Five countries generate half of Africa's GDP

GDP growth projection for 2025:

🇪🇹 Ethiopia: 6.5%
🇰🇪 Kenya: 5%
🇪🇬 Egypt: 4.1%
🇲🇦 Morocco: 3.6%
🇳🇬 Nigeria: 3.2%
🇩🇿 Algeria: 3%
🇦🇴 Angola: 2.8%
🇿🇦 South Africa: 1.5%

According to IMF.

— Stats Globe (@statsglobe) August 2, 2025

AI and economic growth: Short-term vs. long-term constraints

Here's Arnold Ling's whole column (title above) for June 30, 2025:

Luis Garicano writes,

When productivity crushes prices, quantity must rise proportionally to maintain economic weight. But we don't use 40,000x more light than in 1800. Maybe 100x. Human demand has limits.

Pointer from Tyler Cowen. My thoughts:

1. I don’t like using light as an example, because it is not as if a general-purpose technology suddenly appeared. You can argue that the electric lightbulb appeared suddenly, but I think that by that point in history it was not some enabling technology that was going to increase productivity everywhere.
2. That said, the point is well taken that there are sectors of the economy where productivity grows faster than demand, so that relative prices fall. And there are sectors of the economy where demand grows faster than productivity, so relative prices rise.
3. The classic example for many decades is that productivity has risen faster than demand in food and material goods. Demand has risen faster than productivity in health care and education. Hence, Mark Perry’s famous Chart of the Century, which I think people get carried away with.
4. The electric motor was a classic general-purpose technology that eventually pushed productivity up faster in manufacturing than in health care or education.
5. Computers and the Internet are also general-purpose technologies. It seems to me that their big effect showed up in finance and logistics, with Wall Street exemplifying the former and Wal-Mart and Amazon exemplifying the latter.
6. Some people see the new AI models as a general-purpose technology. I believe that is true with 90 percent probability.
7. In the short run, the gain in productivity from AI will appear with a lag, for the same reason that general-purpose technologies always increase productivity with a lag: slow diffusion and cultural resistance.
8. In the long run, the question is how much AI can improve productivity in health care and education. The potential seems quite high. If the gains do show up there, that will break the pattern of the last century-plus. As productivity in those sectors eventually grows faster than demand, relative prices will fall, and resources will move elsewhere. I would bet that we are at least two or three decades away from reaching that point.
9. Because the mix of goods and services shifts so much as technology changes, long-run comparisons of GDP are not at all precise. It is brave to try to come up with a single number that compares an economy that produces horseshoes and wheat to an economy that produces smart phones and pizza delivery.

Garicano's tweet, referenced by Kling, is the first in a stream that eventually points to his blog post, Can AI solve Europe’s problems? Silicon Continent, June 26. 2025.

GDP growth among the G8 for the last decade: The US vs. the rest

Despite the stories about British stagnation, the UK's GDP per capita grew faster than median among the G8 the last 10 years. The real story is the US vs. the rest. pic.twitter.com/083uQIYnZ0

— Benjamin Todd (@ben_j_todd) June 1, 2025

H/t Tyler Cowen.

If the world's a mess, don't blame Donald Trump

Aaron Benanav, There’s a Reason the World Is a Mess, and It’s Not Trump, NYTimes, April 21, 2025.

The world is a mess.

As President Trump upends global trade through a punitive suite of tariffs and redraws America’s alliances, world leaders are scrambling to respond. They are badly placed to deal with such disruption: Across the world, governments have been losing elections — or barely holding on — in the face of rising discontent. From the United States to Uruguay, Britain to India, an anti-incumbent wave swept through democracies in 2024. But not only democracies are in crisis. China, too, is grappling with social unrest and economic instability. Strife, these days, is global.

There are many explanations for this sorry state of affairs. Some see rapid social change, especially around migration and gender identity, fueling a cultural backlash. Others argue that elites flubbed their pandemic responses or have grown detached from their populations, driving a surge in anti-establishment sentiment and support for strongmen. Another argument holds that algorithm-driven social media has made it easier for misinformation and conspiracy theories to spread, giving rise to greater volatility.

There’s something to each of these theories, to be sure. But there is a deeper force underlying today’s disarray: economic stagnation. The world is experiencing a long-term slowdown in growth rates that began in the 1970s, worsened after the 2008 global financial crisis and shows no sign of improving. Stuck with low growth, waning productivity and an aging work force, the world economy is in a rut. This shared economic predicament lies behind the political and social conflicts the world over.

I agree with this much, we can't blame the sorry state of the world on Donald Trump. He's just a power-mad grifter who's figured out how to exploit the mess for his own gain. And, yes, I believe that the economic stagnation is real. While I'm skeptical of the capitalist mantra of "growth, growth, growth, and more growth," I certainly don't think we've reached a point where a steady-state economy would be better (less strain on the environment). I've been following Tyler Cowen for well over a decade now, perhaps a decade and a half, and he called it in this 2011 book, The Great Stagnation. I note, however, that's he's recently come to believe that we're pulling out of it.

Let's go on with the article, which asks why growth has slowed:

One reason is the global shift from manufacturing to services. This has stalled the primary engine of economic expansion: productivity growth. Productivity — the output per hour worked — can rise quickly in manufacturing. A car factory that installs robotic assembly lines, for example, can double production without hiring more workers, perhaps even firing some. But in services, efficiency is much harder to improve. A restaurant that gets busier usually needs more servers. A hospital treating more patients will require more doctors and nurses. In service-based economies, productivity is always slower to rise.

This seismic shift, in the making for decades, has a name: deindustrialization. In America and Europe, we know what that looks like: lost manufacturing jobs, amid declining demand for industrial goods. But deindustrialization is not limited to wealthy economies. The move from manufacturing to services is happening across the G20, dragging down growth rates nearly everywhere. Today about 50 percent of the world’s work force is employed in the service sector.

There’s another reason for global stagnation: slowing population growth. Birthrates surged after World War II, creating strong demand for housing and infrastructure construction and spurring the postwar boom. Demographers once assumed birthrates would stabilize at replacement level, around two children per family. Instead, fertility rates have tended to fall below this threshold. [...]

This is a big problem for the economy.

Because everything shrinks. What to do? A.I. to "improve efficiency in labor-intensive service sectors like health care and education"? Hasn't worked so far. Reindustrialization, "under strict tariff protections"? That's Trump's gambit.

But here, too, there is cause for doubt. For one thing, the decline in manufacturing was not just about trade. Even manufacturing and export powerhouses like Germany and South Korea have seen industrial employment shrink. For another, the industries generally targeted for revival — semiconductors, electric vehicles and renewable energy — employ relatively few workers. The era when manufacturing could provide mass employment is over.

Benanav doubts that increasing the population is a way out, with which I'm sympathetic. He votes for more deficit spending (two paragraphs) and redistribution.

The second approach is redistribution. In the past, the primary rationale for policies that enriched wealthy households was to stimulate growth from the top down, but this strategy has evidently failed. Instead, governments could place much higher taxes on the rich and redistribute income to the rest of society. That would be an uphill battle in the United States and elsewhere, admittedly, but it would bring big benefits, improving consumer demand and strengthening markets both domestically and internationally.

The goal should be not just to raise income levels, which studies show are increasingly disconnected from happiness, but also to build more stable and equitable societies in a slower-growth world. That requires investing to improve people’s lives: repairing ecosystems, rebuilding infrastructure and expanding housing.

Color me sympathetic, deeply sympathetic. But still, I remain skeptical.

I keep thinking that the world is limping along on social, institutional, and political structures grounded in the 19th century, if not even earlier, and those structures are no longer adequate. Why not? That's a tricky one, and I'm not prepared to answer it. But my thinking is grounded in the cultural ranks theory that David Hays and I developed during the 1990s, and that tells me that we need another restructuring of, of, well, of everything. That's a hard case to argue.

Is it over? States and State Systems After Globalism

Christopher Caldwell, This Maverick Thinker Is the Karl Marx of Our Time, NYTimes, Nov. 28, 2024:

Who could have seen Donald Trump’s resounding victory coming? Ask the question of an American intellectual these days and you may meet with embittered silence. Ask a European intellectual and you will likely hear the name of Wolfgang Streeck, a German sociologist and theorist of capitalism.

In recent decades, Mr. Streeck has described the complaints of populist movements with unequaled power. That is because he has a convincing theory of what has gone wrong in the complex gearworks of American-driven globalization, and he has been able to lay it out with clarity. Mr. Streeck may be best known for his essays in The New Left Review, including a dazzling series on the cascade of financial crises that followed the crash of 2008. He resembles Karl Marx in his conviction that capitalism has certain internal contradictions that make it unsustainable — the more so in its present “neoliberal” form. His latest book, “Taking Back Control? States and State Systems After Globalism,” published this month, asks whether the global economy as it is now set up is compatible with democracy. He has his doubts.

The Rubicon:

But starting in the 1970s, things began to change. Sometime after the Arab oil embargo of 1973, investors got nervous. The economy began to stall. This placed politicians in a bind. Workers had the votes to demand more services. But that required making demands on business, and business was having none of it. States finessed the matter by permitting the money supply to expand. For a brief while, this maneuver allowed them to offer more to workers without demanding more of bosses. Essentially, governments had begun borrowing from the next generation.

That was the Rubicon, Mr. Streeck believes: “the first time after the postwar growth period that states took to introducing not-yet-existing future resources into the conflict between labor and capital.” They never broke the habit.

The rise of the technocrats:

At each stage of neoliberalism’s evolution, Mr. Streeck stresses, key decisions have been made by technocrats, experts and other actors relatively insulated from democratic accountability. When the crash came in 2008, central bankers stepped in to take over the economy, devising quantitative easing and other novel methods of generating liquidity. During the Covid emergency of 2020 and 2021, Western countries turned into full-blown expertocracies, bypassing democracy outright. A minuscule class of administrators issued mandates on every aspect of national life — masks, vaccinations, travel, education, church openings — and incurred debt at levels that even the most profligate Reaganite would have considered surreal.

Mr. Streeck has a clear vision of something paradoxical about the neoliberal project: For the global economy to be “free,” it must be constrained. What the proponents of neoliberalism mean by a free market is a deregulated market. But getting to deregulation is trickier than it looks because in free societies, regulations are the result of people’s sovereign right to make their own rules. The more democratic the world’s societies are, the more idiosyncratic they will be, and the more their economic rules will diverge. But that is exactly what businesses cannot tolerate — at least not under globalization. Money and goods must be able to move frictionlessly and efficiently across borders. This requires a uniform set of laws. Somehow, democracy is going to have to give way.

I'm ordering the book. There's much more at the link.

Economic growth in Roman Britain over four centuries

Scott G. Ortman, José Lobo, Lisa Lodwick, Rob Wiseman, Olivia Bulik, Victoria Harbison , and Luís M. A. Bettencourt, Identification and measurement of intensive economic growth in a Roman imperial province, Science Advances, 5 Jul 2024, Vol 10, Issue 27, DOI: 10.1126/sciadv.adk5517

Abstract: A key question in economic history is the degree to which preindustrial economies could generate sustained increases in per capita productivity. Previous studies suggest that, in many preindustrial contexts, growth was primarily a consequence of agglomeration. Here, we examine evidence for three different socioeconomic rates that are available from the archaeological record for Roman Britain. We find that all three measures show increasing returns to scale with settlement population, with a common elasticity that is consistent with the expectation from settlement scaling theory. We also identify a pattern of increase in baseline rates, similar to that observed in contemporary societies, suggesting that this economy did generate modest levels of per capita productivity growth over a four-century period. Last, we suggest that the observed growth is attributable to changes in transportation costs and to institutions and technologies related to socioeconomic interchange. These findings reinforce the view that differences between ancient and contemporary economies are more a matter of degree than kind.

H/t Tyler Cowen.

What about degrowth? Color me both sympathetic and skeptical. I'm thinking.

Jennifer Szalai, Shrink the Economy, Save the World? NYTimes, June 8, 2024. The article opens:

A rising tide and a bigger pie: Economic growth has long been considered such an obvious boon that it’s pursued by governments across the world as a matter of course. But in 2016, when a London professor warned an audience in Newcastle that Brexit would lead to a precipitous drop in Britain’s gross domestic product, that well-worn measure of economic activity, one woman’s heckling caught him by surprise. “That’s your bloody G.D.P.,” she shouted, “not ours!”

The eruption tapped into a suspicion supported by reality: Gains in economic growth have too often buoyed the fortunes of the richest instead of lifting all boats. Prosperity even in the most prosperous countries hasn’t been shared. But all the attention to inequality is just a crack in the edifice of economic orthodoxy. Now a much more radical proposition has emerged, looming like a wrecking ball: Is economic growth desirable at all? [...]

In 1972, the French theorist André Gorz coined the word décroissance to ask whether “no-growth — or even degrowth” in material production was necessary for “the earth’s balance,” even if it ran counter to “the survival of the capitalist system.”

While the idea of "earth's balance" is (at least superficially) attractive, I'm not sure what it means. It does seem to presuppose some line between "the natural" and "the human" such that the human has been messing up the natural. That strikes me as being too much like a repackaging of the idea of original sin. OTOH I've long been suspicious of an economic regime, like capitalism, that positively requires growth in order to function at all. Perhaps that suspicion is a repackaging of medieval Christian objects to usury? But it is also a recognition that we live in a finite world.

Continuing on:

For advocates of degrowth, it’s a core tenet that in high-income countries the constant expansion demanded by capitalism isn’t required to improve people’s lives; instead, the ensuing inequality and environmental havoc have frequently undermined them.

Take Hickel, an anthropologist who teaches in London and Barcelona and is one of the movement’s most spirited exponents. Like other contemporary critics of unfettered growth, he emphasizes the climate crisis. His book begins with scenes of ecological devastation: dying earthworms, declining crop yields, collapsing fish stocks. He points to the connection between growing G.D.P. and energy use, identifying an ideology of “growthism” that he equates with “a kind of madness.” He says that he is not promoting a deliberate reduction in G.D.P. But if G.D.P. stagnates or declines because we conserve energy instead of consuming it, so be it. [...]

Of course, such a sweeping pronouncement is far from uncontested. Economists like Paul Krugman and data scientists like Hannah Ritchie have maintained that technological advances mean that economic prosperity doesn’t have to lead to ecological degradation. But for all the debates over carbon pricing and parts per million and degrees of warming, the distinctive argument that Hickel and other degrowthers make is ultimately a moral one: “We have ceded our political agency to the lazy calculus of growth.”

What a piece of rhetoric: “... the lazy calculus of growth.” Color me sympathetic. Moving on:

As the economist Daniel Susskind notes in his new book, “Growth: A History and a Reckoning,” big questions that were pushed to the margins — about clashing notions of freedom, equality and justice — have roared back with a vengeance. Still, he sees this as cause for ambivalence, not despair. After all, growth has also emancipated much of the world from “an unforgiving struggle for subsistence,” Susskind points out. “Growth has an irresistible promise and an unacceptable price; it is miraculous and devastating; we need a lot more and vastly less.”

Although he denounces the blithe optimism of the economic establishment, Susskind is also highly critical of degrowthers, who are too dismissive of capitalism for his liking.

The article goes on to discuss the ideas of a Japanese Marxist philosopher, whose book, Slow Down: The Degrowth Manifesto, has sold half a million copies.

Saito admits that there is “some truth” to the argument that capitalism produces material wealth, and so he champions degrowth communism only for rich countries, not for poor ones. “Those in the Global North enjoy rich lifestyles enabled by the sacrifices of those in the Global South,” he writes. Degrowth would halt this injustice and offer a form of “reparations”: Reducing the resources and energy used by the Global North would allow the Global South to pursue its own economic growth instead.

Imagination, imagination, who's got imagination?

Even degrowth’s skeptics may find that Saito’s examples of grass-roots organizing sound agreeably democratic and improvisational. But the prospect of global apocalypse that degrowthers keep emphasizing also has the perverse effect of making local measures sound acutely inadequate. Still, Saito says that such experiments do offer something crucial: an enlarged sense of what’s possible. Degrowth’s critics, he writes, suffer from “a poverty of imagination that simply accepts the status quo as unchangeable.”

As it happens, Susskind says precisely the same thing but in the reverse: that it’s degrowth’s advocates who suffer from a “lack of imagination.” The mirrored accusations are striking. Maybe it isn’t a matter so much of imagination scarcity as of where that imagination is directed. Techno-optimists place their faith in innovation; degrowthers place theirs in social movements. Both sides lay claim to being the genuine realists. Each insists that we simply don’t have enough time to do what the other side wants.

Hey! I've got an idea. Let's create a super-intelligent AI and then let it solve the problem.

The Industrial Revolution started earlier than conventional wisdom would have us believe

Fred Lewsey, ‘Nation of makers’: Britain industrialised over a century earlier than history books claim, University of Cambridge, 5 April, 2024.

Britain was well on its way to an industrialised economy under the reign of the Stuarts in the 17th century – over 100 years before textbooks mark the start of the Industrial Revolution – according to the most detailed occupational history of a nation ever created.

Built from more than 160 million records and spanning over three centuries, the University of Cambridge’s Economies Past website uses census data, parish registers, probate records and more to track changes to the British labour force from the Elizabethan era to the eve of World War One.

The research shows that 17th century Britain saw a steep decline in agricultural peasantry, and a surge in people who manufactured goods: from local artisans like blacksmiths, shoemakers and wheelwrights, to an explosion in networks of home-based weavers producing cloth for wholesale.

Historians say the data suggests that Britain was emerging as the world’s first industrial powerhouse several generations before the mills and steam engines of the late 18th century – long credited as the birth of global industry and economic growth.

Distributed manufacture:

Yet in the England of 1700, half of all manufacturing employment was in the countryside. “In addition to village artisans, there were networks of weavers in rural areas who would work for merchants that supplied wool and sold the finished articles,” said Shaw-Taylor.

Industries of textiles, or metalworkers making nails and scythes, were shaped like “factories without machines spread out over hundreds of households” according to Shaw-Taylor – and increasingly produced goods for international markets.

In Gloucestershire, for example, expansions in textiles, footwear and metals saw the share of the male workforce in industry grew from a third (33%) to almost half (48%) over the 17th century.comm

While in Lancashire, the share of men in manufacturing work grew from 42% in 1660 to 61% in 1750, driven by a doubling of textile workers (from 15% to 30%). This all occurred prior to the Industrial Revolution.

Some networks evolved into workshops, and eventually the mills of Blake’s visions as industries migrated to the North of England, where coal was abundant and crops were harder to grow.

This meant that by the mid-18th century – considered the start of the Industrial Revolution – much of England’s South and East had actually lost its long-established industries, and even returned to farm labour, according to the research.

There's more at the link.

H/t Tyler Cowen.

What economic growth and statistical semantics tell us about the structure of the world

Bumping this to the top of the queue on general principle, and because it takes a very abstract view of economic development, which is front and center in Tyler Cowen's current conversation with Stephen Jennings, who is a developer working Kenya.

New working paper. Title above. Download at:

• Academia: https://www.academia.edu/43938531/What_economic_growth_and_statistical_semantics_tell_us_about_the_structure_of_the_world
• SSRN: http://ssrn.com/abstract=3680119
• ResearchGate: https://www.researchgate.net/publication/343836653_What_economic_growth_and_statistical_semantics_tell_us_about_the_structure_of_the_world

Abstract, contents, and first section below.

---

Abstract: The metaphysical structure of the world, as opposed to its physical structure, resides in the relationship between our cognitive capacities and the world itself. Because the world itself is “lumpy”, rather than “smooth” (as developed herein, but akin to “simple” vs. complex”), it is learnable and hence livable. Machine learning AI engines, such as GPT-3, are able to approximate the semantic structure of language, to the extent that that structure can be modeled in a high-dimensional space. That structure ultimately depends on the fact that the world is lumpy. It is the lumpiness that is captured in the statistics. Similarly, I argue, the American economy has entered a period of stagnation because the world is lumpy. In such a world good “ideas” become more and more difficult to find. Stagnation then reflects the increasing costs the learning required to develop economically useful ideas.

Contents

Wending our way in a complex world 2
World, mind, and learnability: On the metaphysical structure of the cosmos 5
Stagnation, Redux: Like diamonds, good ideas are not evenly distributed 10
The complex universe: Further reading 18

Wending our way in a complex world

This paper is based on two very different posts that I’ve written in the last month. One of them takes the statistical semantics of AI engines like GPT-3 as its starting point: “World, mind, and learnability: On the metaphysical structure of the cosmos” (revised considerably for this paper). The other is about economic growth and stagnation: “Stagnation, Redux: Like diamonds, good ideas are not evenly distributed”.

These two very different papers nonetheless share both substance and method. Methodologically, both argue that the situation we observe is intelligible if we assume that the world is structured in a certain way. Their core substance is about that structure: the world must be “lumpy” – a notion I discuss on pages 5 ff. Because the world is lumpy we can learn about it, live in it, talk about it, and write about it. By contrast, a “smooth” world would be unintelligible and hence unlivable. The exhaustive statistical analysis of a large body of text is, in effect, able to recover that structural lumpiness as reflected in language and use it to produce new texts.

However, because the world is lumpy, we begin by learning and benefiting from things close to hand. When those resources have been exhausted we and must travel deeper into the world, expending more and more effort to extract economic benefit. Our current economic stagnation reflects the increasing cost of learning more about the world. A smooth world would no doubt be more convenient, for there would be economic benefit at every turn, either that or economic disaster. That is, if the world were smooth, we wouldn’t be here.

That, I know, this talk of smoothness and lumpiness is very abstract and “featureless”. But then could a resonance between such disparate phenomena as statistical semantics and economic stagnation but be abstract? I’ll provide more substance later in this paper, some diagrams, and some arguments. But first I want to suggest that what I’ve been calling lumpiness is what Ilya Prigogine and many others have called complexity.

Our complex world

Some years ago David Hays and I wondered why natural selection leads to complexity [1]. We argued that, over the long run, natural selection favors organisms with increased ability to process information, and that ability yields benefits in a complex universe. But what did we mean by that, a complex universe? Here is what we said:

It is easy enough to assert that the universe is essentially complex, but what does that assertion mean? Biology is certainly accustomed to complexity. Biomolecules consist of many atoms arranged in complex configurations; organisms consist of complex arrangements of cells and tissues; ecosystems have complex pathways of dependency between organisms. These things, and more, are the complexity with which biology must deal. And yet such general examples have the wrong “feel;” they don't focus one's attention on what is essential. To use a metaphor, the complexity we have in mind is a complexity in the very fabric of the universe. That garments of complex design can be made of that fabric is interesting, but one can also make complex garments from simple fabrics. It is complexity in the fabric which we find essential.

We take as our touchstone the work of Ilya Prigogine, who won the Nobel prize for demonstrating that order can arise by accident (Prigogine and Stengers 1984; Prigogine 1980; Nicolis and Prigogine 1977). He showed that when certain kinds of thermodynamic systems get far from equilibrium order can arise spontaneously. These systems include, but are not limited to, living systems. In general, so-called dissipative systems are such that small fluctuations can be amplified to the point where they change the behavior of the system. These systems have very large numbers of parts and the spontaneous order they exhibit arises on the macroscopic temporal and spatial scales of the whole system rather than on the microscopic temporal and spatial scales of its very many component parts. Further, since these processes are irreversible, it follows that time is not simply an empty vessel in which things just happen. The passage of time, rather, is intrinsic to physical process.

We live in a world in which “evolutionary processes leading to diversification and increasing complexity” are intrinsic to the inanimate as well as the animate world (Nicolis and Prigogine 1977: 1; see also Prigogine and Stengers 1984: 297-298). That this complexity is a complexity inherent in the fabric of the universe is indicated in a passage where Prigogine (1980: xv) asserts “that living systems are far-from-equilibrium objects separated by instabilities from the world of equilibrium and that living organisms are necessarily ‘large,’ macroscopic objects requiring a coherent state of matter in order to produce the complex biomolecules that make the perpetuation of life possible.” Here Prigogine asserts that organisms are macroscopic objects, implicitly contrasting them with microscopic objects.

Economic growth is a false idol; we need a steady-state economy

David Marchese, This Pioneering Economist Says Our Obsession With Growth Must End, NYTimes Magazine, July 17,2022.

But what about the counterintuitive possibility that our current pursuit of growth, rabid as it is and causing such great ecological harm, might be incurring more costs than gains? That possibility — that prioritizing growth is ultimately a losing game — is one that the lauded economist Herman Daly has been exploring for more than 50 years. In so doing, he has developed arguments in favor of a steady-state economy, one that forgoes the insatiable and environmentally destructive hunger for growth, recognizes the physical limitations of our planet and instead seeks a sustainable economic and ecological equilibrium. “Growth is an idol of our present system,” says Daly, emeritus professor at the University of Maryland School of Public Policy, a former senior economist for the World Bank [...] “Every politician is in favor of growth,” Daly, who is 84, continues, “and no one speaks against growth or in favor of steady state or leveling off. But I think it’s an elementary question to ask: Does growth ever become uneconomic?”

There’s an obvious logic to your fundamental argument in favor of a steady-state economy, which is that the economy, like everything else on the planet, is subject to physical limitations and the laws of thermodynamics and as such can’t be expected to grow forever. What’s less obvious is how our society would function in a world where the economic pie stops growing. [...] Is your view of human nature and our willingness to peacefully share the pie just more hopeful than his? First, I’m not against growth of wealth. I think it’s better to be richer than to be poorer. The question is, Does growth, as currently practiced and measured, really increase wealth? Is it making us richer in any aggregate sense, or might it be increasing costs faster than benefits and making us poorer? Mainstream economists don’t have any answer to that. The reason they don’t have any answer to that is that they don’t measure costs. They only measure benefits. That’s what G.D.P. is. There’s nothing subtracted from G.D.P.

What about undeveloped countries?

But how would a country continue to raise its standard of living without growing its G.D.P.? It’s a false assumption to say that growth is increasing the standard of living in the present world because we measure growth as growth in G.D.P. If it goes up, does that mean we’re increasing standard of living? We’ve said that it does, but we’ve left out all the costs of increasing G.D.P. We really don’t know that the standard is going up. If you subtract for the deaths and injuries caused by automobile accidents, chemical pollution, wildfires and many other costs induced by excessive growth, it’s not clear at all. Now what I just said is most true for richer countries. Certainly for some other country that’s struggling for subsistence then, by all means, G.D.P. growth increases welfare. They need economic growth. That means that the wealthy part of the world has to make ecological room for the poor to catch up to an acceptable standard of living. That means cutting back on per capita consumption, that we don’t hog all the resources for trivial consumption.

On the need for global cooperation.

Let’s say that tomorrow the United States government says it recognizes the need for ecological balance and is going to de-emphasize growth. Wouldn’t every other country have to make the same decision for it to have the desired ecological effect? That’s a very difficult question. If you try to enact laws for counting the ecological costs of your production in the United States and then you enter into trading relations with another country that does not count the costs, they have a competitive advantage. They may ruin themselves in the long run, but in the short run they’re going to undersell you. This creates huge problems for the free traders because the answer to the problem is to have a tariff to protect the U.S. industry. At one time I would have tended to favor moving toward a global government. I don’t know what changed my mind. Perhaps spending six years at the World Bank made me think that global governance looks like a chimera. [...] we have a world of interdependent nations, which are fundamentally separate but try to be cooperative. That’s the model that we’re stuck with. So the best road forward is for nations to try to move toward a steady state and accept the fact that you’re going to need to have some tariffs and hope that the resulting benefits are sufficient to convince other nations to follow suit.

There is more at the link.

Is the fact that ideas are nonrival the key to economic growth in the 21st century? Or: What’s an idea? [the peculiarities of economic models]

I’ve been chewing on one particular paragraph, the final one, of Bloom et al. “Are Ideas Getting Harder to Find?”[1] Why? Because it bears on just what (these particular) economists mean by “idea”. Early in the paper they noted that “ideas are hard to measure” (p. 1108), noting that appropriate units of measure are far from obvious. They went on to note that “in some ways a more accurate title for this paper would be ‘Is Exponential Growth Getting Harder to Achieve?’” Which brings up the question of why didn’t they choose that more accurate title? Custom, perhaps? I don’t know.

How do you measure ideas?

I understand the problem. I’m not at all sure that “idea” can even be a properly technical term, thinking perhaps it’s better regarded as an informal common-sense term with but limited use in technical work. In any event, when it comes to actually measuring ideas, the authors use proxies in two of their three case studies. In their study of semi-conductor manufacture they use research effort as measured by wages as a proxy for ideas (p. 1129) and in their study of seed lines they use R & D expenditure (pp. 1120-1121). Their measure was more direct in the case of pharmaceutical development; they counted articles in the PubMed database as identified by appropriate key words (pp. 1125-1126).

I have no problem with that. But it does mean they tend to tread ideas as atomic entities with no properties beyond the fact that they can be counted, if only indirectly, and that they can be shared. And that brings us to the final paragraph of the article.

Key insight: Ideas are nonrival

Economist distinguish between things that are rival and things that are non-rival. When something is a rival good only one person or entity can use it. If Amalgamated Mining owns a particular deposit of iron ore that means that, for example, Universal Minerals cannot mine that deposit. Ideas, in contrast, are nonrival. The fact that Jim Manley knows Newton’s laws of motion doesn’t preclude anyone else from understanding and using them.

With that mind, considered the highlighted passage from the final paragraph (p. 1139) of Bloom et al.:

That one particular aspect of endogenous growth theory should be reconsidered does not diminish the contribution of that literature. Quite the contrary. The only reason models with declining research productivity can sustain exponential growth in living standards is because of the key insight from that literature: ideas are nonrival. For example, if research productivity were constant, sustained growth would actually not require that ideas be nonrival; Akcigit, Celik, and Greenwood (2016) shows that rivalrous ideas can generate sustained exponential growth in this case. Our paper therefore suggests that a fundamental contribution of endogenous growth theory is not that research productivity is constant or that subsidies to research can necessarily raise growth. Rather it is that ideas are different from all other goods in that they can be used simultaneously by any number of people. Exponential growth in research leads to exponential growth in At. And because of nonrivalry, this leads to exponential growth in per capita income.

The first highlighted passage seems to suggest that that idea that ideas are nonrival is due to the tradition of research on endogenous growth theory. That doesn’t make any sense since the nonrival nature of ideas follows from the definition of “nonrival,” which is independent of that research tradition.

What’s going on? Two paragraphs earlier they had noted that: 1) endogenous growth theory assumes constant exponential growth given constant research productivity, and 2) their article reports a variety of work showing that, in fact, over past few decades it requires more and more research to sustain exponential growth. This final paragraph is an effort to reconcile theory with evidence. The rest of the paragraph after the highlighted section does that.

How does it do it? Not very well, it seems to me, not very well. They cite a paper showing that it is possible to get sustained exponential growth from constant productivity if ideas were rival. However, it turns out that productivity is not constant (the burden of the article) and, wouldn’t you know, ideas aren’t rival either. Surely that must be why exponential growth remains possible.

Really? I understand that that works within the bounds of endogenous growth theory. But it seems awfully flimsy to me. It amounts to little more than saying exponential growth remains possible because ideas are ideas. And that’s not very helpful. Ideas were always nonrival; it’s not as though that property miraculously emerged in time to allow endogenous growth theory to save the appearances – a phrase, incidentally, that dates back to Plato.

It might be more useful to figure out what it is about the current run of ideas that makes them less productive. That’s what I’ve done in my working paper, Stagnation and Beyond: Economic growth and the cost of knowledge in a complex world, which is what I’ve done in my recent working paper on stagnation [2]. But there I was concerned with cognitive architecture and the relationship between ideas and the world. I didn’t treat ideas merely as countable atomic units. Whether my argument is going in the right direction, that’s another matter. But it doesn’t depend on a truism.

References

[1] Nicholas Bloom, Charles I. Jones, John Van Reenen, and Michael Webb, Are Ideas Getting Harder to Find? American Economic Review 2020, 110(4), https://doi.org/10.1257/aer.20180338.

[2] William Benzon, Stagnation and Beyond: Economic growth and the cost of knowledge in a complex world, Version 2, Working Paper, August 2, 2019, 62 pp., https://www.academia.edu/39927897/Stagnation_and_Beyond_Economic_growth_and_the_cost_of_knowledge_in_a_complex_world.

Investment and the conditions for exponential growth [#Progress Studies | Tech Evol]

At the end of their article, Are Ideas Getting Harder to Find? (2020), Nicholas Bloom, et al. Begin to draw some conclusions, thus (p. 1134):

The evidence presented in this paper concerns the extent to which a constant level of research effort can generate constant exponential growth, either in the economy as a whole or within relatively narrow categories, such as a firm or a seed type or a health condition. We provide consistent evidence that the historical answer to this question is “no”: as summarized in Table 7, research productivity is declining at a substantial rate in virtually every place we look.

A bit later (p. 1138):

This analysis has implications for the growth models that economists use in our own research, like those cited in the introduction. The standard approach in recent years employs models that assume constant research productivity, in part because it is convenient and in part because the earlier literature has been interpreted as being inconclusive on the extent to which this is problematic. We believe the empirical work we have presented speaks clearly against this assumption. A first-order fact of growth empirics is that research productivity is falling sharply.

Future work in the growth literature should determine how best to understand this fact.

In my 2019 working paper in which I commented on this paper, Stagnation and Beyond: Economic growth and the cost of knowledge in a complex world, I argue that what they see as a decline in research productivity reflects the (unavoidably) increasing costs of obtaining knowledge about the world and then briefly outline that account of cultural ranks that David Hays and I have developed. It is my impression that the growth literature centers on the growth accompanying the Industrial Revolution, which is a reflection of Rank 3 modes of thought, in terms of our account. Perhaps the usual growth models, where “a constant level of research effort can generate constant exponential growth,” are valid for the conditions obtaining during the Industrial Revolution but fail because those conditions no longer obtain. We are moving into a different world which may well require different models.

That is to say, it is inappropriate to search for a growth model that is valid everywhere and always. There is no such thing. Rather different material and cultural circumstances require different models. Note that I am not proposing potentially hundreds or even tens of models. I am proposing only a handful, corresponding to the handful of cultural ranks we have proposed.

And that brings me to another excerpt from Hays’s The Evolution of Technology Through Four Cognitive Ranks (1993). This excerpt is the opening section of Chapter 6, “Investment; with a life-cycle cost analysis of one individual human being.” Hays uses the idea of the factory to characterize rank 3 economic production, though of course he realizes that agriculture continues and that there are rank 3 innovations other than the factory system. I follow this excerpt with a brief comment about the specific case studies Bloom et al. develop in their article.l

As I have mentioned before in this series of excerpts, Hays wrote the book for an online course in the 1990s and distributed the book to students on an MS-DOS disk – chosen by the school, I assume, as the least common denominator among personal computer operating systems. Thus it was written as a text file in a simple hypertext system. It was never published in hardcopy. I reproduce it below more or less as Hays created it, in a mono-spaced font.

Investment

Capital is a concept of rank 3, but investment in skill and land were necessary in ranks 1 and 2. Sapients who believe in the future will attempt to prevent the net worth of Earth from declining.

6.1. INVESTMENT

6.1.1. Stone Tools and Hides Require Skill
6.1.2. The Land
6.1.3. The Factory System

The main investment in rank 1 is the acquisition of lore. For rank 2, the improvement of land for agriculture requires large investment. In rank 3, capital is assembled to invest in the ensembles of machines that produce large quantities of goods – and to invest also in transportation, communication, urban systems, and education.

Day by day a person works and uses the fruits of his (or her) labor for subsistence (food, clothing, shelter), for ritual, for pleasure, and so on. Whatever the rank, if each day's consumption equals each day's income, there is no investment.

Investment is the conversion of a portion of income into capital. The purpose of investment is to increase expected future income. Consumption yields instant gratification; the investor has to postpone gratification. The future increment must be larger than the present decrement to justify investment. Maybe I will put aside a dollar a day this year, but I want to get back two dollars a day next year!

The theory of rank says that the nature of capital changes from rank to rank, according to the technology. Figure 6.1 contains a sort of chronology of investments.

6.1.1. Stone Tools and Hides Require Skill

Rank 1 lives by hunting and gathering. In fact, most people of rank 1 seem to live, or to have lived, mostly by gathering with occasional feasts when the hunters get lucky. Emphasis on hunting appears to be sexist; women do the bulk of gathering. What do rank 1 people have that they do not consume on the day they get it? Some weapon-tools, a little clothing made from hides, and very simple shelter. My impression is that they are willing to leave these things behind and make new ones. An igloo does not pin down an Eskimo as your home holds you.

So rank 1 has almost no material capital; but it does have skill. The best over-simplification is probably that the rank 1 person's head is as full as yours or mine. Our knowledge is more specialized, and I assert that our knowledge is more abstract. One of us can teach video, one can repair automobiles, and so on; I can't teach video, and I suppose that only a few of us can. The rank 1 person is also a specialist, in a way that is not so obvious: The rank 1 person's concrete skills are specific to an environment, a climate, a range of vegetation and animal life, an area on a map.

But these skills are considerable, and take time to acquire. Little or none of them are acquired in situations comparable to schooling. Mostly the children watch adults, help, imitate, and play. No doubt they get some verbal guidance, orally since there is no writing. But not a great deal. The investment necessary to acquire skills is made in childhood. Children work less than adults, or at least less productively. A rank 1 society does not put its children to doing routine simple tasks and thus preclude their acquiring adult skills, as Britain did during the worst part of the Industrial Revolution. But at puberty the children must be ready to play adult roles. The rank 1 adult's skills are as fixed as our speech patterns. Few of us learn a second language after puberty with the exact speech patterns of a native speaker, and no one in rank 1 acquires a new skill after puberty.

Ramble into Fall: Cultural evolution, economic growth and progress, rambling [let's go meta]

Is the study of cultural evolution wrecked?

I’ve been thinking and article comparing cultural with biological evolution for about a month or so. At the end authors asked for feedback. I was wondering whether or not to respond. I’ve finally done so, with a recent blog post, Can the study of cultural evolution be successfully assimilated to a framework that is centered on biology? [No, but the biologists keep trying]. I don’t know whether or not I’ll write directly to the lead author. My problem has been that the article is so relentlessly biological in orientation that I find it hard to imagine that the authors, there are nine, would be able to make use of my remarks.

We’re thinking in different worlds. But the world they represent is, as far as I can tell, the largest more or less organized body of thinkers about cultural evolution – gene-culture co-evolution, or dual inheritance theory. The work these people do is good as far as it goes, but I don’t see how it can handle the kind of phenomena that interest me, music, literature, the arts in general, language, the history of science, and so forth. You simply can’t get to those phenomena from the assumptions guiding their thinking.

That line of thinking dates back to the mid-1980s as does another line of thinking about cultural evolution, memetics. Dawkins came up with the idea in his 1976 book, The Selfish Gene, but it took a decade for the idea to catch on. Two things have come out of that. One the one hand we have the wide-spread popular idea of memes, as in “internet meme.” That is what it is and I have no problems with. What’s more problematic is the attempt to found a science of memetics. As far as I can tell, nothing has come of it, though a bunch of books have been written, a journal was started and failed, and Dan Dennett keeps pushing the idea. While Dawkins original impulse was valid – an account of cultural evolution needs to be built around cultural entities that are the benefactors of the evolutionary dynamic – the thinking that came out of it collapsed onto the idea of memes-in-the-head which then flit about from brain to brain. As far as I can tell, this line of thinking is all but dead.

So, we have one line of investigation that failed, memetics, and another, gene-cultural co-evolution, which is flourishing, but also short-sighted. Is there any chance for an inquiry into cultural evolution that is suited to the subject matter?

Growth and progress

I continue to think about economic stagnation and growth and the prospects for progress along the lines of my post from August 13, Stagnation, Redux: It’s the way of the world [good ideas are not evenly distributed, no more so than diamonds], which I subsequently incorporated into a working paper, What economic growth and statistical semantics tell us about the structure of the world (August 24, 2020), which I like a lot. I’ve been thinking about a new version of that paper in which I would add a new section at the end, one that would knit the two facets of the paper together, growth and semantics.

But the thinking’s been going hard, as has the motivation to actually do the writing. As things moved along, I was getting more ideas about the economic end of the article than about the semantics end. So I decided to drop the idea of a second edition and instead do another working paper where I’d just expand the economic side of the article. Things felt better after I’d arrived at that decision about a week ago.

Yet, the writing was still coming hard, and I’ve been feeling a bit guilty about that. It’s difficult in this kind of situation to determine whether or not I’m just delaying the writing for no particularly good reason or because I still need to do some more thinking before writing. And, of course, the actual writing is always a good way to do some thinking.

Anyhow, I actually did some writing this afternoon and made some real progress. We’ll see how it goes.

My working title for the new paper: The Materiality of Ideas in the Universe of Knowledge and the Prospects for Progress.

Rambling about on rambling

So why do I write these rambles? Because it helps me think. I’ve got a variety of interests and I generally keep several of them working at a time. It sometimes gets a bit difficult to figure out what to work on next and push on through to a complete blog post, working paper, or set of photos. Writing one of these posts is a way of putting a bunch of different things before me and letting them bump up against one another. It’s a way to step back and breath.

Which reminds me, I still need to do some media notes, one on To Catch a Thief, and another on Atelier.

And I’ve got to get back to this Facebook business, not to mention GPT-3 and the future of AI. Yikes!

More later.

The Great Stagnation, another voice heard from, Jason Furman

Tyler Cowen interviews Jason Furman on a variety of things. On productivity:

COWEN: If investment is important, does that make you an economic pessimist, given the apparent end of the savings glut from Asia?

FURMAN: I think I’m an economic realist. You look at Robert Gordon, and he’s been turned into this big pessimist, this pole of prediction that’s this negative. We’ve run out of ideas. Nothing ever is going to happen. It turns out, if you just look at average productivity growth over the last 50 years and assume that’s what you’re going to get over the next 50 years, we’re going to have a GDP growth rate that is around 2 percent, maybe a little bit below it. And that’s just from continuing the last 50 years.

Now, the average of the last 50 years is better than the average of the last 15 years. So, in some ways, I’m an optimist. I think we’ll get back to our historical productivity growth. But the idea that we’re going to get way beyond that certainly could happen, but I don’t think it’s a reasonable forecast of what’s going to happen.

COWEN: Referring to Gordon, here’s another softball question. Why did productivity fall so much after either 1973 or in, say, the last 15 years?

[laughter]

This is the easy podcast.

FURMAN: Yep. I think there’s something. Less infrastructure investment, less R&D. There were some major projects in terms of highways in the 1950s, the lunar landing in the 1960s, et cetera. I’d like to think that was the answer to your question. I think the truth is, when you go and quantify that type of public investment, it’s a couple tenths of a percent of the answer.

In the recent period, I do think the increased concentration we’re talking about might be a tenth or two percentage point of the slowdown that we’ve seen. Some of it may be that you need to invert your question and ask not why did productivity slow down, but why was productivity so fast?

There’s a lot of very special things about the 1950s and the 1960s, just coming off of World War II. And in terms of ’95 to 2005, well, it’s a relatively short period of time. Stuff fluctuates. You have a period of faster growth. But broadly speaking, we’re in a world of 1.5 percent productivity growth if we’re lucky. Unfortunately, it’s been more like 1 [percent] lately, and that’s just what it is.

COWEN: What is your take on the degree of unmeasured benefits from the internet? High, low, intermediate?

FURMAN: Intermediate, but most of them were in the base 5, 10, 15 years ago — Google, online travel, online shopping, Wikipedia. It’s not like adding these are going to add to your measure of productivity growth in the year 2019 or the year 2018. They might add to the level of productivity, but they were in the level. They were in the base a while ago now. And they’ve just continued up. So, I certainly think there’s some things we’re not measuring.

A bunch of it, though, is about the use of our time. YouTube may be better than TV, but it’s only a bit better than TV, so you can’t just take the gross benefits of YouTube. You have to do the net benefits relative to the other activity. And then, if you’re being a paternalist, you could ask, “Is any of this a good use of our time?” But without even going there, I think you get decent-size impact on the level of well-being, a small impact on the growth of well-being over the last decade.

Stagnation, Redux: It’s the way of the world [good ideas are not evenly distributed, no more so than diamonds]

Tyler Cowen has just posted a conversation with Nicholas Bloom, a Stanford economist interested in economic growth. That gives me a chance to revise a working paper I’d written last year, Stagnation and Beyond: Economic growth and the cost of knowledge in a complex world [2], which is based on a paper Bloom had published along with three colleagues, Are Ideas Getting Harder to Find? [3]. I took two of their case studies, Moore’s law and drug discovery, examined them in an informal manner and concluded that (much of) the increasing difficulty of discovering new ideas can be attributed to the cost of finding out more about the world.

At the time I wrote that paper I was unaware of Paul Romer’s 1992 article, Two Strategies for Economic Development [4]. He develops his argument with a toy model that is similar in spirit to the idea I’d advanced in my working paper. The objective of this post is to update that idea in view of Romer’s model by deploying some toys of my own.

First I set the stage with some passages from Cowen’s conversation with Bloom. Then I introduce Romer, after which I offer my elaborations. First I introduce some simple diagrams through which we can visualize the relationship between our conceptual systems (maps) and the world itself (territory). I conclude by anchoring that story in time and space making it one that is, in principle, about the evolution of human society over time.

Bloom’s conversation with Cowen

Bloom sets the stage:

The big picture — just to make sure everyone’s on the same page — is, if you look in the US, productivity growth . . . In fact, I could go back a lot further. It’s interesting — you go much further, and you think of European and North American history. In the UK that has better data, there was very, very little productivity growth until the Industrial Revolution. Literally, from the time the Romans left in whatever, roughly 100 AD, until 1750, technological progress was very slow.

Sure, the British were more advanced at that point, but not dramatically. The estimates were like 0.1 percent a year, so very low. Then the Industrial Revolution starts, and it starts to speed up and speed up and speed up. And technological progress, in terms of productivity growth, peaks in the 1950s at something like 3 to 4 percent a year, and then it’s been falling ever since.
Then you ask that rate of fall — it’s 5 percent, roughly. It would have fallen if we held inputs constant. The one thing that’s been offsetting that fall in the rate of progress is we’ve put more and more resources into it. Again, if you think of the US, the number of research universities has exploded, the number of firms having research labs.

Thomas Edison, for example, was the first lab about 100 years ago, but post–World War II, most large American companies have been pushing huge amounts of cash into R&D. But despite all of that increase in inputs, actually, productivity growth has been slowing over the last 50 years. That’s the sense in which it’s harder and harder to find new ideas. We’re putting more inputs into labs, but actually productivity growth is falling.

Cowen responds by saying, “Let’s say paperwork for researchers is increasing, bureaucratization is increasing. How do we get that to be negative 5 percent a year as an effect?” A bit later he’ll offer:

Doesn’t the explanation have to be that scientific efforts used to be devoted to public goods much more, and now they’re being devoted to private goods? That’s the only explanation that’s consistent with rising wages for science but a declining social output from her research, her scientific productivity.

In his response to Tyler, Bloom makes two suggestions that are consistent with my hypothesis:

Why is it happening at the aggregate level? I think there are three reasons going on. One is actually come back to Ben Jones, who had an important paper, which is called, I believe, “[Death of the] Renaissance Man.” This came out 15 years ago or something. The idea was, it takes longer and longer for us to train.

Just in economics — when I first started in economics, it was standard to do a four-year PhD. It’s now a six-year PhD, plus many of the PhD students have done a pre-doc, so they’ve done an extra two years. We’re taking three or four years longer just to get to the research frontier. There’s so much more knowledge before us, it just takes longer to train up. That’s one story.

A second story I’ve heard is, research is getting more complicated. I remember I sat down with a former CEO of SRI, Stanford Research Institute, which is a big research lab out here that’s done many things. For example, Siri came out of SRI. He said, “Increasingly it’s interdisciplinary teams now.”

His third suggestion repeats one of Cowen’s:

Then finally, as you say, I suspect regulation costs, various other factors are making it harder to undertake research. A lot of that’s probably good. I’d have to look at individual regulations. Health and safety, for example, is probably a good idea, but in the same way, that is almost certainly making it more expensive to run labs…

I am most interested in pursing the notion that ideas are getting harder to find because that’s just how the world is. Even assuming that I am correct, one must still show that that factor is stronger than the one’s Cowen favors and, for that matter, other factors one might suggest. That’s a different kind of argument and one I won’t pursue here.

Romer’s model

Let’s start Paul Romer’s toy model from 1992. Romer sets it up with one that is standard in economics, that of a factory (p. 67):

One of the great successes of neoclassical economics has been the elaboration and extension of the metaphor of the factory that is invoked by a production function. To be explicit about this image, recall the child's toy called the Play-Doh Fun Factory. To operate the Fun Factory, a child puts Play-Doh (a form of modeling compound) into the back of the toy and pushes on a plunger that applies pressure. The Play-Doh is extruded through an opening in the front of the toy. Depending on the particular die used to form the opening, out come solid Play-Doh rods, Play-Doh1-beams,or lengths of hollow Play-Doh pipe.

We use the Fun Factory model or something just like it to describe how capital (the Fun Factory)and labor (the child's strength) change the characteristics of goods, converting them from less valuable forms (lumps of modeling compound) into more valuable forms (lengths of pipe).

But Romer isn’t interest in the production of physical goods. He’s interested in the production of ideas. The child’s chemistry set proves useful (p. 68):

Another child's toy is a chemistry set. For this discussion, the set can be represented as a collection of N jars, each containing a different chemical element. From the child's point of view, the excitement of this toy comes from trying to find some combination of the underlying chemicals that, when mixed together and heated, does something more impressive than change colors (explode, for example). In a set with N jars, there are 2^N–1 different mixtures of K elements, where K varies between 1 and N. (There are many more mixtures if we take account of the proportions in which ingredients can be mixed and the different pressures and temperatures that can be used during mixing.)


As N grows, what computer scientists refer to as the curse of dimensionality
sets in. The number of possible mixtures grows exponentially with N, the dimension of this system. For a modestly large chemistry set, the number of possible mixtures is far too large for the toy manufacturer to have directly verified that no mixture is explosive. If N is equal to 100, there are about 10^30 different mixtures that an adventurous child could conceivably put in a test tube and hold over a flame. If every living person on earth (about 5 billion) had tried a different mixture each second since the universe began (no more than 20 billion years ago), we would still have tested less than 1 percent of all the possible combinations. […]

Continuing on, Romer observes (pp. 68-69):

The potential for continued economic growth comes from the vast search space that we can explore. The curse of dimensionality is, for economic purposes, a remarkable blessing. To appreciate the potential for discovery, one need only consider the possibility that an extremely small fraction of the large number of possible mixtures may be valuable.

What interests me is that this vast search space of possibilities is mostly empty of useful ideas, combinations of chemical elements in this case. Moreover I want to distinguish between the space itself and the strategy we have for searching that space. That strategy is based on our theory or theories about that space, or domain as I sometimes like to call it. I want to examine the relationship between the world, on the one hand, and our ideas of it on the other. To do so I must enter the den of the metaphysician, to borrow a phrase from Warren McCulloch.

On the relationship between the world and our ideas of it

The background space in the following simple diagram represents the space of potential chemical combinations (in this case) while the black dots indicate the useful ones.

Figure 1: Useful ideas in the field of all possible ideas

Notice that some areas are less sparsely populated than others. Now let us superimpose a mental map on it – the orange grid is that map:

Figure 2: Our theory of the domain (in orange)

We can now see that while, yes, some regions of the territory are less populated than others, on the whole the mental map – our theory of the domain – is highly congruent with the territory. Most “bins” in our map contain a useful idea, though it isn’t in the same place in each bin. If we search each bin, then, we will very likely find a useful idea. Some searches will take longer than others, but most searches will be rewarded.

Secular staganation or technological lull?

Ramey, V. A., Secular Stagnation or Technological Lull?, Journal of Policy Modeling (2020), doi: https://doi.org/10.1016/j.jpolmod.2020.03.003.

Abstract: The slow recovery of the economy from the Great Recession and the lingering low real interest rates have led to fears of “secular stagnation” and calls for government aggregate demand stimulus to lift the growth rate of the economy. I present evidence that the current state of the U.S. economy does not satisfy the conditions for secular stagnation, as originally defined by Alvin Hansen (1939). Instead, the U.S. is experiencing a period of low productivity growth. I suggest that long intervals of sluggish productivity growth may be natural in an economy whose growth is driven by technological revolutions that are large, infrequent, and randomly-timed. If this is the case, then the best description of the recent experience of the U.S. economy is a technological lull. In this situation, traditional government aggregate demand stimulus policies are not the appropriate response. Instead policies that can increase the rate of innovation and its diffusion may be more appropriate.

Keywords: secular stagnation, productivity growth, technology, innovation

What is secular stagnation? From the article:

In December 1938, the U.S. economy was recovering from the 1937-38 recession. The unemployment rate had averaged 18.8 percent during the previous eight years and currently stood at 16.6 percent. In his American Economic Association Presidential address, “Economic Progress and Declining Population Growth,” Alvin Hansen (1939) argued that while the business cycle had been the problem of the nineteenth century, chronic underemployment was the main problem of the current time and he attributed it to what he called “secular stagnation.” Hansen explained that the essence of secular stagnation was “sick recoveries which die in their infancy and depressions which feed on themselves and leave a hard and seemingly immovable core of unemployment.” (Hansen (1939), p.4). He argued that full employment could not be reached in a modern economy without robust investment expenditures adequate to fill the gap between consumption expenditures and that level of income which could be achieved were all the factors employed.

Hansen noted three historical drivers of the high rate of investment in the nineteenth century: (i) population growth, (ii) opening of new territory and discovery of new resources, and (iii) technical innovations. He saw little remaining role for the first two going forward from the 1930s. Population growth had slowed dramatically, from an annual growth rate of 2.7 percent during the 19th century, to 1.7 percent between 1900 and 1924, and only 0.9 percent from 1924 to 1938. The immigration laws enacted in 1924 severely curtailed immigration as a source of population growth and the economic hardships caused by the Great Depression had reduced fertility rates. Similarly, the era of developing new territories had ended and there were diminished prospects for the discovery of new resources on existing territories. He concluded: “Thus, the outlets for new investment are rapidly narrowing down to those created by the progress of technology.”

Technological lull? Again, from the article:

I suggest that the main factor behind the slow growth of GDP is a technological lull. As I argue below, two factors are contributing to slow growth in potential GDP: slow population growth and slow labor productivity growth. However, since what ultimately matters for growth in standards of living is the growth of real GDP per capita, slower population growth does not necessarily imply a decrease in the standard of living. The key factor affecting the growth in standards of living is slow productivity growth.

Limits to economic growth?

Christopher F. Jones, The Delusion and Danger of Infinite Economic Growth, The New Republic, October 1, 2019.

The fairytale of infinite growth—which so many today accept as unquestioned fact—is relatively recent. Economists have only begun to model never-ending growth over the last 75 years. Before that, they had ignored the topic for a century. And before that, they had believed in limits. If more people saw the idea of infinite growth as a departure from the history of economics rather than a timeless law of nature, perhaps they’d be readier to reimagine the links between the environment and the economy.

In 1950, the economics profession had surprisingly little to say about growth. That year, the American Economic Association (AEA) asked Moses Abramovitz to write a state-of-the-field essay on economic growth. He quickly discovered a problem: There was no field to review.

Yes, John Maynard Keynes had offered a theory of stagnation, demonstrating the need for government spending to stimulate an economy mired in recession, and Austrian political economist Joseph Schumpeter had studied creative destruction, highlighting the importance of entrepreneurs and innovation. Wesley Mitchell, founder of the National Bureau of Economic Research, had looked at business cycles and others had analyzed monetary forces. But no one had put it all together in a theory of growth. Modern work was “fragmentary” and had “remained on the periphery of economics,” Abramovitz explained to AEA members. Development economist W. Arthur Lewis agreed, noting in 1955 that “no comprehensive treatment of [economic growth] has been published for about a century.”

It was an interesting turn for a field originally quite interested in growth, but convinced it was bounded. The founding fathers of economics—luminaries including Adam Smith, David Ricardo, and John Stuart Mill—shared a belief that growth was finite, and that the reason for limits lay in the natural world.

And then along came Robert Solow:

Solow launched modern growth theory with a pair of pioneering articles written in 1956 and 1957. Still alive today, he has done more to shape growth theory than any other thinker.

Like Abramovitz and Lewis, Solow turned his attention to growth in the 1950s because the topic was “in the air.” Calculations of Gross National Product (GNP) had been pioneered during World War II and were spreading across the globe. Fueled by international competition and the reality of robust economic expansion in many nations, growth had quickly become the catchword of the day in economics departments and government bureaucracies.

Solow advanced these discussions with a new model of growth, one that sought to analyze the relative contributions of capital, labor, and technical progress. Whereas Smith, Ricardo, and Mill had taken for granted that land was one of the three factors of production with labor and capital, Solow assumed that land did not matter. To the extent that land or natural resources merited mention (and they rarely did), they could be seen as a sub-category of capital, interchangeable with money or machines.

Ignoring land meant cutting the natural world out of modern growth theory at its inception. Solow wrote that this seemed the “natural assumption” to make in a theory of growth, though he did not specify why. And since in the 1950s, abundant land and resources appeared available, few would have disagreed. Moreover, Solow was a modeler, and the chief virtue of a good model is that it simplifies. A map of a city that included every detail would be as large as the city itself, of course, and of no real use. With bottomless pools of oil in the Middle East, extensive minerals from developing nations, and swaths of farmland available, why clutter a model by including them?

And then along came the environment movement of the 1960s and the 1972 report, The Limits to Growth, which Solow dismissed. But

...he was a left-of-center thinker committed to government intervention and planetary protection. He wrote about abating pollution and joined a Sierra Club board. And he scoffed at infinite models: The real world is so complex that to predict more than twenty years into the future is foolhardy, he once told a Congressional committee. [...]

The specific blind spot in his model was climate change. When thinking about economic growth, he and other economists focused exclusively on inputs to the production process. Would we have enough coal, oil, iron, and minerals to make new goods? With price signals, substitution, and technological change, Solow and his colleagues were convinced we would. But they did not consider outputs—waste and pollution—to be more than a nuisance. They did not imagine that greenhouse gas emissions could be so consequential as to threaten ecosystem integrity in ways that could affect growth.

Whoops!

H/t 3QD.