# Did We Evolve the Capacity for Sustained Growth?

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

I posted a few pieces (here and here) recently on genetics and growth. The Economist even picked up on Justin Cook’s work on lactose tolerance and development. Justin’s work on both lactose and the HLA system are about very specific genes, while the other research I mentioned is about genetic heritability of certain behaviors associated with growth, without specifying any particular genes.

There is another line of research on evolution and growth pioneered by Oded Galor and Omer Moav. They propose that natural selection over different types of individuals could have led to the onset of sustained economic growth. In particular, they focus on selection over preferences for the quantity and quality of kids. This is very much the second kind of research I mentioned above; it does not identify some specific gene that matters for growth, it suggests a mechanism through which selection could have operated. The original paper is linked here, but they have a nice summary article here that explains the logic without all the math.

Let’s be careful about terminology here. Evolution in general requires both mutation and natural selection. GM is really about natural selection, not mutation. They take as given the presence of two types of people in the population. “Rabbits” like to have large families, but do not invest much in their kid’s human capital. “Elephants” have a few kids, but invest a lot in those kids. Their theory is about the proportions of those types change over time due to economic forces, and eventually how a rising prevalence of Elephants leads to a speed-up in technological change. Yes, at some point there must have been a mutation that led to the differentiation between the types, but we can think of that as happening well back in history. They don’t propose that some mutation occurred at some specific year or a specific place to make this all work.

How does the underlying logic work? In the early Malthusian period, with very low income per capita, the Elephants actually have the evolutionary advantage. Why? In the Malthusian world, everyone is so poor that higher income leads to higher fertility no matter your type. Each Elephant kid has high human capital, and thus relatively high fertility compared to Rabbits. So the proportion of Elephants tends to increase in the population. And a higher proportion of Elephants means that average human capital is rising over time.

As the human capital rises, so does the pace of technological progress. At first this doesn’t do much, as the growth of technology is not sufficient to overcome the force of Malthusian population pressure. But eventually there is high enough human capital that technological change happens so rapidly that people reach the upper limit on fertility rates, and choose to spend any additional income on increasing their kids human capital rather than having more kids. This is the tipping point where human capital and technological change go into a virtuous cycle. Higher human capital leads to higher technological change, which leads to higher human capital, etc.. etc.. and you have sustained growth. Once this occurs, the relationship of income and fertility flips to become negative – the richer you are the fewer kids you have, just the opposite of the Malthusian period. This flip in sign is not unique to their explanation based on natural selection, the same type of flip is central to the general unified growth model in Galor and Weil.

After this transition point, the evolutionary advantage also flips to Rabbits. Why? Because the fertility rates decline with income, and as Elephants are richer due to their human capital, they have fewer kids than Rabbits. So Rabbits begin taking up a larger and larger proportion of the population. But everyone is already relatively rich, so this doesn’t mean that human capital levels are low generally. There is sufficient human capital to sustain technological progress.

Do we know if this exact mechanism is what generated sustained growth? No. To establish that you’d have to identify the precise genes that govern preferences for quantity/quality of kids and show that they varied within the population over time in a manner consistent with the GM model. But there are little bits and pieces of circumstantial evidence that work for GM. Greg Clark’s Farewell to Alms documents his research showing that in fact richer families tended to have more kids in pre-Industrial Revolution England. This fits with the selection mechanism proposed by GM. Similarly, Galor and Marc Klemp have a working paper out on the reproductive success of families in 17th and 18th century Quebec (a place and time with particularly detailed records), and the data shows that it was families with moderate fertility rates that actually had the most kids in subsequent generations, not those with the higher fertility rates. Again, it fits the selection mechanism proposed by GM for the Malthusian era.

Note that even if it isn’t true genetic differences in preferences for quantity/quality, you still need to have selection working for population composition to matter for sustained growth. Let’s say that quantity/quality preferences are purely cultural, passed on from parents to kids imperfectly but with some fidelity over time. Then the GM mechanism could still hold up, but it would be the cultural spread of preferences for high quality that generated the take-off, not the spread of specific genes.

There are reasons to be skeptical about this explanation, just as you should be skeptical about any hypothesis. But don’t dismiss it on the basis that natural selection moves far too slowly for this to have mattered for human populations. Galor and Moav have a number of very telling examples regarding the speed of selection within populations over just a few generations. The classic story is peppered moths during the Industrial Revolution. Peppered moths tend to be white, with little black spots on them – hence the name. But there are black varieties. With the rise of coal in the UK black moths became far more prevalent, as they were harder to spot for predators against the blackened sides of buildings. Within a few years the population jumped from predominantly white to predominantly black. And then flipped back to white when clean air regulations came into force. Given the variation in the population already exists, natural selection can take place very quickly to change population composition. So imagining that human population composition could change substantially over hundreds or thousands of years is reasonable.

Last, does GM mean that generating growth in poor countries is doomed to failure because their genetic composition is “wrong”? No. GM is a story about the rise of sustained growth at the global level. Suggesting that poor countries need to get their genetic mix right in order to grow is like suggesting that they need to adopt steam engines and telegraphs before they can step up to gas engines and mobile phones. The question of how to catch up to the frontier is an entirely different question than explaining how we got a frontier in the first place.

# Plows were the Robots of the 13th Century

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

Jury duty this morning, which meant lots of quiet reading time and in the end no *actual* jury duty (yeah for settlements!).

I am reading Rural Economy and Country Life in the Medieval West, by Georges Duby. I came across the following description of how the development of improved harnesses and plows in the Medieval period displaced a large fraction of rural labor (p. 116):

On the other hand, manual laborers without draught animals underwent no technical progress and sustained no rise in yields: on the contrary there was a relative fall in their living conditions…..That the increased value of farming equipment strengthened the hold of the wealthy over the peasantry cannot be denied….Everywhere the lord maintained his authority over his men by helping them to acquire livestock or by threatening them with its confiscation. When in some provinces in the thirteenth century servitude was born anew and flourished, it was the need to acquire agricultural equipment, efficient though costly, which led poorer peasants to bind themselves into dependence. The same needs held them in servitude, for although they had the right to decamp….they could do so only…by giving up their plough animals. In fact because of this, agricultural growth appears to have been a very powerful agent of social differentiation.

A couple of things struck me about the passage. First, the analysis of the disruption caused by the introduction of a new technology embodied in capital goods (plows, harnesses, and horses) sounds similar to some worries regarding the introduction of robots. With capital owned by only a few, those without capital become dependent on the wealthy and have their living standards driven down. Second, innovation favors those with the skills to work with the new technology. Skilled ploughmen – who only got that way by having a team of horses and a plough to begin with – were the high human capital workers of their day.

Mainly, though, it is just an interesting example of how the same issues with innovation, technology, and displacement have been occurring forever. The question of what happens when robots are plentiful is not a question unique to robots, it is a question about how we adapt to disruptive technology. The evidence suggests that whoever owns the technology or the capital associated with it will use it as leverage over those who do not, just like always.

By the way, I think the lady next to me in the jury room would have looked less shocked if I had told her I was reading a porn magazine.

# These are Not the (Modeling Assumptions About) Droids You are Looking For

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

Let me start by saying that all future arguments about robots should use the word “droids” instead so that we can use more Star Wars references.

Benzell, Kotlikoff, LaGarda, and Sachs (BKLS) have a new NBER working paper out on robots (sorry, I don’t see an ungated version). They are attempting to do what needs to be done: provide a baseline model of economic growth that explicitly accounts for the ability of software in the form of robots to replace human workers. With such a baseline model we could then see under what conditions we get what they call “immiserating growth” where we are actually made worse off by inventing robots. Perhaps we could then use the model to test out different policies and see how to alleviate or prevent such immiserating growth.

Thus I am totally on board with the goals of the paper. But I don’t know that this particular model is the right way to think about how robots will affect us in the future. There are several reasons:

Wealth Distribution. The model has skilled workers and unskilled workers, yes, but does not distinguish between those with high initial wealth (capable of saving a lot in the form of robots) from those with little or none. This eliminates the possibility of having wealthy robot owners run the wage down so far that no human is employable anymore. While I don’t think that is going to happen, the model should allow for it so we can see under what conditions that might be right or wrong.

Modeling Code. The actual model of how capital (robots) and code work together seems too crude. Essentially, robots and code work together in a production function. Code today is equal to some fraction of the code from yesterday (the rest presumably becomes incompatible) plus whatever new code we hire skilled workers to write. The “shock” that BKLS study is a dramatic increase in the fraction of code that lasts from one period to the next. In their baseline, zero percent of the code lasts, meaning that to work with capital we have to continually reprogram them. Robotics, or AI, or whatever it is that they are intending to capture then shocks this percent up to 70%.

Is this how we should think about code? Perhaps it is a stock variable we could think about, sure. But is the coming of robots really a positive shock to the persistence of that code? I feel like I can tell an equally valid story about how robots and AI will mean that code becomes less persistent over time, and that we will continually be reprogramming them to suit our needs. Robots, by operating as general purpose machines, can easily be re-programmed every day with new tasks. A hammer, on the other hand, is “programmed” once into a heavy object useful for hitting things and then is stuck doing that forever. The code embedded in our current non-robot tools is very, very persistent because they are built for single tasks. Hammers don’t even have USB ports, for crying out loud.

Treating Code as a Rival Good. Leaving aside the issue of code’s persistence, their choice of production function for goods does not seem to make sense for how code operates. The production function depends on robots/capital (K) and code (A). Given their assumed parameters, the production function is

$\displaystyle Y = K^{\alpha}A^{1-\alpha}, \ \ \ \ \ (1)$

and code is treated like any other rival, exclusive factor of production. Their production function assumes that if I hold the amount of code constant, but increase the number of robots, then code-per-robot falls. Each new robot means existing ones will have less code to work with? That seems obviously wrong, doesn’t it? Every time Apple sells an iPhone I don’t have to sacrifice an app so that someone else can use it.

The beauty of code is precisely that it is non-rival and non-exclusive. If one robot uses code, all the other robots can use it too. This isn’t a problem with treating code as a “stock variable”. That’s fine. We can easily think of the stock of code depreciating (people get tired of apps, it isn’t compatible with new software) and accumulating (coders write new code). But to treat it like a rival, exclusive, physical input seems wrong.

You’re going to think this looks trivial, but the production function should look like the following

$\displaystyle Y = K^{\alpha} A. \ \ \ \ \ (2)$

I ditched the ${(1-\alpha)}$ exponent. So what? But this makes all the difference. This modified production function has increasing returns to scale. If I double both robots and the amount of code, output more than doubles. Why? Because the code can be shared across all robots equally, and they don’t degrade each other’s capabilities.

This is going to change a lot in their model, because now even if I have a long-run decline in the stock of robots ${K}$, the increase in ${A}$ can more than make up for it. I can have fewer robots, but with all that code they are all super-capable of producing goods for us. The original BKLS model assumes that won’t happen because if one robot is using the code, another one cannot.

But I’m unlikely to have a long-run decline in robots (or code) because with IRS the marginal return to robots is rising with the number of robots, and the marginal return to code is rising with the amount of code. The incentives to build more robots and produce more code are rising. Even if code persists over time, adding new code will always be worth it because of the IRS. More robots and more code mean more goods produced in the long-run, not fewer as BKLS find.

Of course, this means we’ll have produced so many robots that they become sentient and enslave us to serve as human batteries. But that is a different kind of problem entirely.

Valuing Consumption. Leave aside all the issues with production and how to model code. Does their baseline simulation actually indicate immiseration? Their measure of “national income” isn’t defined clearly, so I’m not sure what to do with that number. But they do report the changes in consumption of goods and services. We can back out a measure of consumption per person from that. They index the initial values of service and good consumption to 100. Then, in the “immiserating growth” scenario, service consumption rises to 127, but good consumption falls to 72.

Is this good or bad? Well, to value both initial and long-run total consumption, we need to pick a relative price for the two goods. BKLS index the relative price of services to 100 in the initial period, and the relative price falls to 43 in the long-run.

But we don’t want the indexed price, we want the actual relative price. This matters a lot. If the relative price of services is 1 in the initial period, then initial real consumption is

$\displaystyle C = P_s Q_s + Q_g = 1 \times 100 + 100 = 200. \ \ \ \ \ (3)$

In the long-run we need to use the same relative price so that we can compare real consumption over time. In the long-run, with a relative price of services of 1, real consumption is

$\displaystyle C = 1 \times 127 + 72 = 199. \ \ \ \ \ (4)$

Essentially identical, and my guess is that the difference is purely due to rounding error.

Note what this means. With a relative price of services of 1, real consumption is unchanged after the introduction of robots in their model. This is not immiserating growth.

But wait, who said that the relative price of services had to be 1? What if the initial price of services was 10? Then initial real consumption would be ${C = 10 \times 100 + 100 = 1100}$, and long-run real consumption would be ${C = 10 \times 127 + 72 = 1342}$, and real consumption has risen by 22% thanks to the robots!

Or, if you feel like being pessimistic, assume the initial relative price of services is 0.1. Then initial real consumption is ${C = .1 \times 100 + = 110}$, and long-run consumption is ${C = .1 \times 127 + 72 = 84.7}$, a drop of 23%. Now we’ve got immiserating growth.

The point is that the conclusion depends entirely on the choice of the actual relative price of services. What is the actual relative price of services in their simulation? They don’t say anywhere that I can find, they only report the indexed value is 100 in the initial period. So I don’t know how to evaluate their simulation. I do know that their having service consumption rise by 27% and good consumption fall by 28% does not necessarily imply that we are worse off.

Their model is too disconnected from reality (as are most models, this isn’t a BKLS failing) that we cannot simply look at a series from the BLS on service prices to get the right answer here. But we do know that the relative price of services to goods rose a bunch from 1950 to 2010 (see here). From an arbitrary baseline of 1 in 1950, the price of services relative to manufacturing was about 4.33 in 2010. You can’t just plug in 4.33 to the above calculation, but it gives you a good idea of how expensive services are compared to manufacturing goods. On the basis of this, I would lean towards assuming that the relative price of services is bigger than 1, and probably significantly bigger, and that the effect of the BKLS robots is an increase in real consumption in the long-run.

Valuing Welfare. BKLS provide some compensating differential measurements for their immiserating scenario, which are negative. This implies that people would be willing to pay to avoid robots. They are worse off.

This valuation depends entirely on the weights in the utility function, and those weights seem wrong. The utility function they use is ${U = 0.5 \ln{C_s} + 0.5 \ln{C_g}}$, or equal weights on the consumption of both services and goods. With their set-up, people in the BKLS model will spend exactly 50% of their income on services, and 50% on goods.

But that isn’t what expenditure data look like. In the US, services take up about 70-80% of expenditure, and goods only the remaining 20-30%. So the utility function should probably look like ${U = 0.75 \ln{C_s} + 0.25 \ln{C_g}}$. And this changes the welfare impact of the arrival of robots.

Let ${C_g}$ and ${C_s}$ both equal 1 in the baseline, pre-robots. Then for BKLS baseline utility is 0, and in my alternative utility is also 0. So we start at the same value.

With robots, goods consumption falls to 0.72 and service consumption rises to 1.27. For BKLS this gives utility of ${U = 0.5 \ln{1.27} + 0.5 \ln{0.72} = -.045}$. Welfare goes down with the robots. With my weights, utility is ${U = 0.75 \ln{1.27} + 0.25 \ln{0.72} = 0.097}$. Welfare goes up with the robots.

Which is right? It depends again on assumptions about how to value services versus goods. If you overweight goods versus services, then yes, the reduction of goods production in the BKLS scenario will make things look bad. But if you flip that around and overweight services, things look great. I’ll argue that overweighting services seems more plausible given the expenditure data, but I can’t know for sure. I am wary, though, of the BKLS conclusions because their assumptions are not inconsequential to their findings.

What Do We Know. If it seems like I’m picking on this paper, it is because the question they are trying to answer is so interesting and important, and I spent a lot of time going through their model. As I said above, we need some kind of baseline model of how future hyper-automated production influences the economy. BKLS should get a lot of credit for taking a swing at this. I disagree with some of the choices they made, but they are doing what needs to be done. I do think that you have to allow for IRS in production involving code, though. It just doesn’t make sense to me to do it any other way. And if you do that goods production is going to go up, not down, as they find.

The thing that keeps bugging me is that I have this suspicion that you can’t eliminate the measurement problem with real consumption or welfare entirely. This isn’t a failure of BKLS in particular, but probably an issue with any model of this kind. We don’t know the “true” utility function, so there is no way we’ll ever be able to say for sure whether robots will or will not raise welfare. In the end it will always rest on assumptions regarding utility weights.

# Harry Potter and the Residual of Doom

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

The productivity term in an aggregate production function is tough to get one’s head around. When I write down

$\displaystyle Y = K^{\alpha}(AL)^{1-\alpha} \ \ \ \ \ (1)$

for aggregate GDP, the term ${A}$ is the measure of (labor-augmenting) productivity. What exactly does ${A}$ mean, though? Sure, mathematically speaking if ${A}$ goes up then ${Y}$ goes up, but what is that supposed to mean? ${Y}$ is real GDP, so what is this thing ${A}$ that can make real GDP rise even if the stocks of capital (${K}$) and labor (${L}$) are held constant?

I think going to Universal Studios last week provided me with a good example. If you take all the employees (about 12,000 people) and capital (building supplies, etc..) at Universal Studios and set up a series of strip malls along I-4 in Orlando, then you’ll generate a little economic activity between people shopping at the Container Store and eating lunch at Applebee’s. But no one is flying to Orlando to go to those strip malls, and no one is paying hundreds of dollars for the right to walk around and *look* at those strip malls. The productivity, ${A}$, is very low in the sense that the capital and labor do not generate a lot of real GDP.

But call that capital “Diagon Alley” and dress the employees up in funny robes, and it is thick with thousands of people like me shelling out hundreds of dollars just for the right to walk around a copy of a movie set based on a book. Hundreds. Each.

This is pure productivity, ${A}$. The fictional character Harry Potter endows that capital and labor in Orlando with the magical ability to generate a much higher level of real GDP. No Harry Potter, no one visits, and real GDP is lower. The productivity is disembodied. It’s really brilliant. Calling this pile of capital “Gringotts” and pretending that the workers are wizard guards at a goblin bank creates real economic value. Economic transactions occur that would otherwise not have.

We get stuck on the idea that productivity, ${A}$, is some sort of technological change. But that is such a poor choice of words, as it connotes computers and labs and test tubes and machines. Productivity is whatever makes factors of production more productive. That is pretty great, because it means that we need not hinge all of our economic hopes on labs or computers. But it also stinks, because it means that you cannot pin down precisely what productivity is. It is necessarily an ambiguous concept.

A few further thoughts:

• It doesn’t matter what is bought/sold, real GDP is real GDP. Spending 40 dollars at Universal to buy an interactive wand at Ollivander’s counts towards GDP just the same as spending 40 dollars on American Carbide router bits (We bought two. Wands, not router bits). There is no such thing as “good” GDP or “bad” GDP. Certain goods (tools!) do not count extra towards GDP because you can fix something with them.
• Yes, you can create economic value out of “nothing”. Someone, somewhere, is writing the next Harry Potter or Star Wars or Lord of the Rings, and it is going to create significant productivity gains as someone else builds the new theme park, or lunch box, or action figure. This new character or story will endow otherwise unproductive capital and labor with the ability to produce GDP at a faster rate than before. ${A}$ will go up just from imagining something cool.
• This kind of productivity growth makes me think that we won’t necessarily end up working only 10 or 12 hours a week any time soon. The Harry Potter park doesn’t work without having lots of people walking around in robes playing the roles. It’s integral to the experience. So we pay to have those people there. Those people, in turn, pay to go see a Stones concert, where it is integral to have certain people working (Keith and Mick among others). We keep trading our time with each other to entertain ourselves. Markets are really efficient ways of allocating all of these entertainers to the right venues, times, etc.. so it wouldn’t surprise me if we all keep doing market work a lot of our time in the future.
• “Long-tail” creative productivity gains like Harry Potter exacerbate inequality, maybe more than robots ever will. You can buy shares in the robot factory, even in a small amount. But you cannot own even a little bit of Harry Potter. You can’t copy it effectively (*cough* Rick Riordan *cough*). So J.K. Rowling gets redonkulously rich because ownership of the productivity idea is highly concentrated.

# Techno-neutrality

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

I’ve had a few posts in the past few months (here and here) about the consequences of mechanization for the future of work. In short, what will we do when the robots take our jobs?

I wouldn’t call myself a techno-optimist. I don’t think the arrival of robots necessarily makes everything better. But I do not buy the strong techno-pessimism that comes up in many places. Richard Serlin has been a frequent commenter on this blog, and he generally has a gloomy take on where we are going to end up once the robots arrive. I’m not bringing up Richard to pick on him. He writes thoughtful comments on this subject (and lots of others), and it is those comments that pushed me to try and be more clear on why I’m “techno-neutral”.

The economy is more creative than we can imagine. The coming of robots to mechanize away our jobs is the latest in a long, long, long, history of technology replacing workers. And yet here we still are, working away. Timothy Taylor posted this great selection a few weeks ago. This is a quote from Time Magazine:

The rise in unemployment has raised some new alarms around an old scare word: automation. How much has the rapid spread of technological change contributed to the current high of 5,400,000 out of work? … While no one has yet sorted out the jobs lost because of the overall drop in business from those lost through automation and other technological changes, many a labor expert tends to put much of the blame on automation. … Dr. Russell Ackoff, a Case Institute expert on business problems, feels that automation is reaching into so many fields so fast that it has become “the nation’s second most important problem.” (First: peace.)
The number of jobs lost to more efficient machines is only part of the problem. What worries many job experts more is that automation may prevent the economy from creating enough new jobs. … Throughout industry, the trend has been to bigger production with a smaller work force. … Many of the losses in factory jobs have been countered by an increase in the service industries or in office jobs. But automation is beginning to move in and eliminate office jobs too. … In the past, new industries hired far more people than those they put out of business. But this is not true of many of today’s new industries. … Today’s new industries have comparatively few jobs for the unskilled or semiskilled, just the class of workers whose jobs are being eliminated by automation.

That quote is from 1961. This is almost word for word the argument you will get about robots and automation leading to mass unemployment in the future. 50 years ago we were just as worried about this kind of thing, and in those 50 years we do not have massive armies of unemployed workers wandering the streets. The employment/population ratio in 1961 was about 55%, and then it steadily rose until the late 90’s when it topped out at about 64%. Even after the Great Recession, the ratio is still 59% today, higher than it was in 1961.

This didn’t happen without disruption and dislocation. And the robots will cause similar dislocation and disruption. Luddites weren’t wrong about losing their jobs, they were just wrong about the economy losing jobs in aggregate. But I don’t see why next-generation robots are any different than industrial robots, mainframes, PC’s, tractors, mechanical looms, or any other of the ten million innovations made in history that replaced labor. We can handle this with some sympathy and try to smooth things out for those dislocated, or we can do what usually happens and let them hang out to dry. The robots aren’t the problem here, we are.

What exactly are those new jobs that will be created? If I knew, then I wouldn’t be writing this blog post, I’d be out starting a company. The fact that I cannot conceive of an innovation myself is not evidence that innovation has ceased. But I do believe in the law of large numbers, and somewhere among the 300-odd million Americans is someone who *is* thinking of a new kind of company with new kinds of jobs.

Robots change prices as well as wages. An argument for pessimism goes like this. People have subsistence requirements, meaning they have a wage floor below which they cannot survive. Robots will be able to replace humans in production and this will drive the wage below that subsistence requirement. Either no firm will hire workers at the subsistence wage or people who do work will not meet subsistence.

The problem with this argument is that it ignores the impact of robots on the price of that subsistence requirement. Subsistence requirements are in real terms (I need clothes and housing and food), not nominal terms (I need $2000 dollars). The “subsistence wage” is a a real wage, meaning it is the nominal wage divided by the price level of a subsistence basket of goods. Robots lowering marginal costs of production lowers the nominal human wage, but it also lowers the price of goods. It is not necessary or even obvious that real wages have to fall because of robots. History says that despite all of the labor-saving technological change that has gone on over the last few hundred years, real wages have risen as the lower costs outweigh the downward pressure on wages. Who is going to buy what the robots produce? Call this the “Henry Ford” argument. If you are going to invest in opening up a factory staffed entirely by robots, then who precisely is supposed to buy that output? Ford raised wages at his highly mechanized (for the time) plants so that he had a ready-made market for his cars. The Henry Fords of robot factories are going to need a market for the stuff they build. Rich people are great, but diminishing marginal utility sets in pretty quick. That means robot owners either need to lower prices or raise wages for the people they do hire in order to generate a big enough market. Depending on the fixed costs involved in getting these proverbial robot factories up and running, robot owners may be a strong force for keeping wages high in the economy, just like Henry Ford was back in the day. The wealthy are wealthy because they own productive assets. A tiny fraction of the value of those assets is due to the utility to the owner of the widgets they kick out. The majority of the value of those assets is due to the fact that you can *sell* that output for money and use that money to buy other widgets. Rockefeller wasn’t wealthy because he had a lot of oil. He was wealthy because he could sell it to other people. No other people, no wealth. Just barrel after barrel of useless black gunk. The same holds for robot owners. Those robots and robot factories have value because you can sell them or the goods they make in the wider economy. And that means continuing to exchange with the non-wealthy. You cannot be wealthy in a vacuum. Bill Gates on an island with robots and a stack of 16 billion dollar bills is Gilligan with a lot of kindling. Wealthy robot owners will do what wealthy (fill in capital stock here) owners have done for eons. They’ll trade access to the capital, or the goods it produces, to the non-wealthy in exchange for services, effort, flattery, and new ideas on what to do with that wealth. Wealth concentration would be a problem with or without robots. The worry here is that because the wealthy will be the only ones able to build the robots and robot factories, they will control completely the production of goods and the demand for labor. That’s not a problem that arises with robots, that is a problem that arises with, well, settled agriculture 10,000 years ago. Wealth concentration makes owners both monopolists (market power selling goods) and monopsonists (market power buying labor), which is a bad combination. It gives them the ability to drive (real) wages down to minimum subsistence levels. This is bad, absolutely. But this was bad when (fill in example of a landed elite) did it in (fill in historical era here). This is bad in “company towns”. This is bad now, today. So if you want to argue against wealth concentration and the pernicious influence it has on wages, get started. Don’t wait for the robots, they’ve got nothing to do with it. Again, be clear that in arguing against techno-pessimism I am not arguing that robots will generate a techno-utopia with ponies and rainbows. I just do not buy the dystopian view that somehow it’s all going to come crashing down around our ears because of the very particular innovations coming in the near future. # Technology and “Good Jobs” NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site. I got a number of comments and e-mails regarding a recent post on technological change, jobs that produce goods, and “good jobs”. This is a follow up meant to clarify some points and solidify others. 1. The entire point of my post was to say that the exact tasks people do is unrelated to whether they have a “good job”. Working in manufacturing does not make a job “good”, and working in services does not make a job “bad”. Yes, “good” and “bad” are fuzzy terms. 2. I’m not denying that technology is replacing manufacturing jobs. It is. It will. We may well end up with robots making everything. If so, then you want to make sure that the jobs that people do have are “good jobs”. 3. Service jobs are not, even to a first approximation, poor people doing things for rich people. So no, we won’t run out of jobs because rich people can only get so many massages or restaurant meals. The vast majority of workers in the US for the last 60 years have been non-rich people doing service-like things for other non-rich people. [Teachers, cops, firemen, nurses, waiters, store clerks, everyone in HR, everyone in accounts payable, secretaries, receptionists, every computer programmer, truck drivers, warehouse workers, chefs, everyone who works on any TV show, record, or movie, claims adjusters, insurance agents, financial analysts, everyone at your local bank, your IT guys, everyone working in state or federal government, priests, librarians, florists, pizza delivery guys, photographers, personal trainers, dietitians, optometrists, dentists, physical therapists, veterinarians, security guards, dishwashers, hostesses, exterminators, HVAC workers, plumbers, electricians, roofers, rodeo clowns, pit bosses, morticians, barbers, day-care attendants, real estate brokers, airline pilots, car mechanics, flight attendants, taxi drivers, and yes, even used car salesmen. Just to give a few examples.] We are very good at finding things to do for each other. We’ll continue to be good at that 4. No, you cannot “work any day you want to”. Ask the day laborers that hang out at the Home Depot near my house how they are doing. Some days you pick the wrong parking lot. Some days it’s raining. Some days there just isn’t anyone with a job. The frictions and costs of working day-to-day are huge. 5. Personally, I think that the following characteristics are associated with “good jobs”. (A) Security/steadiness. As per #2, knowing that your job will be there next week/month/year is incredibly valuable. It allows you to undertake long-run commitments, like marriage, home-ownership, and schooling. (B) Family flexibility. You can deal with your life (i.e. all the crap you need to get your kids to) without the fear of being fired for it. (C) Pay/Benefits. Enough money to afford decent health insurance, or decent health insurance provided by the employer. In short, I think people want stability more than anything. The attraction of those mid-20th century union jobs for workers was that they had lock-it-down certainty about the future. 6. Yes, it is possible to make any kind of job a “good job”. I used the Costco/Wal-mart distinction as an example. Justin Wolfers and Jan Zilinsky just posted a piece containing further examples. In short, worker productivity is not a fixed value, and paying higher wages is associated with getting higher productivity from the same workers. Costco has a wage/benefit structure that encourages their workers to be productive. In return, Costco saves money from lower turnover. What Wolfers and Zilinsky show is that this works in a variety of settings. 7. The original post made it sound as if unions were the only way to generate the conditions of “good jobs”. That is not true, and not what I intended to say. Unions were one way to elicit those good conditions from employers, and manufacturing workers were particularly well placed to unionize and negotiate those conditions. But unions aren’t necessary for this. Costco isn’t unionized. [CORRECTION: About 15,000 Costco workers are part of the Teamsters. Roughly 174,000 total Costco workers. DV 1/20/15] We need companies to recognize the value of becoming a “good job” employer, but there are lots of ways to do that. # The Industrial Revolution and Modern Development NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site. I’m not an economic historian, but like most growth economists I am an avid consumer of economic history. Maybe it’s our version of “physics envy”. Regardless, it isn’t always obvious why growth economists look backwards so much for motivation, examples, and inspiration. Let me try to give an example of the usefulness of economic history by looking at recent “big theories” of the British Industrial Revolution (IR). If you have any interest in learning about the IR, then you could do a lot worse than reading the following two books: Mokyr’s theory is that there was a unique intellectual environment created in Britain during the Enlightenment, and that this generated cultural conditions that valued innovation as a valuable activity in and of itself, as well as a supply of trained engineers that took advantage of these conditions. What made the IR British was its adoption of science and reason as tools of economic progress. Allen’s theory has to do with relative factor prices. The IR was British because Britain had a unique combination of high wages (persisting after the Black Death) and low fuel costs (due to cheap coal) that made labor-saving and fuel-using innovations (e.g. the steam engine) profitable. Other countries failed to adopt, or lagged in adopting, because they had different relative prices for labor and fuel. There is some sense that these two have set up competing explanations of the Industrial Revolution, diametrically opposed. Mokyr does tend to downplay the “coal made the IR” idea. Allen does tend to downplay the notion that Britain was unique in its potential for innovation. But there is more subtlety to their arguments than that. The theories do not contradict each other, because they are fundamentally concerned with explaining different phenomenon. There are two different questions about the IR in Britain that we want to answer. First, why did several particularly important innovations take place in Britain, and not in other places? Second, of all the innovations available, why were they adopted first (or with greater speed) in Britain than in other areas of Europe? Mokyr’s theory is very much an answer to the first question, and provides a sound answer to the second. Newcomen and Watt and Arkwright and Darby and Hargreaves were all British. Perhaps more important than these noted innovators, according to Mokyr, is the small army of highly skilled engineers that patiently but steadily made improvements to the steam engine, spinning jenny, coke smelting, and other technologies. What set Britain apart from China (where most of the big innovations had occurred earlier) or France (which quickly had knowledge of the big innovations) were those engineers. Without them, you have curiosities. With them, you have industrialization. Britain led the IR because the Enlightenment took hold and produced both the original innovators and that army of engineers. Allen’s theory is very much an answer to the second question, but is relatively weak on the first. That is, we can use factor prices to understand why Britain adopted the steam engine or spinning jenny first, but they don’t explain why those things were invented in Britain. Allen suggests that those same factor prices played a role in inducing innovation, but that is shakier ground. Anton Howes just posted a reaction to Allen’s work that focuses precisely on that failure. So Mokyr’s theory is more comprehensive, but it lacks a compelling explanation for the failure of other countries to follow Britain quickly into industrialization. Allen’s work is really a theory of growth and development, articulated with examples from the British IR. We can easily adopt his concepts for other time periods and places, whereas Mokyr’s work is far more context-specific. Thus Allen’s theory is more relevant than Mokyr’s to thinking about the general process of development. The second question above – why do some places fail to adopt or lag in adopting new innovations? – is in some sense the central question of development. Research on development has been focusing a lot lately on the distribution of productivity across firms (see my reading list on misallocation). In China, India, or Mexico, for example, the ratio of labor productivity of the top firms to bottom firms is on the order of 10-1 or more. Even in the U.S. there are productivity gaps of something like 2-1 between the best and worst firms. Not all firms use the best techniques. Poor countries have particularly bad distributions, with the vast majority of their firms using low productivity technologies. If we could understand that distribution, we could understand a lot about the gap in income per capita between poor and rich countries. So far, most of the explanations hinge on firms facing some implicit distortion to factor costs, which makes them choose a sub-optimal level of inputs. Firms that may be very productive perhaps face high distortions, making factors expensive, and leading them to be too small. Firms that are unproductive face low distortions, making factors cheap, leading them to be too big. What this literature could learn from Allen is that the choice of technology itself is in play when factor prices are distorted. In particular, distortions that change the costs of materials relative to capital or labor could be instrumental in keeping firms from adopting leading technologies in poor countries. Cheap labor may make a firm inefficiently large in a poor country, yes. But it also removes the incentive to adopt a capital-using, labor-saving high technology production technology, even if the firm has full knowledge of the technology. This isn’t a brand new idea by Allen. Hicks talked about it in 1932. Hayami and Ruttan talked about induced innovation and the choice of technology with respect to agriculture in developing countries long ago. Banerjee and Duflo’s chapter on distortions considers the role of borrowing constraints (i.e. expensive capital) in generating a fat tail of small labor-intense firms in India. Daron Acemoglu‘s theory of directed technical change is basically induced innovation based on differentials in factor prices. Allen, though, provides a clear and compelling story about the power of factor prices in technology adoption. Think of his work as a “proof of concept” that induced innovation has a lot of explanatory power for differences between rich and poor countries. It is an excellent example of how studying economic history can produce insights into modern questions about development and growth. Factor price differences created decades-long lags in technology adoption across Europe, perhaps we shouldn’t be surprised at decades-long delays in adoption in developing countries. Relative factor prices may be a worthwhile avenue to explore, possibly as the lever on which institutions (hypocrite!?) or geography push to generate differences in living standards. [I appear to have slighted Mokyr’s work here in favor of Allen, but right now someone else is reading his book and gleaning from it some idea about culture and development that I missed completely. From the growth economist’s perspective, the purpose is not to decide who’s right in these economic history debates, it is to mercilessly steal all the good ideas.] # Job Quality is about Policies, not Technology NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site. Nouriel Roubini posted an article titled “Where Will All the Workers Go?”. A few pulls: “The risk is that robotics and automation will displace workers in blue-collar manufacturing jobs before the dust of the Third Industrial Revolution settles.” “But, unless the proper policies to nurture job growth are put in place, it remains uncertain whether demand for labor will continue to grow as technology marches forward.” “Even that may not be sufficient, in which case it will become necessary to provide permanent income support to those whose jobs are displaced by software and machines.” The worry here is that technology will replace certain jobs (particularly goods-producing jobs) and that there will literally be nothing for those people to do. They will presumably exit the labor market completely and possibly need permanent income support. Let’s quickly deal with the “lump of labor” fallacy sitting behind this. Technology reduces the demand for labor in some industries, so fewer workers are employed there. Which raises the supply of labor in all the other industries. For that supply shock to generate no other employment you have to assume that the$15 trillion dollar a year U.S. economy is so rigidly inflexible that it has a definitely fixed set of jobs that can be filled. That’s ridiculous.

To a rough approximation, just about the exact same number of people work in goods-producing industries in 2013 (19 million) as did in 1950 (17 million). And yet somehow the rest of us have figured out what to do with ourselves in the interim. Between 1950 and 2013 the U.S. economy expanded from 28 million service jobs to 117 million service jobs (All stats from the BLS). You think that somehow it won’t be able to figure out what to do with more workers that are displaced by technology? We’ve been creating new kinds of jobs for two hundred years.

So let’s ignore the phantom worry that tens of millions workers suddenly find themselves completely at a loss to find work. The economy is going to find something for these people to do. The question is what kind of jobs these will be.

Will they be “bad jobs”? McJobs at retail outlets, wearing a nametag? These aren’t “good jobs”, real jobs. Making “stuff” is a real job, not some made-up bullshit service job.

We can worry about the quality of jobs, but the mistake here is to confound “good jobs” with manufacturing or goods-producing jobs. Manufacturing jobs are not inherently “good jobs”. There is nothing magic about repetitively assembling parts together. You think the people at Foxconn have good jobs? There is no greater dignity to manufacturing than to providing a service. Cops produce no goods. Nurses produce no goods. Teachers produce no goods.

Manufacturing jobs were historically “good jobs” because they came with benefits that were not found in other industries. Those benefits – job security, health care, regular raises – have nothing to do with the dignity of “real work” and lots to do with manufacturing being an industry that is conducive to unionization. The same scale economies that make gigantic factories productive also make them relatively easy places to organize. They have lots of workers collected in a single place, with definitive safety issues to address, and an ownership that can be hurt deeply by shutting down the cash flow they need to pay off debt. To beat home the point, consider that what we consider “good” service jobs – teacher, cop – are also heavily unionized. Public employees, no less.

If you want people to get “good jobs” – particularly those displaced by technology – then work to reverse the loss of labor’s negotiating power relative to ownership. Raise minimum wages. Alleviate the difficulty in unionizing service workers.

You want to smooth the transition for people who are displaced, and help them move into new industries? Great. Let’s have a discussion about our optimal level of social insurance and support for training and education. But the sectors people leave or eventually enter are irrelevant to that.

You want to worry about downward wage pressure as the demand for labor falls? Great. Worry about that. See the above point about raising labor’s negotiating power relative to ownership.

Hoping or trying to recreate the employment structure of 1950 is stupid. We don’t need that many people to assemble stuff together any more because we are so freaking good at it now. The expansion of service employment isn’t some kind of historical mistake we need to reverse.

Any job can be a “good job” if the worker and employer can coordinate on a good equilibrium. Costco coordinates on a high-wage, high-benefit, high-effort, low-turnover equilibrium. Sam’s Club coordinates on a low-wage, low-benefit, low-effort, high-turnover equilibrium. Both companies make money, but one provides better jobs than the other. So as technology continues to displace workers, think about how to get *all* companies to coordinate on the “good” equilibrium rather than pining for lost days of manly steelworkers or making the silly presumption that we will literally run out of things to do.

# Meta-post on Robots and Jobs

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

I don’t know that I have anything particularly original to say on the worry that robots will soon replace humans in many more tasks, and what implications this has for wages, living conditions, income distribution, the introduction of the Matrix or Skynet, or anything else. So here I’ve just collected a few relevant pieces of information from about the inter-tubes that are useful in thinking about the issue.

Let’s start with some data on “routine” jobs and what is happening to them. Cortes, Jaimovich, Nekarda, and Siu have a recent voxeu post (and associated paper) on the flows into routine versus non-routine work. In the 1980’s, about 1/3 of American workers did “routine” work, now this number is only about 1/4. Routine work tended (and tends) to be middle-waged; it pays pretty well. What the authors find is that the decline in the share of people doing these middle-wage routine jobs is due to slower flows *in* to those jobs, but not due to faster flows *out*. That is, routine workers were not necessarily getting let go more rapidly, but companies were simply not hiring new routine workers.

Unsurprisingly, people with more education were better able to adapt to this. Higher education meant a higher likelihood of shifting into non-routine “cognitive” tasks, which also is a move up the wage scale (upper-middle wages, say). Perhaps more surprising is that women have been more likely, holding education constant, to move into these cognitive tasks. It is low education males who represent the group that is failing to get routine middle-wage jobs. To the extent that these lower-educated males get work, it tends to be in “brawn” jobs, low-wage manual work.

This last fact is somewhat odd in the context of the robot-overlord thesis. Robots/computers are really good at doing routine tasks, but so far have not replaced manual labor. If there was a group that should have a lot to worry about, I’d think it would be low-education males, who could well be replaced as robots become more robust to doing heavy manual labor. One thought I have is that this indicates that manual work (think landscaping) is not as low-skill as routine tasks like data entry. I think there is more cognitive processing that is going on in these jobs than we tend to give them credit for (where to dig, how deep, should I move this plant over a little, what if I hit a root?, does this shrub look right over here, etc.. ), and that their wages are low simply because the supply of people who can do those jobs is so large.

Brad DeLong took on the topic by considering Peter Thiel‘s comments in the Financial Times. Thiel is relatively optimistic about the arrival of robots – he uses the computer/human mix at Paypal to detect fraud as the example of how smarter machines or robots will benefit workers. Brad worries that Thiel is making a basic error. Yes, machines relieve us of drab, boring, repetitive work. But whether workers benefit from that (as opposed to the owners of the machines) depends not on the average productivity of that worker, but on the productivity of the marginal worker who is not employed. That is, if I can be replaced at Paypal by an unemployed worker who has no other options, then my own wage will be low, regardless of how productive I am. By replacing human workers in some jobs, robots/machines drive up the supply of humans in all the remaining jobs, which lowers wages.

To keep wages high for workers, we will need to increase demand for human-specific skills. What are those? Brad likes to list 6 different types of tasks, and leaves humans with persuasion, motivation, and innovation as things that will be left for humans to do. Is there sufficient demand for those skills to keep wages elevated? I don’t know.

David Autor has a recent working paper that is relatively optimistic about robots/machines. He thinks there is more complementarity between machines and humans than we think, so it echoes Thiel’s optimism. Much of Autor’s optimism stems from what he calls “Polyani’s Paradox”, which is essentially that we are incapable of explaining in full what we know. And if we cannot fully explain exactly what we know how to do (whether that is identifying a face in a crowd, or making scrambled eggs, writing an economics paper, or building a piece of furniture) then we cannot possibly program a machine to do it either. The big limit of machines, for Autor, is that they have no tacit knowledge. Everything must be precisely specified for them to work. There is no “feel” to their actions, so to speak. As long as there are tasks like that, robots cannot replace us, and it will require humans – in conjunction with machines, maybe – to actually do lots of work. Construction workers are his example.

But I am a little wary of that example. Yes, construction workers today work with a massive array of sophisticated machines, and they serve as the guidance systems for those machines, and without construction workers nothing would get done. But that’s a statement about average product, not marginal product. The wage of those workers could still fall because better machines could make *anyone* capable of working at a construction site, and the marginal product of any given worker is very low. Further, adding better or more construction machines can reduce the number of construction workers necessary, which again only floods the market with more workers, lowering the marginal product.

Autor gets interviewed in this video from Ryan Avent at the Economist. It’s a fairly good introduction to the ideas involved with robots replacing workers.

# Robots as Factor-Eliminating Technical Change

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

A really common thread running through the comments I’ve gotten on the blog involve the replacement of labor. This is tied into the question of the impact of robots/IT on labor market outcomes, and the stagnation of wages for lots of laborers. An intuition that a lot of people have is that robots are going to “replace” people, and this will mean that wages fall and more and more of output gets paid to the owners of the robots. Just today, I saw this figure (h/t to Brad DeLong) from the Center on Budget and Policy Priorities which shows wages for the 10th and 20th percentile workers in the U.S. being stagnant over the last 40 years.

The possible counter-arguments to this are that even with robots, we’ll just find new uses for human labor, and/or that robots will relieve us of the burden of working. We’ll enjoy high living standards without having to work at it, so why worry?

I’ll admit that my usual reaction is the “but we will just find new kinds of jobs for people” type. Even though capital goods like tractors and combines replaced a lot of human labor in agriculture, we now employ people in other industries, for example. But this assumes that labor is somehow still relevant somewhere in the economy, and maybe that isn’t true. So what does “factor-eliminating” technological change look like? As luck would have it, there’s a paper by Pietro Peretto and John Seater called …. “Factor-eliminating Technical Change“. Peretto and Seater focus on the dynamic implications of the model for endogenous growth, and whether factor-eliminating change can produce sustained growth in output per worker. They find that it can under certain circumstances. But the model they set is also a really useful tool for thinking about what the arrival of robots (or further IT innovations in general) may imply for wages and income distribution.

I’m going to ignore the dynamics that Peretto and Seater work through, and focus only on the firm-level decision they describe.

****If you want to skip technical stuff – jump down to the bottom of the post for the punchline****

Firms have a whole menu of available production functions to choose from. The firm-level functions all have the same structure, ${Y = A X^{\alpha}Z^{1-\alpha}}$, and vary only in their value of ${\alpha \in (0,\overline{\alpha})}$. ${X}$ and ${Z}$ are different factors of production (I’ll be more specific about how to interpret these later on). ${A}$ is a measure of total factor productivity.

The idea of having different production functions to choose from isn’t necessarily new, but the novelty comes when Peretto/Seater allow the firm to use more than one of those production functions at once. A firm that has some amount of ${X}$ and ${Z}$ available will choose to do what? It depends on the amount of ${X}$ versus the amount of ${Z}$ they have. If ${X}$ is really big compared to ${Z}$, then it makes sense to only use the maximum ${\overline{\alpha}}$ technology, so ${Y = A X^{\overline{\alpha}}Z^{1-\overline{\alpha}}}$. This makes some sense. If you have lots of some factor ${X}$, then it only makes sense to use a technology that uses this factor really intensely – ${\overline{\alpha}}$.

On the other hand, if you have a lot of ${Z}$ compared to ${X}$, then what do you do? You do the opposite – kind of. With a lot of ${Z}$, you want to use a technology that uses this factor intensely, meaning the technology with ${\alpha=0}$. But, if you use only that technology, then your ${X}$ sits idle, useless. So you’ll run a ${X}$-intense plant as well, and that requires a little of the ${Z}$ factor to operate. So you’ll use two kinds of plants at once – a ${Z}$ intense one and a ${X}$ intense one. You can see their paper for derivations, but in the end the production function when you have lots of ${Z}$ is

$\displaystyle Y = A \left(Z + \beta X\right) \ \ \ \ \ (1)$

where ${\beta}$ is a slurry of terms involving ${\overline{\alpha}}$. What Peretto and Seater show is that over time, if firms can invest in higher levels of ${\overline{\alpha}}$, then by necessity it will be the case that we have “lots” of ${Z}$ compared to little ${X}$, and we use this production function.

What’s so special about this production function? It’s linear in ${Z}$ and ${X}$, so their marginal products do not decline as you use more of them. More importantly, their marginal products do not rise as you acquire more of the other input. That is, the marginal product of ${Z}$ is exactly ${A}$, no matter how much ${X}$ we have.

What does this possibly have to do with robots, stagnant wages, and the labor market? Let ${Z}$ represent labor inputs, and ${X}$ represent capital inputs. This linear production function means that as we acquire more capital (${X}$), this has no effect on the marginal product of labor (${Z}$). If we have something resembling a competitive market for labor, then this implies that wages will be constant even as we acquire more capital.

That’s a big departure from the typical concept we have of production functions and wages. The typical model is more like Peretto and Seater’s case where ${X}$ is really big, and ${Y = A X^{\overline{\alpha}}Z^{1-\overline{\alpha}}}$, a typical Cobb-Douglas. What’s true here is that as we get more ${X}$, the marginal product of ${Z}$ goes up. In other words, if we acquire more capital, then wages should rise as workers get more productive.

The Peretto/Seater setting says that, at some point, technology will progress to the point that wages stop rising with the capital stock. Wages can still go up with general total factor productivity, ${A}$, sure, but just acquiring new capital will no longer raise wages.

While wages are stagnant, this doesn’t mean that output per worker is stagnant. Labor productivity (${Y/Z}$) in this setting is

$\displaystyle \frac{Y}{Z} = A \left(1 + \beta \frac{X}{Z}\right). \ \ \ \ \ (2)$

If capital per worker (${X/Z}$) is rising, then so is output per worker. But wages will remain constant. This implies that labor’s share of output is falling, as

$\displaystyle \frac{wZ}{Y} = \frac{AZ}{A \left(Z + \beta X\right)} = \frac{Z}{\left(Z + \beta X\right)} = \frac{1}{1 + \beta X/Z}. \ \ \ \ \ (3)$

With the ability to use multiple types of technologies, as capital is acquired labor’s share of output falls.

Okay, this Peretto/Seater model gives us an explanation for stagnant wages and a declining labor share in output. Why did I present this using ${X}$ for capital and ${Z}$ for labor, not their traditional ${K}$ and ${L}$? This is mainly because the definition of what counts as “labor”, and what counts as “capital”, are not fixed. “Capital” might include human as well as physical capital, and so “labor” might mean just unskilled labor. And we definitely see that unskilled labor’s wage is stagnant, while college-educated wages have tended to rise.

***** Jump back in here if you skipped the technical stuff *****

The real point here is that whether technological change is good for labor or not depends on whether labor and capital (i.e. robots) are complements or substitutes. If they are complements (as in traditional conceptions of production functions), then adding robots will raise wages, and won’t necessarily lower labor’s share of output. If they are substistutes then adding robots will not raise wages, and will almost certainly lower labor’s share of output. The factor-eliminating model from Peretto and Seater says that firms will always invest in more capital-intense production functions and that this will inevitably make labor and capital substitutes. We happen to live in the period of time in which this shift to being substitutes is taking place. Or one could argue that it already has taken place, as we see those stagnant wages for unskilled workers, at least, from 1980 onwards.

What we should do about this is a different question. There is no equivalent mechanism or incentive here that would drive firms to make labor and capital complements again. From the firms perspective, having labor and capital as complements limits their flexibility, because they then depend on the other. They’d rather have the marginal product of robots and people independent of one other. So once we reach the robot stage of production, we’re going to stay there, absent a policy that actively prohibits certain types of production. The only way to raise labor’s share of output once we get the robots is through straight redistribution from robot owners to workers.

Note that this doesn’t mean that labor’s real wage is falling. They still have jobs, and their wages can still rise if there is total factor productivity change. But that won’t change the share of output that labor earns. I guess a big question is whether the increases in real wages from total factor productivity growth are sufficient to keep workers from grumbling about the smaller share of output that they earn.

I for one welcome….you know the rest.