Follow-up on "How rich would 1 billion Americans be?"

Causality is tricky, but the policy implications are clear.

Apr 09, 2024

I got a good number of comments on my post "How rich would 1 billion Americans be?" so I thought I’d write a follow up12.

Can the correlation be used as a forecast?

One point made by several people is that the correlation between population and wealth can’t be used to forecast the future. In the post, I don’t claim to predict the future, but I do say that “… there’s an argument to be made for this being a good forecast of the future conditional on the U.S. actually growing.”

I think this claim stands. Assuming that the process that produced the correlation continues to operate in the future, the trend will hold at higher populations. It doesn’t matter what the causal relationship is for the forecast to work. Cumulative U.S. Nobel laureates and cumulative U.S. gold medalists are probably pretty correlated, because both series grow linearly with time. It’s unlikely that there’s a direct causal effect, but we can still forecast things into the future just fine.

Research on the relationship between population and wealth

The correlation alone isn’t enough, we want to know something about the causal relationship between wealth and population in order to inform policy.

After looking at the literature more, there’s a clear bifurcation between theory and experiment. In growth theory, it’s pretty common to assert that population plays at least some role in driving innovation. But empirically, the situation is messier. From this review:

Regarding causality (Granger causality), a diverse range of outcomes is observed.
(1) p → y, unidirectional causality, population growth stimulates economic growth: Darrat et al. (1999), Yao et al. (2007), Liu et al. (2013), Ali et al. (2013), Furuoka (2013), Musa (2015) and Sebikabu et al. (2020).
(2) y → p, unidirectional causality, economic growth stimulates population to grow: Nakibulla (1998).
(3) p <=> y, bidirectional causality, population growth stimulates and is stimulated by economic growth: Garza-Rodriguez et al. (2016), Alvarez-Diaz et al. (2018) and Furuoka (2018).
(4) Noncausality, population growth neither stimulates nor is stimulated by economic growth: Dawson and Tiffin (1998), Thornton (2001) and Mulok et al. (2011).
(5) Mixed results: Jung and Quddus (1986), Kapuria-Foreman (1995), Tsen and Furuoka (2005) and Chang et al. (2017)

It’s also informative to break down population growth down into growth from immigration and growth from fertility.

For immigration, there’s a consensus among economists that both high-skilled and low-skilled immigration is good for U.S. citizens. The literature finds generally positive impacts of immigration on local economies in the U.S.

For fertility, I haven’t been able to find research that looks at how fertility causally effects long term growth34. I’m tempted to say that babies today are just immigrants from the future, meaning that their impacts on the local economy should be similar to that of immigrants, just displaced in time by 20 years. But things get more complicated when you consider the time parents spend raising their children, which temporarily reduces their productivity. For now, I’m going to assume that native fertility also boosts local economies in developed countries until I see evidence to the contrary.

Causality and policy

So the empirical data is messy, let’s list the possible causal relationships between population and wealth:

Population causes wealth.
Wealth causes population
Population and wealth cause each other
Some other variable causes both
There’s no relationship whatsoever between the two

That being said, its hard to make the case that 4 and 5 are true and that population has no effect on wealth at all. To steelman the argument, I can think of two theories where this might be the case:

The Hephaestus model where only a fixed number of researchers contribute to innovation at a given time. Perhaps only the 100 most talented researchers drive virtually all of the innovation, regardless of the size of the population. Norman Borlaug could be one example.

I'm pretty skeptical of this story, for one, the number of researchers has been increasing for a long time, how could they have no impact? For another, our fixed set of innovators would have to increase in productivity over time to keep raising per capita GDP for a larger and larger population. This isn’t consistent with data showing that research productivity has declined5.

Technological determinism is another possibility. Perhaps technology marches to the beat of its own drum: one innovation follows another in a natural progression. When the time is right, someone discovers electricity, a predetermined time later someone invents the lightbulb, and after that someone figures out how to manufacture lightbulbs at scale. It doesn’t matter who does what, discoveries will occur when the time is right. The steady pace of progress would cause both population and wealth to rise in lockstep without any causal relationship between them.

I think this is more plausible and one argument in its favor is multiple discovery, evidence that some ideas are simply “in the water supply” and arise naturally within a particular context. You can also see a steady progression within an established field like semiconductor manufacturing, where low-hanging fruit gets picked and the industry collectively moves on to other ideas in a relatively predictable fashion.

But this can’t be the whole story, since many of our most important inventions came from intentionally investing a lot of effort, such as Haber-Bosch, high-yield wheat, nuclear weapons, and Moore’s law. Perhaps the timing of these efforts was predestined, but we had to actually throw more people and money at the problem to get a result.

Regardless, the technological determinism story can’t be used to argue against population growth policy. Even if we granted that innovation happens independent of population, we might as well let the population grow; it won’t harm wealth.

In fact, notice that all the options except 2 recommend population growth policy. If 1 or 3 are true, then we can get both by boosting the population. If 4 or 5 are true, then we can boost population without effecting wealth, which is still a good thing (see footnote 1).

So let’s focus on option 2. If wealth drives growth, external increases in population could potentially reverse the correlation between the two and make everyone poorer. Something like this was true in Malthusian eras of the past; temporary increases in crop yields led to more children being born which lead to deaths of starvation when yields regressed to the mean6.

What about today? Let’s once again break population growth down into growth from immigration and growth from fertility.

Setting aside the previous discussion of the benefits of immigration, can wealth also cause immigration? Some papers do find that rising wealth also causes more immigration to a country. But while rising wealth causes more people to want to immigrate to a country, policy determines how many actually do. In recent decades, immigration rate to the U.S. has been falling even as RGDP per capita increases. It’s hard to make the case that wealth causes more immigration if this trend continues.

What about fertility? Does wealth cause more births? In practice, richer countries tend to have lower fertility and fertility falls as countries grow richer over time. At the micro level it seems intuitive that wealthier parents would have more children, but instead we see lower fertility at higher income levels. Like with immigration, it’s hard to argue that wealth causes higher fertility when the two are inversely correlated.

Taken together, these facts make it unlikely that option 2 is the dominant contributor to the correlation between population and wealth. This leaves us with options 1, 3, and 4, which suggests that population causes wealth to some degree.

Conclusion

The correlation between population and wealth remains a mystery. Will the forecast hold? What is the causal relationship between wealth and population? We could devote an entire book to these topics, but we already have enough information to take a stance on policy.

With falling fertility, we have two choices: intervene to try to return to population growth or allow the population to stagnate. Pro-growth policies probably won’t cause per capita GDP to fall, which means that sustainable increases in fertility and immigration in the U.S. are a good idea long term78. Better yet, pursuing population growth and economic growth simultaneously would address concerns that we have the arrow of causation backwards.

Will policy intervention destroy the fortuitous correlation between population and wealth? Perhaps. But historically, the relationship between the two has been robust to shocks such as legislation, generational shifts, war, and mass migration. It’s unlikely that small policy changes will have an impact9.

Even accepting the value of population growth, some argue that there’s no need to grow the U.S. population since it’s really world population that drives innovation, not the population of a particular country. This is less true than we might hope. The U.S. produces a disproportionate amount of global innovation and moving to the U.S. directly causes people to be more productive. Technology has to be passed down through training for it to be effective and without a way to pass down tacit knowledge, technology can get lost. Just look at how hard it is for countries to establish semiconductor fabs or import fracking technology. For these reasons, it’s also important that innovative countries continue to grow.

Others argue that we should instead boost innovation with interventions like better education or scientific funding reform. I support these initiatives, but they’re not an argument against simultaneously pursuing population growth. Devoting attention to one thing doesn’t take resources away from another thing; this model of scarce attention is usually a bad framing.

Turning to the emotional part of this debate, people react to the prospect of population growth like people react to cilantro. Most are fine with it, but some people find it disgusting. I think if we can set aside our emotional reactions to these ideas, the pro-growth and anti-growth factions can find a way to build a better world. The wealth created by steady population growth can help us birth the first sustainable generation, heal nature, and ensure that this prosperity is shared with everyone.

A particular thank you to GrandBurdensomeCount for offering a better way to do the statistics. My initial attempts to redo the analysis based on their suggestion gave me conflicting results. I realize that I should really use data that disaggregates fertility and immigration and applies different lags to each. For now, I’m going to lean on the published research instead of my own analysis.

For the purposes of the discussion, I’m going to assume that having more people with higher consumption is a good thing and that it’s feasible to have 1 billion people living in the United States (see here for more discussion of the latter point).

In lieu of a full argument for more people and more consumption, I’ll note that:

In population ethics, neutrality about happy lives is uncommon amongst the general population and academic philosophers alike. In other words, most people share the intuition that more happy people is a good thing, all else equal.
Few would argue that consumption is bad in and of itself, but many are concerned with the impact of higher aggregate consumption on the environment. This deserves a more thorough treatment, but for now I’ll point out that total land use has stayed pretty flat for over 80 years, despite population growing by over 260% in that time. As for pollution, per capita emissions have been falling across the world for decades, I see no reason why they can’t hit net zero. Regardless, if population really does drive innovation, more people means more clean technology development, a boon for the environment.

If you know of research like this, send it my way!

There has been some interesting work on whether the correlation between a country’s fertility and wealth reverses at high enough incomes. Though see the debate here.

Even if we had strong evidence that world growth is propped up by an unchanging number of highly productive researchers, I would still be trying to train more of them evidence be damned.

“Capital dilution” is another theory of how higher population could reduce per capita wealth.

I want to emphasize that I’m not advocating for drastic measures, returning to replacement fertility for example is achievable with relatively small policy changes.

Even if I’m wrong, we benefit from learning as we go. If RGDP stagnates you can simply stop doing population growth policy, having learned how to boost growth and knowing more about the causal relationship between wealth and population. Doing nothing leaves us in the dark.

Even if it did, it’s not clear that that would be a bad thing. If policy successfully raises population and wealth at the cost of eliminating the correlation between the two, has anything really been lost? Choosing subsequent policies is harder once the correlation is gone, but a win is a win.

ScottB

Apr 17

GDP per capita is not a measure of wealth, it’s a measure of income. We don’t have great measures of wealth, particularly for natural resources or environmental wealth, but it’s not a stretch to assume that our wealth has been declining—climate change, microplastics, forever (and other) chemicals, exponentially growing use of minerals, deteriorating infrastructure, etc. A billion people in the US would probably result in a faster decline of wealth, which at some point shows up in income. I’m open to other opinions with some evidence.

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J.K. Lund

Apr 10

Great follow up piece Sam. Its stands to reason that more people creates more opportunities for breakthrough ideas and innovations that help propel economic growth.

I am somewhat sympathetic of the technological determinism argument. As I and many others have noted, innovations seem to come about simultaneously, invented by different individuals at the same time: https://www.lianeon.org/p/invention-vs-innovation

But as you note, there are those ‘Moonshot’ projects that defy this phenomenon, whereby throwing enough resources at a project, we can dramatically accelerate the course of innovation.

I contend that landing humans on the Moon was a 21st Century event that was supposed to take place after the invention of reusable rocketry. Instead, the government invested a significant percentage of GDP into the Apollo program that pulled the event into the 20th Century instead, albeit at a cost that was unsustainable.

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