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When the Robots Take Your Job

Some Intuitions From Recent Models of Automation

Published onJun 03, 2024
When the Robots Take Your Job

In What if we could automate innovation? I looked at a model of economic growth where part (or all) of the innovation process could be automated. A key takeaway from that post was that the rate of economic growth was related to the rate at which innovation tasks got handed off to machines, rather than the share of the innovation process that had been automated - unless that share is 100%, in which case things get weird fast. It matters a lot if we automate 2% of the remaining innovation tasks each year or if we automate 20% per year, but if the overall share of automated tasks is 1% of 99% it doesn’t make a big difference (100% is a different story). Today I want to talk about something that seems quite similar, but has some different implications: automation of non-innovation tasks.

Economists typically think about three major inputs to making all the stuff in the economy: ideas, labor (us) and capital (machines, buildings, tools - all the non-labor stuff that doesn’t get used up in production). Normally, we think of these inputs as being, to a large degree, complements to each other. More of the one makes the other more useful. Let’s set ideas aside and focus on the complementarity of labor and capital. Think about how a farm worker gets more productive when they have a tractor, and how a tractor is more productive when it has a driver.

But it doesn’t have to be that way. Sometimes capital is a substitute, rather than a complement, to a worker. For example, maybe it used to be that a farm manager oversaw a bunch of laborers driving tractors, but then those tractors become autonomous and now it’s the one manager overseeing a fleet of robot tractors. In this case, we get the same output with fewer workers.

There’s a flourishing literature that looks at the consequences of this latter kind of capital - the kind that replaces, rather than augments, human workers. For example, Acemoglu and Restrepo (2018)Acemoglu and Restrepo (2022), and Korinek and Suh (2024). In this post, I want to talk about a very simple equation that is inspired by the ideas in these papers, and which I think is a useful thinking tool. That equation is:

KL>N(A)NN(A)\frac{K}{L}>\frac{N(A)}{N – N(A)}

Let’s see where it comes from and what it implies.

Tasks and Effort

To start, this literature likes to think of the economy of being composed of a large set of different tasks. Tasks are not the same thing as jobs; instead a job usually consists of many different tasks. For example, running a farm requires tasks like plowing a field, planting seed, applying pesticide, harvesting, negotiating terms of sale, planning the operation, repairing equipment, etc. As you can see, producing and selling any good or service probably requires stringing together many such tasks, but set that aside for now and just focus on individual tasks.

Let’s next assume that performing tasks requires effort, where effort might be supplied by human labor or machine labor. The more effort you supply, the better the task is performed. A key assumption we’ll make is that effort has diminishing returns; the first bit of effort you supply makes a big difference, the second bit of effort not as much, the third bit of effort increases task performance by even less and so on.

We’ll assume some tasks can be only done by humans, and some can be performed by either humans or machines (we could also assume there are some tasks that only machines can do, but it wouldn’t affect our story). We’ll call the tasks that only humans can do “manual” tasks and the tasks that machines can do “automated” tasks. A key point is that the set of automated tasks grows over time as we invent new and more capable technologies. At the same time, the set of manual tasks grows as well, as people invent new things for people to do (possibly in conjunction with machines doing other tasks): think tasks that didn’t used to exist, such as writing code, influencing over social media, and writing living literature reviews.

Finally, we’ll assume one more thing: among the manual tasks, humans are interchangeable. Likewise, among the automated tasks, the machines are interchangeable. This isn’t realistic and later I’ll talk a little bit about how things change if we make the more realistic assumption that some people can do some things but not others. But as a starting place, this is perhaps not as unjustified an assumption as it seems at first. We can assume humans are flexible and can be trained to do just about any task. For machines, there are two ways you can think about this interchangeability. First, we might imagine there’s a market (say, abroad) where you can sell and buy capital. If you need to redeploy a tractor from the task of plowing to the task of assembling aircraft, what’s really happening is that we’re selling the tractor and using the proceeds to buy an industrial robot. Second, there might actually be some kinds of capital that are interchangeable. For example, maybe generative AI will eventually be capable of performing many different kinds of tasks; in the more distant future, humanoid robots might be very adaptable to different kinds of tasks.

An Equal Division of Effort

So now we’ve got an economy composed of manual and automated tasks. Here’s our next important simplification; assume all the tasks are equally valuable and equally responsive to effort. That’s not a crucial assumption, but it makes it much easier to illustrate an interesting consequence of the above scheme. Specifically, if all tasks are equally valuable and all tasks respond to effort in the same way, then that implies we will want to put the same level of effort towards each task.

To see why, imagine we have two tasks: Task X which currently enjoys the effort of three people, and Task Y which has no effort at all. If we have a fourth worker, should they work on Task X or Y? Well, given the assumption that effort has diminishing returns, the fourth worker will make a bigger difference if they work on Y, which currently has no one working on it, compared to task X, which already has 3 people on it. Remember, we’re also assuming tasks are equally valuable. Suppose the fourth person goes to work on Task Y, so that there are now three people working on Task X and one person working on Task Y. We can actually do better yet, if we take the third person working on X and ask them to go work on Y instead. That’s because we assume the drop in performance for Task X, as we go from three workers to two, is less than the gain in performance for Task Y, as we go from one worker to two. With two workers on X and two workers on Y, we produce the most from our four workers. Just so with the entire economy; we produce the most if effort is distributed equally among all tasks.

I’ve described this as if there is some decision-maker who directs people to tasks, and that might be a good description of a business deciding how to allocate workers among different tasks it performs. But the same result can also arise through competition between rival firms; imagine one business specializes in Task X and another in Task Y. If both tasks are equally valuable and equally responsive to effort, the business specializing in Task Y wants a worker more than the business specializing in X; getting that worker will lead to a greater gain in performance for them. So absent market power, they’ll pay more for it, and they’ll keep paying more for workers until they have the same number of workers as the business specializing in Task X.

OK, so the economy is going to want to divide up total effort evenly among all the tasks. But there’s a problem. Neither labor nor capital can do every task. So we might now be able to equalize effort across all tasks. 

To be concrete, let’s put some labels on things. We’ll assume the number of automated tasks is N(A) and the number of manual tasks is N(M), and the total number of tasks is N (so N(A) + N(A) = N). And we’ll assume the total available supply of capital is K and the total available supply of labor is L. Assume the units of labor are measured in worker-hours and the units of capital are measured in equivalent units - one unit of labor or capital supplies the same effort to a task.

OK, so we want to divide up effort equally across tasks. Can we do it? The easiest way to check is to start by diving up all the labor across all the manual tasks. That will result in L/N(M) effort per manual task. For all the automated tasks, we’ll divide the capital up across them, resulting in K/N(A) effort per automated task. Let’s assume the effort put into each manual task is not equal to the effort put into each automated tasks. That means we will want to shuffle some effort around in order to equalize effort per task, if we can. There are two possibilities.

  1. L/N(M)>K/N(A): In this case there’s more effort on the manual tasks, so we need to shift some of that effort to the automated tasks until they are equalized. Concretely, that means shifting human labor away from manual tasks, and towards automated tasks – remember we assume that machines or humans can do those tasks.

  2. L/N(M)<K/N(A): In this case, there’s more effort on the automated tasks. We would ideally like to shift some of that machine effort to the manual tasks, but we can’t: only humans can do manual tasks. We won’t be able to equally divide effort among tasks. Instead, the best we can do is evenly divide capital among the automated tasks, and human labor among the manual tasks.

These two situations have very different implications for workers.

Who is relatively scarce?

In the second situation (L/N(M)<K/N(A)), human labor is relatively scarce. We want to put more effort into manual tasks, but we’re stuck. There are only so many people, and we don’t know how to build machines that can replace people at these tasks.

This is a decent description of the world we live in today, so from here on let’s call this the status quo scenario. It’s a world where a worker-hour of human labor is more valuable than a worker-hour of capital, since it can do things the machines cannot, and which we want to do more of. Most importantly, people earn a higher wage than their machine equivalents in the status quo scenario.

In the first situation (L/N(M)>K/N(A)), it is capital that is relatively scarce, or equivalently, we have too much human labor relative to the number of manual tasks. In that world, the amount someone would be willing to pay a person to work on a manual task is less that the amount they would be willing to pay for them to work on an automated task.

If most people earn income primarily through their wages (and don’t own machines that they rent out to do other tasks), then this is probably a bad situation. To be concrete, suppose someone is an artist and the main task they perform is making images. Initially, this is a manual task, but if generative AI is able to make images that are just as preferred by the market, then the task becomes automated. The wage this person will be able to earn from image making will probably collapse, since generative AI can make images for very cheap and now this artist has to compete with generative AI on cost. More generally, we usually assume capital is fairly abundant, and all else equal abundant things earn lower prices. If humans are competing with abundant capital, they will earn lower prices for their effort.

Let’s call this scenario, where labor is relatively abundant, the wage collapse scenario.

Which Tasks?

So long as we live in a world where most people’s income comes from selling their labor, we want to avoid falling into the wage collapse scenario. We want to live in the world described by the status quo scenario, where L/N(M)<K/N(A). Recall that the total number of tasks is N; that implies we N(M) = NN(A). Let’s substitute N – N(A) for N(M) and then rearrange that equation to the following:

KL>N(A)NN(A)\frac{K}{L}>\frac{N(A)}{N – N(A)}

(status quo condition)

This equation - which I’ll call the status quo condition - describes a world where capital cannot substitute for human labor, and so human wages are high, relative to the price of capital. I think this equation embodies a pretty powerful idea (though they use a different notation scheme, it’s a key equation in Korinek and Suh 2024). Let’s consider a few implications of the status quo condition.

One of the first implications is that for human wages to collapse to the price of machine labor, we don’t need machines to be able to do everything. We simply need the number of automated tasks (N(A)) to rise to a sufficiently high level, relative to the other variables, such that the right-hand side of the equation is no longer less than the left-hand side. 

This is an important difference from the results of models of economic growth I discussed in my post What if we could automate innovation? That post also looked at a model where there were tasks, some of which could be performed by machine and some by labor. In that post, the number of automated tasks grew in every period, but so long as we assumed they could not quite do everything, the impact on the economy’s growth rates didn’t really change. But, the model discussed in this post implies the story is different when we’re talking about wages. Now we don’t need machines to be able to do everything (N(A) = N) in order for there to be dramatic changes to the economy from automation. If N(A) is high enough, the status quo condition might no longer be true, and wages can collapse.

A second implication is that, from the perspective of any one individual, the important question is not whether the tasks you do in your particular job get automated, but rather whether the overall status quo condition holds. In this model, if your tasks get automated, but the overall status quo condition holds, then you can just transition to another set of manual tasks. So long as the status quo condition holds, manual tasks still pay more for effort than automated tasks. On the other hand, if the overall status quo condition fails, it doesn’t matter whether or not the tasks you do, in particular, get automated. Your wage will collapse nonetheless. If, for example, you practice some kind of uniquely human task, say, performing live music, and the status quo condition fails, your wage collapses not because machines start to perform live music, but because you begin to compete with displaced human workers who start performing, after the jobs they used to perform got automated.

As an aside, this second implication depends on the assumption that any human can work on any manual task. You can drop that assumption if you like. Instead, assume people have innate talents for different kinds of tasks, and cannot be retrained to do a task they don’t have talent for. To get some intuitions about this kind of world, you can think of there now being more than one status quo condition, one for each set of tasks. If the tasks you do get sufficiently automated, people who do those tasks experience a wage collapse, but people who do other tasks don’t. That’s because, just as we can’t shift machine effort into manual tasks, we can’t shift the human effort of people skilled in one task onto tasks where they lack the skill. Under these set of assumption, it’s possible for wage labor to become extremely unequal. That would happen if some people perform tasks that no one else can do (machine or other humans), and earn high wages for their scarce effort, while other people can only do tasks where there has been a wage collapse.

Pause or Accelerate

A third implication of the status quo condition is that there are (at least) two distinct routes out of the wage collapse trap, and those routes have interesting echoes in different contemporary views on what we should do about advancing artificial intelligence.

For example, some have recently argued that we should pause the development of artificial intelligence, or slow it down (for example, to put into place better frameworks for evaluating its capabilities). This perspective is motivated by a range of concerns, including many unrelated to the impact on worker wages, but in the context of the model discussed in this post we can think of it as a call to slow (or stop) the increase in N(A), that is, the number of automated tasks. Among other things, slowing or stopping N(A) keeps us in the world where the status quo condition holds. Slowing the pace of automation is one way of avoiding the wage collapse scenario.1

On the other hand, others of various stripes have focused on the value of accelerating economic growth. If that acceleration energy is focused on more quickly growing N(A), then as we’ve seen, this could lead to a wage collapse - good for the people who own the machines, bad for people whose income comes from selling labor. But if acceleration is focused on increasing K - for example, by focusing on reforms that lets people more easily build capital and companies to distributes capital - then the opposite is actually true. Note that a higher value of K makes it more likely the left-hand side of the status quo equation is greater than the right-hand side, which is what we want. Making more capital is a way of keeping humans relatively scarce and avoiding the wage collapse scenario.

A related implication is that anything which slows the growth of capital could also push us into (or keep us in) the wage collapse scenario. For example, Korinek and Suh (2024) consider the case where building capital (or any other good or service) requires something besides capital and labor, which is in a fixed supply. This could be, for example, various kinds of finite natural resources. If we this scarce input halts our ability to grow the capital stock, then if N(A) advances (and N) doesn’t change, we’ll eventually fall into the wage collapse scenario.

Time to Build

So far we’ve seen that there are two ways to keep the price of human effort higher than the price of machine effort (we’ll talk about some other ways shortly): slow N(A) or speed up K. But while both routes can keep the price of human effort above the price of machine effort, in other ways they are not equivalent.

Let’s suppose we are in the world where labor is relatively scarce. Again, that world is described by our equation:

KL>N(A)NN(A)\frac{K}{L}>\frac{N(A)}{N – N(A)}

(status quo condition, again)

So long as we are inside the status quo situation, it turns out to be the case that wages probably increase if we build more capital. That’s pretty intuitive - as we noted at the very beginning of this post, economists usually assume that labor and capital are complementary. The way that this works in these kinds of task-based models is that we essentially assume that producing stuff in the economy requires chaining together lots of tasks.2 Instead of saying “how well a task is performed is based on effort” now we’ve moved the frame to “how much stuff of economic value you produce is based on how well lots of different tasks are performed.” Usually we assume tasks are in some sense multiplicative: if building something depends on how well my task and your task is performed, the impact of my effort is higher if you do your task well, than if you do it poorly. When tasks are multiplicative like this, it means that if there are more machines allocated to a task (because we have so much more capital), then those tasks get performed better and that is multiplicative to the impact of the human effort.

It’s also worth thinking about what happens to wages when automation is advancing (so N(A) is rising and N(M) is falling), but we’re still in the status quo scenario. In that setting, there are two dynamics that pull in opposite directions. As the set of manual tasks shrinks, more and more humans crowd into the shrinking set of tasks they can do. As the supply of people relative to the number of tasks they can do rises, wages will get pulled down, since effort has diminishing returns – you get less and less increase in performance for each additional worker. 

On the other hand, if we’re in the status quo scenario, recall that we wanted to apply more machine effort to the tasks humans are doing, but we couldn’t because only humans knew how to do those tasks. When we figure out how to invent a new kind of machine that can do what humans previously did, that eases that constraint. In general, as automation advances, effort on those tasks will go up, relative to when they were just performed by humans.3 And since how much we ultimately produce comes from chaining together lots of tasks, more automation lets us do some tasks better. That will tend to pull wages up. In practice, Korinek and Suh show that the relationship between wages and automation (in the status quo) is an upside U shape. If you hold everything fixed and start automating more things that humans can do, at first wages go up, but eventually they start to go down, as you get closer and closer to the wage collapse trap.

The figure below shows a simulation of this dynamic from Korinek and Suh (2024), for an economy where there is 10x as much capital as labor. On the horizontal axis we have the share of tasks that machines can do. On the vertical axis, how much economic output goes to labor (green) and capital (red). As you can see, as we automate a larger share of tasks, labor wins out, taking home more and more economic output, since spreading the capital across more tasks lets us do those tasks more effectively. Since producing goods requires chaining lots of tasks together, that makes human effort more productive. But at some point, this trend reverses. Once the number of tasks machines can do gets sufficiently large, further automation begins to hurt wages, because the set of tasks only humans can do grows small enough that the diminishing returns of having ever more labor available for those tasks overwhelms the multiplicative power of improving performance on automated tasks. Eventually, wages collapse and stay flat so long as we are in the wage collapse scenario.

From Korinek and Sun (2024)

What People Do

So far we have focused on the capital side of the equation. But that’s only half the equation. What about the people? Just as we can stay out of the wage collapse trap by expanding capital until it is abundant or holding back the tides of automation, we can also escape by curtailing labor supply (so as to make capital more abundant relative to labor) or by increasing the number of manual tasks. In math terms, to make the left-hand side bigger than the right-hand side, we can either shrink the denominator on the left (L) or increase the denominator on the right (N – N(A) or N(M)).


(status quo condition, yet again)

Acemoglu and Restrepo’s papers think hard about these dynamics. Let’s start with reductions in the supply of human labor (L). In practice, this is usually modeled as people choosing to work less, not that we actually have fewer people. The idea is pretty intuitive; when the price of human effort falls, people might choose to exit the work force on many different margins - they might retire early, they might choose to be a stay-at-home parent, they might spend more time investing in their education, they might opt to live off non-labor income (could be welfare, could be investments, whatever). So if wages actually do collapse, one way out of that trap might be people deciding not work if wages are sufficiently low (this is probably more likely if they also other sources of income support - maybe everyone owns a share of capital in this scenario). Note that if L falls, then the left-hand side of the status quo condition rises, since we are dividing K by a smaller number, and that makes it more likely to hold. And we might not have to wait until we enter the wage collapse scenario to hold for this escape valve to trip - as noted in the previous section, wages can begin to fall in the status quo scenario, if the number of automated tasks gets too high. If falling wages triggers people to exit the labor force, that could stabilize things.

The other option is expanding the supply of manual tasks. That would increase N(M) (which is just another way of saying N – N(A)) and divide the right-hand side of the status-quo condition by a bigger number, making it smaller and hence more likely for the condition to hold. Manual tasks don’t come from nothing - they are invented by entrepreneurs trying to think of services they can sell to people. And the profit you can earn from inventing a new task using human labor is higher if the cost of human labor is lower. This creates another kind of escape valve: as human labor becomes abundant relative to the number of tasks it can perform, the profit from inventing new tasks relying on human labor rises. This leads to an increase in N(M), which can keep us out of the wage collapse trap.

Indeed, creating new tasks is probably how we have historically escaped the wage collapse trap. Here’s an obligatory chart about the share of people (in the USA) who work on agricultural tasks. The ones who no longer do agricultural tasks didn’t primarily exit the labor force - they transitioned to new tasks.

Can we just repeat this trick forever? Korinek and Suh worry we can’t. The way they think about this is that, just as molecules are made out of more fundamental atoms, tasks are made out of more fundamental cognitive and physical capabilities. Capabilities here might refer to things like understanding language, doing symbolic reasoning, moving objects in 3D space, etc. We have so far not found a way to cost-effectively automate all those capabilities, which means we have a bunch of capabilities that only humans can do, which we can combine and recombine in new ways to make new manual tasks. But (they argue) there’s no reason advanced AI and robotics can’t eventually be invented that can perform every one of these fundamental capabilities. And if so, then advanced AI and robotics will be able to perform any task that is built up from combining them, and hence we’ll no longer be able to invent new tasks that combine capabilities that only humans have. If you think that eventually the number of manual tasks will drop to zero, then there is no amount of expanding capital (K) or restricting labor supply (L) that will keep you out of the wage collapse trap.

Thinking Through A Scenario

One thing I like about this framework is that it can help you think through various scenarios for the future. Here’s one I worry about.

Let’s assume Korinek and Suh are correct that tasks can be decomposed into a small and finite set of capabilities. Most of these are cognitive and physical capabilities, but not all of them. For instance, we also have conscious experience, we have a certain kind of empathy for others, we can confer social status, etc. Let’s call these “feeling” capabilities. Feeling capabilities can also be used in economic tasks: for example, coaching might be more effective when it comes from a human (rather than a robot), because we worry about how the coach feels about us. We might enjoy watching humans play sports because we empathize more with them then we would from mechanized players. We might prefer a live concert because we believe the performer is feeling some echo of the emotions she is expressing through song.

Let’s assume in this scenario, though, that most manual tasks are built from physical and cognitive capabilities rather than feeling capabilities. Let’s also assume the current technological trajectory will lead to the complete automation of all cognitive and physical capabilities, but not feeling capabilities.4 (If you want, you can also imagine most but not all cognitive and physical capabilities will be automated and you’ll get the same flavor of result) What happens?

The model we’ve been exploring implies we could pass through several stages:

  1. As automation of physical and cognitive capabilities advances, wages rise at first, since human effort is multiplied by increasingly good automated task performance.

  2. At some point (now?) there is a major acceleration in automation, as scaling up large language models leads to the rapid automation of cognitive capabilities and machine learning applied to robotics quickly automates physical work. The pace of automation outpaces our ability to grow our capital stock. Wages fall.

  3. This process continues until the status quo condition fails and wages collapse. Eventually, all cognitive and physical work is automated, though not tasks based on feeling capabilities. Unfortunately, this is a very small number of tasks, and so we are in the wage collapse scenario.

  4. Over time, the capital stock grows. Meanwhile, people begin to invent new manual tasks that rely on combining different combinations of feeling capabilities, which are not automated.

  5. Eventually the rise of the capital stock and the number of new feelings-based tasks leads to the return of the status quo scenario. Wages go back to rising as the capital stock is built up more quickly than the automation of these feeling-based capabilities.

This is a story of the status quo condition initially holding (stages 1-2), then failing (stages 3-4), before eventually holding again (stage 5). It’s not an entirely pessimistic story, since it ends with wage-earning humans doing alright, but neither is it really good, since we have to go through a wage collapse. And note, this simple economics model isn’t particularly well suited to helping us figure out what happens if wages collapse; what happens politically in a world where wages have collapsed and almost all the economic output flows to the owners of capital? I have opinions, but they’re not really informed by this model. Nonetheless, I think it remains a useful framework to carry around.

As it happens, Korinek and Suh (2024) run a simulation of something quite like this scenario. In the scenario they model, all physical and cognitive capabilities get automated in the next 5 years, but then there remains a long-tail of other capabilities that never get fully automated (though we continue to make slow progress on them). Their simulation proceeds through most of the five steps laid out above (skipping the first one). Wages fall, then collapse, as the pace of automation leaps ahead of our ability to build and deploy capital. But in the long run, eventually human labor becomes scarce on tasks that are sufficiently valuable that wages reach all-time highs.

From Korinek and Suh (2024)

But that period of wage collapse in the middle is certainly concerning.

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Cites the Above

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Articles Cited

Acemoglu, Daron, and Pascual Restrepo. 2018. The Race between Man and Machine: Implications of Technology for Growth, Factor Shares, and Employment. American Economic Review 108(6): 1488-1542.

Acemoglu, Daron, and Pascual Restrepo. 2022. Tasks, Automation, and the Rise in U.S. Wage Inequality. Econometrica 90(5): 1973-2016.

Korinek, Anton, and Donghyun Suh. 2024. Scenarios for the Transition to AGI. NBER Working Paper 32255.

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