Reaction Wheel

I do not see how one can look at [growth] figures like these without seeing them as representing possibilities. Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia’s or Egypt’s? If so, what, exactly? If not, what is it about the ‘nature of India’ that makes it so? The consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think about anything else. — Robert Lucas¹

In a state of nature, people get what the earth gives them. If we want more, we have to make it ourselves: what we make is pretty much what we get.

Economists have tried to figure out why economies grow since at least Adam Smith, and there’s a well-developed body of work on it. The gist of it is: people use tools to make things, so if you want to make more things you have to:

1. Increase the number of workers or the amount they work,
2. Give the workers more or better tools, or
3. Make the methods of production more efficient.

In a formula, the amount produced, call it Y, is some increasing function of labor (L), capital (the tools, K) and the productivity of labor and capital together (A).

\(Y = F(A,L,K)\).

This formula doesn’t really tell you anything, it’s just an organizing principal. I think, to get a feel for these things, it’s best to look at the actual numbers. This post runs through historical labor, capital, and productivity in the United States since 1948 using charts, so you (and I) can get a fact-driven feel for where economic growth comes from.

Gross Domestic Product

When we talk about economic growth, we’re usually talking about growth in Gross Domestic Product (GDP). US GDP is the dollar value of all the final goods and services produced in the US. “Final” means that you can’t just add up the dollar value of all the things everyone sells, because you would be counting the same things more than once. If a car manufacturer buys the tires for its cars from a tire manufacturer, you can’t count the revenue of the car company and the revenue of the tire company in GDP, you would be double-counting the tires. GDP is calculated, in part, by trying to get at the “value added” from each company, not the value of goods sold.

GDP is a decent measure of average well-being, since what you make is what you get. Like many of the quantities in this post, GDP is measured in dollars, but it is what is being measured—the sum of the things made—that is important.

A couple of things to note about these charts. First, I am using inflation-adjusted amounts, “real” dollars, indexed to 2017, unless I note otherwise. Also, I often use four year moving averages (centered) when I show growth rates. This makes it easier to see trends. The actual growth rate per year and per quarter fluctuates a lot more, as you may have noticed. But if you go back and look at the chart of GDP, you can see the overall growth in GDP overwhelms the near-term fluctuations. The charts that use moving averages say so in the subtitle. Last, many people try to emphasize changes by only showing part of the vertical axis—from 50% to 60%, say—but I think this is misleading. These charts always show the full range, including zero.

GDP has to be shared among the population, so GDP per capita is a better corollary of average well-being.

US real GDP per capita has grown, on average, about 2% per year since 1950.

When GDP per capita grows, it means we are making more things or more valuable things per person, and so, on average, each person gets to have more things and more valuable things.² “More stuff” doesn’t sound like a great goal, but compare what more stuff means to people over the course of years. As real GDP per capita increased from ~$7 thousand in 1901 to ~$67 thousand in 2023 (a more than 900% increase, or about 1.9% per year), people got more food (68% increase), healthcare (2000% increase), more education (1000% increase), more house (660% increase), more entertainment (1500%), and more travel (the amount spent on transportation isn’t even counted in 1901). This doesn’t count the improvement in quality people don’t have to pay for: despite people having more and better clothing today, the expense per person is essentially the same in 2023 as in 1901.³ So “more stuff” doesn’t just mean more flat-screen TVs, it also means more healthcare, more education, more travel, etc.

Countries that have had higher GDP per capita have lower poverty, of course, but they also have a higher life expectancy, better human development, and higher life satisfaction. If GDP per capita had grown at 1% instead of 2% since 1950, the US GDP per capita would be half what it is, and many of these good things would have happened less. Growth is important.

Of course, GDP per capita is not everything when it comes to material well-being or happiness. First, there are things that make people well-off and happier that can’t be measured by money. Second, GDP per capita is an average; if most of that value is accruing to just a few people, then those people might be well off, but the median person will not be. This post is going to focus on growth, but keep in mind that the difference between a golden age and a gilded age is how wealth is distributed.

Where GDP Comes From

Land, labor, and capital, of course. Labor is the work that people do, and capital is the tools and machinery they do it with. The farmer is labor, the tractor is capital. In basic theories of economic growth, land—which includes natural resources—is neglected because it doesn’t change much so it doesn’t affect growth. The labor to extract or use the natural resources does, and this is what’s counted. So, a simple theory of the economy is that the amount of output (GDP) is a function of labor and capital.

\(Y = F(L,K)\).

F is the production function. I’m not going to dwell on theory here, I gave you some resources above. But I need to lay some groundwork, so bear with me.

The relation of labor and capital to output isn’t linear. There is a balance needed between labor and capital. If you double the number of farmers but don’t double the number of tractors, you won’t double the output of the farms. And if you double the number of tractors but don’t double the number of farmers, you won’t double the output of farms. Economists crunch the numbers to figure out what that balance is at any point in time. The tradeoff over the course of the numbers in this post looks roughly like this (the various curves—n=1, n=1.5, n=2—show the tradeoff at various levels of output):

Imagine labor and capital were equal but then you triple the capital used in production and halve the labor: you maintain the same level of output. If you tripled the labor, you could quarter the capital.⁴ Or, if you wanted to increase output by 50% with the same level of labor, you could increase capital by about 160%. This makes sense! Labor and capital work together: they aren’t substitutes.

That way you put that chart into a formula⁵ is as a geometric weighted average:

\(Y = AK^\alpha L^{1-\alpha}\)

\(\alpha\) is the measure of the tradeoff, which is relatively constant. The first variable, A, is the productivity parameter, used to measure how productive labor and capital are.⁶

Business Output

Enough theory, let’s look at the numbers.

To make this whole thing tractable, we are not going to look at GDP, we are going to look at business output. (This is technically “private business value-added output”, but we will just call it “business output”.) This excludes government-generated GDP because government-generated GDP is a can of worms, so it both wouldn’t teach us much and may teach us way too much at the same time. Business output is a large fraction of GDP and tracks it pretty well.

Labor Productivity

The economy is for the benefit of people. And while people are dependent on the economy, they are more important than it. In this sense, I center my economic thinking around what people can produce because what a person can produce determines, on average, their economic well being, and their well-being is the point of the economy. The most important number, the number everything else in this post serves, is labor productivity, Y/L: output per unit of labor.

L, the amount of labor used to produce goods and services is a product of several factors:

• Total population;
• Labor force participation;
• Hours each worker works;
• Labor composition.

Let’s start with population. The more people who live here, the more there are to work. This doesn’t make any difference to GDP per capita, of course, because population divided by population cancels out. But having a large GDP is, in itself, important. There are scale effects to both industry and research, and political power depends in part on how much weight you swing. Consider, as an example, the US unease over the growth of China. China’s GDP has grown from 11% of US GDP in 1960 to 64% in 2024 ($18.7 trillion in 2024 versus $29.2 trillion for the US).⁷ They are catching up fast! But because they have such a large population, their GDP per capita is nowhere close: $13,303 per person in China, just 15% of the US’s $85,810. While the Chinese people are nowhere near as well-off economically as we are, the geopolitical implications of Chinese control of what might soon be the world’s largest economy are still worth thinking about.

That said, creating per capita growth is only secondarily a function of the size of the population. It is more immediately affected by the proportion of the population that works, the labor force participation rate.

Labor force participation has changed pretty radically since 1960. A big part of the increase to 2000 was woman entering the workforce, slowed a bit by teenagers staying in school. The decrease since 2000 is partly baby boomers aging out. The 2000s also saw a big decline in the number of teens working, partly as a result of higher school enrollment rates, though there was also a decline among those who were not in school. In addition, there has been a much discussed decline in male labor participation since the 1960s.⁸ There’s a lot to explore here.

But business output is growing faster than the number of employees: business output per worker quadrupled since the end of World War II, shown in the chart below. (I also show GDP per all workers so you can see that they grow similarly.)

Output per worker has grown most years since 1948 except for a few years around 1980, when there was a severe recession.

One drag on business output per worker is the decline in the number of hours each worker works per year. All else being equal, if someone works fewer hours, they produce less.

This decline in the number of hours per worker seems to be due to a rise in part-time work because of changes in the composition of the American economy.⁹ Services businesses like retail are more amenable to part-time work than manufacturing.

To get a sense of how productive workers really are, we should look at business output per worker hour.

Output per labor hour is called, unsurprisingly, labor productivity. You can see this has grown, even during the early 1980s recession.

Some of the improvement in labor productivity per hour is because workers are better trained than they used to be. Economists call this labor composition because it is measured by sampling the productivity of variously-skilled workers in specific industries, and it is the composition of skills that determines average output.¹⁰ But it strongly implies that more training—both on and off the job—and more experience increase the average worker’s effectiveness. Because wages are used as a proxy for skill, but wages differ by industry for other reasons, labor composition is expressed as an index so it can be compared and combined across industries. You can see it has grown by about 30% since 1948.

More highly-skilled workers produce more. In the below chart, the upper line shows actual output per hour since 1948 while the lower line shows what output per hour would have been if workers had not become better at their jobs through training and experience.

In summary, real US business output increased by about 12x from 1948 to 2023. 29% of this growth can be attributed to changes in the labor force.

• +25% from more people working (which is mostly because the population has grown but also because a higher proportion of people are working);
• -5% from fewer hours worked per person; and
• +9% from a better trained workforce.¹¹

The chart below is how labor affected growth by decade. So, for instance, in the 1960s, business output grew by 54.8%. Of this, growth in the labor input accounted for 12.5% (the other 42.3% was…something other than labor; we’ll get to that next.) Of the labor growth, 1.8% was due to improvement in labor composition, 14.4% was due to more workers—9.3% because there were just more people in the country and 5.1% because more of them worked—and a decrease of 3.7% was due to fewer hours per worker.

When you think about growing the labor component of production (aside from population growth because it has only an indirect effect on GDP per capita) then there are three things to work on:

1. Labor force participation: take away obstacles to working; ease working-age immigration.
2. Hours worked per worker: provide the ability for more people to work more hours, if they choose.
3. Labor composition: provide more training and education; encourage skilled immigration.

But increases in labor are only part of growth, and not the largest part.

The blue part of each bar is labor. The orange part is non-labor, a big part of which is growth in capital.

Capital

Labor productivity increases when workers have more tools. The measure of this is the capital cost. The higher the capital costs, the more productive workers are.

Capital cost isn’t how much it costs to buy the tools, it is a measure of the productive capacity of the tools being used. This is found by looking at total capital stocks and then estimating the rental price of those assets; converting stocks into flows. (Note also that capital costs do not include the cost of financial capital: there is no industry I can think of where workers directly use currency as a tool.)

Capital grows when businesses decide to invest. There are all sorts of reasons for this, of course, but things like interest rates, tax policy, confidence in the future (low uncertainty, predictable government policies, faith in institutions, etc.) all play into it. I have overlaid US recessions, in gray, in the chart of growth in capital costs below and you can see a correlation (though I am not going to vouch for causality.)

When looking at labor productivity, what matters is not the amount of capital by itself—if you double the capital but triple the labor, each worker will be less productive—but the capital per labor unit, called the capital intensity.

When worker hours go down, as they did during the pandemic, capital intensity goes up—capital isn’t usually really rented, so it can’t change as quickly as worker hours can—so the remaining workers become more productive. If you look back at the chart titled business output per worker hour, you can see the corresponding blip in labor productivity during the pandemic. This reverts when the economy recovers because the previous worker/capital level was probably closer to the correct tradeoff (that’s why it was the previous level: businesses are always looking for the right tradeoff because that’s where they maximize profits.)

Growth in capital intensity—called capital deepening—means each worker gets more (or better) tools, increasing their productivity.

Since 1948, 40% of the increase in business output has been a result of increases in capital.

Below is a chart showing the contributions of labor and capital to growth by decade. So, in the 1960s, business output grew by 54.8%. 12.5% of this was attributable to growth in labor, as described above. 16.5% was attributable to increases in spending on capital. 25.7% was something else.

TFP

The something else, the blue “other” in the above chart, is an improvement that is not an increase in labor or capital. This could plausibly be a measurement error, an artifact of a complex economy, or a change in the labor/capital mix. But if it had been one of these, it would have been discovered or been temporary. The blue is both consistently present and compounds (ie. this is growth in each period, so today’s GDP reflects all previous growth in blue.) It is also as important as labor and capital in explaining growth.

By process of elimination, this “other” has to be an increase in our production function’s productivity parameter, A. This is called Total Factor Productivity (TFP; or, by some economists, Multifactor Productivity, MFP) because it is the productivity of all inputs together (as opposed to, say, just labor productivity.)

Most economists think TFP increases because of technological progress. For example, US farms, from 1910 to 2007, have kept the amount of labor and capital inputs pretty constant. Yet farm output in 2007 was 3.6 times more than in 1910. All of this increase had to be because of increased TFP.¹²

Farming saw massive technological change over that period. Not just trucks, tractors, combines, and balers, but fertilizers, new plant breeds, and an improved understanding of how to maximize crop yield. While the tractor, say, is capital, the increase in productivity here is not more money being spent, but tractors being more productive than an equivalent amount spent on horses and horse-driven plows. Better technology can improve the productivity of labor and capital.

The chart below shows annual US TFP growth (blue) and a ten year moving average (red).

The first thing that pops out at you is that TFP growth is pretty variable year to year. If it were just progress that shouldn’t be the case. Technology did not go backwards in 1980, for instance. Productivity can change as a result of other things, but these changes are usually temporary. As the San Francisco Fed notes:

When the pandemic struck in 2020, the economy was thrown into disarray. Productivity initially soared well above its pre-pandemic trend…But by the beginning of 2023, productivity had retreated to its slower trend…a qualitatively similar experience occurred around the Great Recession of 2007 to 2009. Labor productivity rose sharply above its pre-recession trend, then gradually returned to trend over a few years. This pattern suggests that productivity growth more generally has a systematic relationship with the business cycle.¹³

They give several reasons for this.

1. A change in labor composition as lower-skilled workers lost their jobs at a higher rate.
2. As workers are laid off but capital stays the same, capital intensity increases (economists call this “capital deepening”) making each worker more productive.
3. Different industries have different rates of productivity, so if the output mix changes—as it did early in the pandemic, when services companies, who typically have lower labor productivity, temporarily shut down—it can show in the productivity stats.
4. After a downward shock, companies may deal with uncertainty by hiring more slowly and asking existing employees to work harder for a period of time. (It is reasonable to assume this is not sustainable, otherwise they would always ask.) Because labor is measured in hours worked, not intensity, this would increase productivity.

The first two effects (labor composition and capital intensity) can be seen in their respective charts. The third shows up in those two charts as well. The fourth would not show up in labor or capital so would be captured by the “residual”, TFP.

But in the longer term, each of these things would swing back towards where they were prior to the shock, due to the invisible hand of the market. Employees would not work harder unless they were paid more, and replacing the less-skilled workers with higher-skilled workers would require higher salaries. Both of these would show up as an increase in the labor input, since labor is measured in dollars. Retaining an elevated capital intensity would require more capital spending as employees are re-hired, etc. Businesses try as best they can to optimize their labor and capital inputs and, to the extent they have been generally successful at this in the past, we should not expect to see large or permanent growth from changes in the mix.

There are changes that we would probably not consider “technological” that can improve productivity. Adam Smith’s pin factory, for instance—the division of labor—improves productivity. But we might not consider this technology because we have a limited view of what technology means. When you think about it as implementing new ideas about how to do things (or, as Paul Romer calls it, “better recipes”¹⁴) division of labor fits the definition. There was (and is) a possibility that remote work, as another example, could be a permanent boost to productivity in some jobs, if implemented correctly. Even though it is not a new “technology,” it might be a better recipe.

Long Term Growth

Over the course of human history, economic growth has had two eras. In the first, prior to the industrial revolution, there was no consistent growth in income per person. Whenever there was an increase in production, and thus in resources, more humans survived to enjoy it, keeping per capita income the same. But around 1800 or so, some of humanity escaped this Malthusian trap, and took control of their own destiny.¹⁵ Much of humanity is still catching up.

Some economists¹⁶ argue that this era of growth was an anomaly and that we have returned to the pre-industrial status quo ante. If this is so, and remains so, we (well, our children and granchildren) may experience a regression in developed country well-being as production and resources are eventually more evenly globally distributed and population growth outpaces economic growth. This would, as you can imagine, cause exceptional difficulties.

There are three ways to promote economic growth:

1. Increase the total hours worked and quality of labor;
2. Deepen capital; and
3. Create and deploy improved technologies.

The first is, obviously, limited both practically (while there is room for improvement in training and skills, there is not unlimited room) and morally (making anyone besides investment banking analysts work 160 hours a week is inhumane.) The second is also limited, though less obviously: there is an optimal capital/labor ratio with any given set of technologies and spending more (or less) on capital after this point diminishes economic growth by misallocating resources. It is important to allow the economy and society to find the best way to allocate labor and capital, and this is more than fine-tuning. Compare the US to countries that manage their economies less well and you can see the difference in living standards; this is something worth getting right.

But the third piece—innovation—is worth focusing on. It is important and has infinite room to improve. We also aren’t sure exactly how it works. Since 1948, some 80% of US per capita economic growth can be attributed to increases in TFP, but we don’t know how, exactly, to promote the innovation to keep this up; economists sometimes call TFP the “measure of our ignorance.”¹⁷ Obviously, it is in our best interests to do what we know works: invest in training innovators and doing basis science and research. But it is also important that we embrace the close connection between knowledge, innovation, and progress.

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1. Lucas, Robert E. Jr., “On the Mechanics of Economic Development”, Journal of Monetary Economics 22 (1988) 3-42, p.5. ↩

2. This post is going to ignore exports and imports because they don’t make a huge difference to the explanation, which is already too complicated. ↩

3. Data sources: BLS, “100 Years of U.S. Consumer Spending“, Report 991, May 2006; and Meyers, S., Paulin, G.D., and Thiel, K., “Consumer expenditures in 2023“, BLS, Report 1112, December 2024. ↩

4. In reality, these tradeoffs probably only really apply when you don’t change labor or capital that much, which the economy as a whole doesn’t. There are other ways to conceptualize this, but we’re using this one. It works for the kind of perturbations in a functioning economy. ↩

5. Called the Cobb-Douglas production function. ↩

6. This is, as economists’ equations are, a model. It works pretty well, but consider what would happen in a place where there was no tools, only labor. Since K would be zero, the equation says there could be no output. Of course, we can imagine a situation where this is not true. But the model seems to work reasonably well in our economy, and that’s all we need it for here. ↩

7. World Bank data: https://data.worldbank.org/indicator/NY.GDP.MKTP.CD?locations=US-CN ↩

8. BLS, “Labor force participation: what has happened since the peak?”, September 2016. https://www.bls.gov/opub/mlr/2016/article/labor-force-participation-what-has-happened-since-the-peak.htm ↩

9. Shawn Sprague, “Why are average weekly hours worked declining?” Beyond the Numbers: Productivity, vol. 13, no. 3 (U.S. Bureau of Labor Statistics, April 2024), https://www.bls.gov/opub/btn/volume-13/why-are-average-weekly-hours-worked-declining.htm ↩

10. BLS, “New Method for Estimating Labor Composition for Total Factor Productivity Measurement”, November, 2022. https://www.bls.gov/productivity/technical-notes/labor-composition-for-total-factor-productivity-using-new-method-nov-2022.htm ↩

11. Note that the percents attributable to growth are less than the percent these things themselves have grown because labor is only two-thirds of the geometric weighted average from the production function above. ↩

12. Pardey, P.G., Alston, J.M., “The Drivers of U.S. Agricultural Productivity Growth”, Federal Reserve Bank of Kansas City, 2021. https://www.kansascityfed.org/Agriculture/documents/7107/the-drivers-of-us-agricultural-productivity-growth.pdf ↩

13. Fernald, Li, et al., “Productivity During and Since the Pandemic”, FRBSF Economic Letter 2024-31, November 25, 2024. ↩

14. https://paulromer.net/deep_structure_growth/ ↩

15. Chart from Clark, G., A Farewell to Alms. ↩

16. Notably, Robert Gordon in his Rise and Fall of American Growth. ↩

17. Abramovitz, M., “Resource and Output Trends in the United States Since 1870”, NBER, 1956, p. 11. http://www.nber.org/books/abra56-1. ↩