exploded and although a million other things also changed, the GDP rate kept calm and didn’t change.

  10. Hi, I’m Jose Luis Ricon, ths author of and regular reader of statmodeling. I saw where someone linked to a post I did on GDP growth trends. I agree with you that the trend post-WWII is different from the pre-WWII one. In fact, it may not even be the same after the great financial crisis . The point of my post was not to say that the best explanation for GDP growth is a single trendline that spans centuries, but to try to say why don’t we see 10x changes in growth rates.
    On the concrete question of trend breaks, Kealey, etc, I do think the evidence is compatible with what he is saying, I wrote a post on that . But note that different time series yield different results (Or, if one looks at TFP rather than GDP to look at productivity, different ways to calculate TFP, what to do about the post-WWII population boom etc).

    • Phil says:

      Thanks for weighing in. As I noted in a response to jim (above), I saw that your blog post did not claim that there are no practically significant changes to the growth of productivity, just that it doesn’t vary a whole lot. I agree that’s a very interesting observation that merits explanation. I didn’t see anything in your post that makes me think I could earn money by disagreeing with it!

  11. Dale Lehman says:

    I’ll admit it – I am an economist and I have not kept up with the field (at least not like I did in past years). But the quote “he said, in essence, no it isn’t: economists agree that the slope is the same before and after” is crying out for some type of citation. If you had asked me if I thought the slope was approximately the same (or even similar), I would probably have said “I don’t know.” So, if this is generally agreed upon, that’s news to me. And, if this just shows how out of touch I am with the profession, then I guess I’m thankful for that.

    • Phil says:

      The claim that “economists agree” there wasn’t a change in growth rate after WWII was made by a blog commenter. I didn’t actually take it seriously. After all, it’s economists who are behind this data collection in the first place, and they do quantify things like changes in productivity with time.
      But it’s certainly true that Kealey claims there was not a change that is of practical significance — you can find the Scientific American interview from which I pulled the quote. So _some_ economists make that claim. But since the claim is false, it would be very odd indeed if “economists agree” about it.
      For that matter, it would be very odd indeed if economists agree on anything. If you want three opinions, ask two economists!

  12. J Storrs Hall says:

    If you look closely at the curve, I think you’ll find that during the 20’s it tracks the blue trend line just about as well as it does after 1950. Clearly before 1920 the slope was lower. So the GDP/cap was accelerating (relative to the constant growth factor trendline) before government research funding, and flatlined thereafter.

  13. Phil says:

    I think it’s fair to look at the data and try to figure out where things happened and how big they were.

    Back when I was in high school, the standard teaching about the Roaring Twenties and the Great Depression was that the Roaring Twenties were fueled by unwise investment — essentially a big bubble — and the Great Depression was the result. But somehow the Dust Bowl played a role too. I’m not sure whether it’s the message that was unclear or whether I just wasn’t paying attention in history class. (The latter is definitely true, I’m just not sure about the former). Anyway I’d guess every bump and wiggle in the graph has an explanation, although some of them may be reporting errors of some kind.

    If you were trying to make a case for government investment in science causing a change, you could argue that the 1920s bump and the 1930s depression go together so you should either include them both or exclude them both, and either way you get a slope change in the 1940s. But you can make a Just So story about anything, and I wouldn’t hang my hat on any of them.

    Really I think “GDP growth” is not nearly a sharp enough tool to dissect what is going on with the effect of government science funding. If it really were constant then maybe Kealey would have an argument based on this, but since it isn’t, he doesn’t.

    • Phil, one thing I think is wrong with social science is that people haven’t figured out dimensionless analysis…

      If I wanted to use GDP as a measure of human welfare (which it’s not great at) I’d look at integrate(GDP/capita / CostOfGoodsBasket,t=t0,t=t0+life_expectancy(t0))

      Where CostOfGoodsBasket would be a basket of very basic goods that need to be consumed each year: food, shelter, clothing, education, healthcare

      Note two things about this measure:

      1) It’s dimensionless (GDP = dollars/yr, capita = a count, CostOfGoodsBasket = $, and the variable of integration = dt = yr, so the units are dollars/yr /dollars * yr = 1

      2) It depends on the entire expected lifetime of a person born in year t0, for all t0… so it is a function of the “whole life experience of a person born at time t0” rather than basically “what happened just in t0”

Leave a Reply