My central takeaway from learning the Solow growth model as an undergrad was not the limits of investment but the idea that long term, sustainable growth depends ultimately on “total factor productivity” growth, which is most easily thought of as exogenous technology improvements.
In my mind, China didn’t grow its economy over the last two decades just been building a lot of physical capital but also by copying technology left and right. It will continue to do so. Meanwhile, it is now publishing more technical papers than the US and is innovating in its own right. Solow’s model would predict much more growth to come for China.
Perhaps, but TFP growth has been slowing down quite a lot in China. Estimates vary, but Chinese TFP is probably now growing at around 1%, which is around the typical rate for the U.S.
One issue here is that TFP isn't actually just technology. It also has to do with institutions -- i.e., how efficiently technology is used to create things that people want. And here China may be stumbling, with a crackdown on the IT industry, excessive reliance on real estate (now being unwound), and a shift back from private to state-owned enterprises.
Just to add... innovation is one part of the question, but embracing creative destruction is another. The front of the pipeline can be healthy, but if you don't allow the massively destructive effects to percolate through your economy, you don't get a fundamental shift in the economy. The soviets had some of the best scientists in the world. Centrally controlled economies have great difficulty with the latter point.
BTW..I would be very wary of the patent/publication numbers as any real indication of innovation... this is especially the case in the last 20 years with the massive inflation in academic conferences.
“Solow’s model would predict much more growth to come for China”
I think you would be correct if China were a Democracy with open and transparent institutions.
The corruption and government prioritization of power over growth will limit China’s ability to innovate. Your argument is basically that innovation can save China’s economy, but I think your optimism is misplaced. China has repeatedly killed its own long term growth via crackdowns on various industries that Xi dislikes, the one child policy, the hukou system, over investment in infrastructure, and aggressive antagonism of Western nations that have resulted in strict export controls. An open society and vibrant democracy with transparent institutions wouldn’t have made these mistakes and China would still be growing rapidly. I am almost certain that the CCP will continue to make similar mistakes and inevitably kill its own R&D.
Weirdly, I learned this in grade school playing Sid Meier's Alpha Centauri. It also teaches that this same lesson applies to both military forces and territorial expansion: "more stuff" means more expenses, and expanding *anything* too far eventually exceeds your ability to economically support it. That game was genuinely quite a teaching tool.
Learning a lot about the state-of-the-art in economic modeling from your columns. As a technologist looking from the outside, there seems to be a big hole in economic theories around handling technology. As you said, "A mysterious quantity called “total factor productivity” (TFP), usually abbreviated as “A”, which some people associate with technology" well said.
It appears most economic theories build models with the core idea of conservation of capital/labor with a more or less static mapping between inputs and outputs. This works ok when looking backwards as the rate of change due to technology looking back is always a slower rate. However, it does not work too well looking forward...especially when technologies introduce large non-linearities into the economy.
Hopefully someone in the economics research realm is thinking about this issue because it seems to be the key issue in meaningfully building predictive models of future growth.
Same. Had I more free time (and inclination), I'd go looking for updated econ theories around software. We've been shifting greater and greater portions of our investments (in the USA and some of the west) away from physical goods where marginal utility, cost, and depreciation are better understood. As a career software nerd and now geek-wrangler for decades, I'm not convinced that we can apply the same physical model to software assets: code, data, models, etc. Software assets don't have the same characteristics as bridges, roads, buildings, or even phones.
If you understand depreciation as the effect of the 2nd law of thermodynamics on assets, it also applies to software: irreversible changes in the software's context of use reveal new flaws (from bugs or limitations) that need to be addressed by costly maintenance.
Dave... LOL... let's generalize SW to Intellectual Goods. I think you are very right.
In my professional career, I moved from shipping HW (computer systems) to SW. I found it very interesting how basic accounting was challenged by the key characteristics of SW...with concepts around "inventory" or "shipped product." Of course, SW/IP has the very interesting property that it scales easily in non-linear terms.
Now.. here is the interesting part.... SW directly and materially impacts the physical world. Take ecommerce as a simple example, the change in investment in physical assets is massive... often in a nonlinear fashion. Imagine the impact of autonomy or AI SW agents.
It’s more difficult to understand capitalization and depreciation of software than most physical capital due to a lot of software tends to be in constant change but that doesn’t mean it isn’t happening. Most large scale software systems, particularly software developed at publicly listed US technology companies, are capitalized and depreciated. In fact, the constant change acknowledges that the software is depreciating.
While created for different reasons, the principle of continuous delivery enabled the financial innovation of subscription software models which innovation saw modern software businesses valued higher than most others in the market.
The profession has moved on to incorporate more than labor and capital. Paul Romer developed a well regarded endogenous growth theory that explains how technology develops. I don’t pretend to have studied it, but he won a Noble Prize for it.
The personal experience version of the theory: As you start adding property to your life, you will increasingly lack time to enjoy it, since you are busy with maintenance.
“ . . . the easiest type of physical capital to imagine is a machine tool — a sewing machine, or a drill press, or a lathe, or a nanolithography machine.”
I first invested in ASML in 2013. Its EUV machines are the only way to make AI widely adaptable. The amount of compute power required for training AI modeling is multiples more than exists today. The payback in much higher productivity of repetitive tasks makes this affordable.
Canon’s cheaper chip lithography machine would be a significant leap forward. I wouldn’t underestimate Canon’s CEO or its expertise. It could play a crucial role in the future of EUV-produced chips for smaller market niches — a startup or developer’s dream. Imagine the knock-on effects of making production affordable for all the lone geniuses designing their own bespoke chips. Inevitably, EUV-produced chips will become affordable for nano-caps, micro-caps, and mid-caps. This would, of course, level the playing field and stimulate exponential growth of more companies in the lower tiers of the high-tech sector.
ASML owns the market in EUV, but Canon could create its own market with a cheaper machine.
China, which the pundits predicted would dominate AI/ML, isn’t even in the game.
Could this also apply to all that military buildup? The zillions of ships they’re building could be a long term maintenance burden, since nothing is more expensive to maintain that a boat.
“The general rule is that technology transfer is overwhelmingly difficult without and even with extensive written documentation, and usually requires skilled and knowledgeable people with a deep understanding of the processes being adopted. The Soviet government before WWII could not set up its machine tools that it had bought from the U.S. auto industry without the comprehensive and hands-on direction and help from American engineers.”
-- Brad DeLong
This sounds like what’s happening with TSMC’s build out of a chip fab in Arizona. American engineers have little experience building a chip fab housing an ASML 3nm machine, nor building at the pace of East Asia countries.
Does the Solow model also suggest the potential impact of AI? For example, one ostensibly straightforward application of AI would be to increase marginal returns to capital (e.g., self-driving cars), and potential future applications could mitigate depreciation (maintenance robots).
Why isn't AI possible to model within the Solow model? It could add both to labor and "efficiency" in the form of faster innovation and better processes throughout many parts of the economy?
The Solow model takes technology as given; companies can't affect technology. That's why to model the interactions between technology and the rest of the economy, you need an endogenous growth model. I'll do a post soon explaining some of these.
When I see the word ‘savings’ I think of personal saving accounts and the like. Where do Chinese savings in the context of your explanation get extracted from and reside?
Chinese people and companies deposit money in banks, and they buy bonds ("trust products", "wealth management products") offered by a variety of financial organizations that are collectively known as shadow banks.
So is the high savings rate more of a cultural phenomenon than a government policy? Sounds like they could just spend more of their money if they wanted to.
Ouch. Doesn't bode well for Indonesia - the last decade under Jokowi they've built a lot of physical stuff. Hopefully it doesn't get caught in this deprecation trap!
Indonesia will eventually hit this wall, but they have a long way still to run before they do. For Indonesia, the most important task now is to pivot from resource exports back to manufacturing, since manufacturing is a good way to import foreign technology and upgrade business skills!
A nice explanation of the Solow model and a nice tribute to a great economist. But the basic point was made by Ricardo, and was a standard feature of classical economics. Given diminishing marginal rates, and *no technological change*, capital accumulation eventually leads to the stationary state.
Things are much less clear with endogenous growth theory. At least in some versions, a country could invest lots of capital to dominate industries with lots of growth potential, and then capture the resulting technological advances.
Nice explanation of Solow's model. Charles Hall, a founder of Biophysical Economics (could be called, Economics as if there is a real world with laws of physics), ran regressions adding fossil fuel consumption and found most of the huge Solow residual went away. A lot of economic growth is explained by exploiting new energy sources. The ratio of energy in to energy out or EROI energy return on investment, is a determinant of standard of living or per capita output. The energy slaves idea reveals this: Americans have the fossil fuel energy output equal to a couple of hundred human slaves working for each of us. That's why we are rich. Luckily, EROI of solar and wind aren't bad, so the world can stay prosperous if we don't wreck it by climate change, extinctions, etc.
My central takeaway from learning the Solow growth model as an undergrad was not the limits of investment but the idea that long term, sustainable growth depends ultimately on “total factor productivity” growth, which is most easily thought of as exogenous technology improvements.
In my mind, China didn’t grow its economy over the last two decades just been building a lot of physical capital but also by copying technology left and right. It will continue to do so. Meanwhile, it is now publishing more technical papers than the US and is innovating in its own right. Solow’s model would predict much more growth to come for China.
Perhaps, but TFP growth has been slowing down quite a lot in China. Estimates vary, but Chinese TFP is probably now growing at around 1%, which is around the typical rate for the U.S.
One issue here is that TFP isn't actually just technology. It also has to do with institutions -- i.e., how efficiently technology is used to create things that people want. And here China may be stumbling, with a crackdown on the IT industry, excessive reliance on real estate (now being unwound), and a shift back from private to state-owned enterprises.
Just to add... innovation is one part of the question, but embracing creative destruction is another. The front of the pipeline can be healthy, but if you don't allow the massively destructive effects to percolate through your economy, you don't get a fundamental shift in the economy. The soviets had some of the best scientists in the world. Centrally controlled economies have great difficulty with the latter point.
BTW..I would be very wary of the patent/publication numbers as any real indication of innovation... this is especially the case in the last 20 years with the massive inflation in academic conferences.
“Solow’s model would predict much more growth to come for China”
I think you would be correct if China were a Democracy with open and transparent institutions.
The corruption and government prioritization of power over growth will limit China’s ability to innovate. Your argument is basically that innovation can save China’s economy, but I think your optimism is misplaced. China has repeatedly killed its own long term growth via crackdowns on various industries that Xi dislikes, the one child policy, the hukou system, over investment in infrastructure, and aggressive antagonism of Western nations that have resulted in strict export controls. An open society and vibrant democracy with transparent institutions wouldn’t have made these mistakes and China would still be growing rapidly. I am almost certain that the CCP will continue to make similar mistakes and inevitably kill its own R&D.
Weirdly, I learned this in grade school playing Sid Meier's Alpha Centauri. It also teaches that this same lesson applies to both military forces and territorial expansion: "more stuff" means more expenses, and expanding *anything* too far eventually exceeds your ability to economically support it. That game was genuinely quite a teaching tool.
Sid Meier develoed some great games. I like Civilization.
Learning a lot about the state-of-the-art in economic modeling from your columns. As a technologist looking from the outside, there seems to be a big hole in economic theories around handling technology. As you said, "A mysterious quantity called “total factor productivity” (TFP), usually abbreviated as “A”, which some people associate with technology" well said.
It appears most economic theories build models with the core idea of conservation of capital/labor with a more or less static mapping between inputs and outputs. This works ok when looking backwards as the rate of change due to technology looking back is always a slower rate. However, it does not work too well looking forward...especially when technologies introduce large non-linearities into the economy.
Hopefully someone in the economics research realm is thinking about this issue because it seems to be the key issue in meaningfully building predictive models of future growth.
Same. Had I more free time (and inclination), I'd go looking for updated econ theories around software. We've been shifting greater and greater portions of our investments (in the USA and some of the west) away from physical goods where marginal utility, cost, and depreciation are better understood. As a career software nerd and now geek-wrangler for decades, I'm not convinced that we can apply the same physical model to software assets: code, data, models, etc. Software assets don't have the same characteristics as bridges, roads, buildings, or even phones.
If you understand depreciation as the effect of the 2nd law of thermodynamics on assets, it also applies to software: irreversible changes in the software's context of use reveal new flaws (from bugs or limitations) that need to be addressed by costly maintenance.
Dave... LOL... let's generalize SW to Intellectual Goods. I think you are very right.
In my professional career, I moved from shipping HW (computer systems) to SW. I found it very interesting how basic accounting was challenged by the key characteristics of SW...with concepts around "inventory" or "shipped product." Of course, SW/IP has the very interesting property that it scales easily in non-linear terms.
Now.. here is the interesting part.... SW directly and materially impacts the physical world. Take ecommerce as a simple example, the change in investment in physical assets is massive... often in a nonlinear fashion. Imagine the impact of autonomy or AI SW agents.
It’s more difficult to understand capitalization and depreciation of software than most physical capital due to a lot of software tends to be in constant change but that doesn’t mean it isn’t happening. Most large scale software systems, particularly software developed at publicly listed US technology companies, are capitalized and depreciated. In fact, the constant change acknowledges that the software is depreciating.
While created for different reasons, the principle of continuous delivery enabled the financial innovation of subscription software models which innovation saw modern software businesses valued higher than most others in the market.
Good read as usual Noah.
The profession has moved on to incorporate more than labor and capital. Paul Romer developed a well regarded endogenous growth theory that explains how technology develops. I don’t pretend to have studied it, but he won a Noble Prize for it.
The personal experience version of the theory: As you start adding property to your life, you will increasingly lack time to enjoy it, since you are busy with maintenance.
“ . . . the easiest type of physical capital to imagine is a machine tool — a sewing machine, or a drill press, or a lathe, or a nanolithography machine.”
I first invested in ASML in 2013. Its EUV machines are the only way to make AI widely adaptable. The amount of compute power required for training AI modeling is multiples more than exists today. The payback in much higher productivity of repetitive tasks makes this affordable.
Canon’s cheaper chip lithography machine would be a significant leap forward. I wouldn’t underestimate Canon’s CEO or its expertise. It could play a crucial role in the future of EUV-produced chips for smaller market niches — a startup or developer’s dream. Imagine the knock-on effects of making production affordable for all the lone geniuses designing their own bespoke chips. Inevitably, EUV-produced chips will become affordable for nano-caps, micro-caps, and mid-caps. This would, of course, level the playing field and stimulate exponential growth of more companies in the lower tiers of the high-tech sector.
ASML owns the market in EUV, but Canon could create its own market with a cheaper machine.
China, which the pundits predicted would dominate AI/ML, isn’t even in the game.
Could this also apply to all that military buildup? The zillions of ships they’re building could be a long term maintenance burden, since nothing is more expensive to maintain that a boat.
“The general rule is that technology transfer is overwhelmingly difficult without and even with extensive written documentation, and usually requires skilled and knowledgeable people with a deep understanding of the processes being adopted. The Soviet government before WWII could not set up its machine tools that it had bought from the U.S. auto industry without the comprehensive and hands-on direction and help from American engineers.”
-- Brad DeLong
This sounds like what’s happening with TSMC’s build out of a chip fab in Arizona. American engineers have little experience building a chip fab housing an ASML 3nm machine, nor building at the pace of East Asia countries.
Does the Solow model also suggest the potential impact of AI? For example, one ostensibly straightforward application of AI would be to increase marginal returns to capital (e.g., self-driving cars), and potential future applications could mitigate depreciation (maintenance robots).
The Solow Model doesn't take AI into account. For that you need more advanced models:
https://www.nber.org/papers/w23928
Why isn't AI possible to model within the Solow model? It could add both to labor and "efficiency" in the form of faster innovation and better processes throughout many parts of the economy?
The Solow model takes technology as given; companies can't affect technology. That's why to model the interactions between technology and the rest of the economy, you need an endogenous growth model. I'll do a post soon explaining some of these.
Please! I’m very interested in refreshing what I know about growth models. It’s been a while (since the 90s)!
Triple play post! Homage, exposition, thoughtful diagnosis of China woes. Rest in power, Prof Solow.
When I see the word ‘savings’ I think of personal saving accounts and the like. Where do Chinese savings in the context of your explanation get extracted from and reside?
Two places: banks and shadow banks.
Chinese people and companies deposit money in banks, and they buy bonds ("trust products", "wealth management products") offered by a variety of financial organizations that are collectively known as shadow banks.
So is the high savings rate more of a cultural phenomenon than a government policy? Sounds like they could just spend more of their money if they wanted to.
Savings fund bank loans, which fund investments.
Ouch. Doesn't bode well for Indonesia - the last decade under Jokowi they've built a lot of physical stuff. Hopefully it doesn't get caught in this deprecation trap!
Indonesia will eventually hit this wall, but they have a long way still to run before they do. For Indonesia, the most important task now is to pivot from resource exports back to manufacturing, since manufacturing is a good way to import foreign technology and upgrade business skills!
I guess there's a lot of value to be gleamed from the low end of this graph that Indonesia will reap before they reach equilibrium.
A nice explanation of the Solow model and a nice tribute to a great economist. But the basic point was made by Ricardo, and was a standard feature of classical economics. Given diminishing marginal rates, and *no technological change*, capital accumulation eventually leads to the stationary state.
Thanks for this fascinating article!
Things are much less clear with endogenous growth theory. At least in some versions, a country could invest lots of capital to dominate industries with lots of growth potential, and then capture the resulting technological advances.
I appreciate these occasional lessons in proper economic theory. Not as a full time thing, but like every couple months. Thanks!
Nice explanation of Solow's model. Charles Hall, a founder of Biophysical Economics (could be called, Economics as if there is a real world with laws of physics), ran regressions adding fossil fuel consumption and found most of the huge Solow residual went away. A lot of economic growth is explained by exploiting new energy sources. The ratio of energy in to energy out or EROI energy return on investment, is a determinant of standard of living or per capita output. The energy slaves idea reveals this: Americans have the fossil fuel energy output equal to a couple of hundred human slaves working for each of us. That's why we are rich. Luckily, EROI of solar and wind aren't bad, so the world can stay prosperous if we don't wreck it by climate change, extinctions, etc.