# Handy Book of Economic Growth

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

I thought it would be nice to post some overview articles of significant research in economic growth.

1. Culture, Entrepreneurship, and Growth. Doepke and Zilibotti
2. Trust, Growth, and Well-Being, Algann and Cahuc
3. Long-term Barriers to Economic Development, Spolaore and Wacziarg
4. Family Ties, Alesina and Giuliano
5. The Industrial Revolution, Clark
6. Twentieth-Century Growth, Crafts and O’Rourke
7. Historical Development, Nunn
8. Institutions and Economic Growth in Historical Perspective, Ogilvie and Carus
9. What Do We Learn from Schumpeterian Growth Theory? Aghion, Akcigit, and Howitt
10. Technology Diffusion: Measurement, Causes, and Consequences, Comin and Mestieri
11. Health and Economic Growth, Weil
12. Regional Growth and Regional Decline, Breinlich, Ottaviano, and Temple
13. The Growth of Cities, Duranton and Puga
14. Growth and Structural Transformation, Herrendorf, Rogerson, and Valentinyi
15. The Chinese Growth Miracle, Yang Yao
16. Growth From Globalization? A View from the Very Long Run, Meissner

If I were an enterprising publisher, I would go find some editors. Maybe Philippe Aghion and Steven Durlauf, just to throw some names off the top of my head. I’d have them put these together into a nice volume. Oh, wait

Quick update: I posted this list under the “Papers” page on this site if you want a more permanent place to find them.

More updates: Thanks to Pseudoerasmus for the links on the Yao and Meissner papers.

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

Things that I pretend I will have smart things to say about in the future:

• Lemin Wu on whether we are thinking about Malthusianism correctly. A general point from this paper is that once you stop thinking of output as a single homogenous good, how you choose to weight different goods in your GDP/real wage/utility calculation matters a lot for your conclusions.
• David Autor will take your job. Or something like that. I lost the thread of this article when I came upon this sentence: “Mr. Autor—who always sports a single gecko-shaped silver earring, his trademark symbol also pasted on his iPhone—says the fear has outpaced reality.”?!?!?
• Ogilvie and Carus handbook chapter on institutions and economic growth in historical perspective. Whenever economic historians write something called “XXXXX in historical perspective”, the punch line is that “XXXXXX is wrong”. They do not definitively ruin the institutions/growth relationship, but do provide a lot of needed skepticism regarding the relationship. If you are going to argue that institutions matter for growth, then you have to do so in more of a case-by-case basis, and not using crude measures in cross-country regressions. I feel like I’ve heard that before
• I like this Krugman post from earlier this week. Expanding education is not necessarily the answer to inequality. The idea that education levels are the key to higher wages is very useful for employers. Few people can or will leave work for 2 or 4 years to increase their education once they are working, and so they are willing to accept the low wages they currently have.
• Ortman, Cabaniss, Sturm, and Bettencourt on settlement scaling and increasing returns in ancient society. They look at pre-Hispanic Mexico and find that the larger the settlement sizes/cities, the larger the monuments they built. Not surprising. But the relationship indicates IRS, which is. A ten-fold increase in settlement size led to a greater than 10-fold increase in the scale of monuments built.
• Jane Humphries and Jacob Weisdorf look at women’s wages in England from 1260-1850. Female servant wages did not appear to be affected by the Black Death, which is problematic for the theory that the plague led to the emergence of the European Marriage pattern (see here). Women’s wages also did not track with men’s during the run-up to the Industrial Revolution, which may be problematic for the theory that high wages were part of the explanation for adoption of labor-saving technology (see here). Stupid data, always ruining things for everyone.

What I read on the plane rides to and from DC this week.

• Medieval Technology and Social Change, Lynn White Jr. Probably best known for the “plows changed social structure” thesis. This is incredibly readable, and is less a definitive argument regarding technology and social change than a very nicer primer on the basic idea.
• Mohammed and Charlemagne, by Henri Pirenne. A classic on the influence of Islam on the West. The first part of the book establishes that despite all the invasions of Huns, Goths, and the like, the areas of the Roman Empire remained fundamentally “Roman” throughout. The true disruption of Roman culture didn’t take place until Islam restructured the Mediterranean world. Like White’s book, very readable.
• Annihilation, by Jeff VanderMeer. Fiction. First of a trilogy about unnamed scientists exploring the mysterious Area X. It sets up so much, I hope he can pull off a meaningful conclusion. Please don’t be like Lost. Please don’t be like Lost. Please don’t be like Lost….

For Chris Blattman, who needs kids book suggestions. These should work for 4-6 year olds, and were approved by my 11 and 9 year old as books they enjoyed a lot.

• Magic Treehouse books. Kids explore different times, places, ideas in each book. As a bonus, they do companion non-fiction “Fact Tracker” books with more information on the topic.
• Junie B. Jones. Barbara Park absolutely nails exactly how little kids talk and act. I loved reading these to my girls.
• Roald Dahl. These are definitely too advanced for 4-6 year olds to read themselves, but we found they could start paying attention long enough to listen to a whole chapter. You have to stop sometimes to explain what is going on, or remind them the next night what is happening in the book, but reading James and the Giant Peach is soooooo much better then reading If You Give a Mouse a Cookie again, and again, and again.
• Fancy Nancy. Shorter and good for helping them start to read. I resisted early on, but Fancy Nancy (including her many sequels) kind of grows on you. Perhaps that is just a coping mechanism.

# 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.

# Significant Changes in GDP Growth

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

A relatively quick post to highlight two other posts that recently came out regarding GDP growth. First, David Papell and Ruxandra Prodan have a guest post up at Econbrowser regarding the long-run effects of the Great Recession. They use the CBO projections of GDP into the future (similar to what I did here) and look at whether there was a statistically significant break in the level of GDP at the Great Recession. Short answer, yes. Their testing finds that the break was 2008:Q2, not a surprising date to end up with.

It is important to remember that David and Ruxandra are testing for a break in the level of GDP, and not GDP per capita. It is entirely possible to have a structural break in GDP while not having a structural break in GDP per capita. The next thing to remember is that they cannot reject that the growth rate of GDP is the same after 2008:Q2 as it was before. What I mean is easier to see in their figure than it is to explain:

Before and after the break, the growth rate is identical. It is just the level that has changed.

The second post is from Juan Antolin-Diaz, Thomas Drechsel, and Ivan Petrella. They use only existing data (not CBO projections) and find that there is statistical evidence of a change in the growth rate of U.S. GDP. They see a slowdown in growth starting in the mid-2000’s, consistent with John Fernald’s suggestions regarding productivity growth. It takes until 2015 to see this break statistically because you need several years of data to confirm that the growth slowdown was not a temporary phenomenon.

Note the subtle but very, very, very important difference between the two posts. Papell/Prodan find a significant shift in the level of GDP, while Antolin-Diaz, Drechsel, and Petrella (ADP) find a significant shift in the growth rate of GDP. The former sucks, but the latter is far more troubling. If the growth rate is truly lower, then we will get farther and farther away from the pre-GR trend, and the ratio of actual GDP to pre-GR trend GDP will go to zero. If it is just a level shift, then the ratio of actual GDP to pre-GR trend GDP will go to one as both become arbitrarily large.

I find the Papell/Prodan result more convincing. Keep in mind that David is my department chair and if I knocked on my office wall right now I could interrupt the phone call he is on. Ruxandra’s office is all of 20 feet from mine. I see these people every day. But regardless of the fact that I know them personally, I think they are right.

ADP are getting a false result showing slow growth because of the level shift that David and Ruxandra identify. If ADP do not allow for the level shift, then over any window of time that includes 2008:Q2 the growth rate will be calculated to be low. But that is just a statistical artifact of this one-time drop in GDP. It doesn’t mean that the long-run growth rate is in fact different. Put it this way: if they re-run their tests 25 years from now, they’ll find no statistical evidence of a growth change.

Of course, if the CBO is wrong about the path of GDP from 2015-2025, then Papell/Prodan could be wrong and ADP could be right. But given the current CBO projections, there is strong evidence of a negative level shift to GDP, but no change in the long-run growth rate.

# When an Op-Ed About Growth Fails

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

There’s a column in the NYT today by Daniel Cohen, titled “When the Growth Model Fails“. It is…well, I don’t know what it is. A lament? A rant?

Daniel Cohen is a good economist, so it is a shame that the column reads like the work of a politician who occasionally reads the business section of a newspaper. It is a series of disconnected tropes without any meaningful point. It is thick with “truthiness”, but nothing in the form of actual facts.

Let’s take a look:

And yet, at least in the West, the growth model is now as fleeting as Proust’s Albertine Simonet: Coming and going, with busts following booms and booms following busts, while an ideal world of steady, inclusive, long-lasting growth fades away.

But in its desperate search for scapegoats, the West skirts the key question: What would happen if our quest for never-ending economic growth has become a mirage? Would we find a suitable replacement for the system, or sink into despair and violence?

What does it mean that the “growth model” is fleeting? Is Bob Solow fading in and out of existence? I presume that the implication is that economic growth is fleeting, and is coming and going.

Am I supposed to believe that booms and busts are a new feature of Western economies? That is patently untrue, and Cohen knows this. Business cycles did not start happening in the last decade. A few minutes looking at long-run data (like here) will show you that even in France the frequency and severity of booms and busts were both much, much higher before World War II than after. Took me 10 minutes to download the data for France, plot it, and run some quick regressions. 10 minutes.

“..steady, inclusive, long-lasting growth fades away”. You have to unpack this with care. Steady, inclusive, and long-lasting are three separate characteristics, and there is nothing that necessitates that they appear together or in any particular combination when growth occurs. Steady? Again, look at some data. What I see is from 1820 to 1940 steady growth at about 1.2% per year, punctuated by severe recessions and booms. After 1980, I see steady growth at 1.4% per year, higher than the pre-war rate. In between WWII and 1980 I see a country experiencing a level shift to a higher balanced growth path, probably due in part to integration within Europe and technology adoption.

Long-lasting? France has been experiencing steady GDP per capita growth for 190 years. Am I supposed to believe that the downturn you can see at the tail end of the figure in 2007 represents the end of that? That the dip in French GDP per capita in 2007 implies that we either have to “replace the system”, whatever that means, or sink into despair and violence? Get some perspective.

I think what Prof. Cohen means is that the era of rapid transitional growth that France experience from 1950 to 1980 is over. Yes, it is. But did you really think that growth of 3.8% was going to last forever, when there is not a single example – ever – of a country growing at that rate in the long run? Again, perspective.

Inclusive? Now here is where we get some traction. Cohen cites that 80 percent of Americans have not seen real wage growth in 30 years. You can quibble with the exact figure, but he’s right on. The last three decades have not been good for everyone, particularly in the U.S. We do not have a problem with “the growth model”, meaning a problem with economic growth. We have a problem with the “distribution model”. So write an op-ed proposing changes to tax rules, or supporting education, or opposing excessive licensing of occupations.

Moving on:

Will economic growth return, and if it doesn’t, what then? Experts are sharply divided.

No, not really. Cohen cites Robert Gordon as a growth pessimist. Gordon is, but he doesn’t predict that growth is ending. Gordon thinks that the growth rate of GDP per capita will drop from the historical 1.8-2% per year to about 0.9-1.2% per year. This is primarily due to a slowdown in the accumulation of human capital as the population ages and the rates of college and high school completion level off. So even the pessimists don’t believe growth is over, just that it will be slower. Gordon also assumes that total factor productivity growth will be lower than in the past, which is completely unknowable. Gordon gets very “cranky old man” about how useless innovations today are (those kids and their Insta-Snap-gram-Book!).

To decide who is right, one must first recognize that the two camps aren’t focusing on the same things: For the pessimists, it’s the consumer who counts; for the optimists, it’s the machines.

Uh, no. To decide who is right we need data. Like several more years of data to see if in fact growth rates have fallen significantly. I wrote a post about this a while back. We won’t be able to to definitively say if growth has fallen below 2% per year until about 2025. Until then, there will be too much noise in growth rates to extract a signal.

What matters is whether they will substitute for human labor or whether they will complement it, allowing us to be even more productive.

Uh, no. Regardless of whether machines/robots/Skynet are a substitute or complement for human labor, we as an aggregate economy will be more productive. Whether particular individuals find themselves displaced and unable to find work depends on their own set of skills. How we treat those people is a distributional question, not a growth question.

The logical conclusion, then, is that both sides in this debate are right: We’re living an industrial revolution without economic growth. Powerful software is doing the work of humans, but the humans thus replaced are unable to find productive jobs.

Uh, no. See above regarding economic growth. It hasn’t ended just because we had a recession, and a very bad one at that. On the job replacement thing, see here. We experienced similar kinds of disruptions in the past. Can we handle this with more sympathy towards those temporarily displaced by technology? Yes. Absolutely. Again, that is a distributional problem, not a growth problem.

The point is this: If workers are to be productive again, then we must come up with new motivation schemes. No longer able to promise their employees higher earnings over time, companies will now have to adjust, compensate, and make work more inspiring.

Wait, who said workers were unproductive? Did I miss the part where everyone forgot how to do their job? And this seems close to 180 degrees from how companies would respond to an economy that stopped growing. No growth would mean a lack of new firms and/or new types of jobs, so workers wouldn’t have outside options. Firms would have even more power to motivate through fear of losing your job, because there wouldn’t be new jobs out there to escape to.

Cohen suggests that firms will have to focus on giving workers autonomy to keep them happy. He cites the Danish situation as one that produces happy workers. They are treated respectfully and given autonomy, and in return they are very productive. They have a significant safety net in place so that people don’t have to keep bad jobs just to pay the bills. Denmark self-reports as being very happy.

I am all for “the Danish model”. Here’s the thing. It’s a good idea no matter what happens to economic growth. Why should I wait to see if growth slows down to encourage companies to adopt a more positive work environment? If anything, higher growth rates would make it easier to transition to a system like this because economic growth gives people outside options.

The biggest sin of this op-ed is the lack of perspective. It presumes that we are living through not just a shift in long-run growth rates, but a cataclysmic collapse of them. If you want to make that case, then you have to bring some…what’s the word? Evidence.

But bonus points for the Proust quote to give it that affected tinge of world-weary seriousness.

# Is the U.S. Really Below Potential GDP?

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

The CBO just released a new projection of both GDP and the budget out to 2024. In short, the CBO sees the U.S. staying below potential GDP for several years. Menzie Chinn just did a short review of how people use inflation and/or unemployment to try and figure out the difference difference between actual and potential GDP.

From a growth perspective, I wanted to take a look at the projections a little differently. First, I don’t much care about the level of aggregate GDP, I care about the level of GDP per capita. So I took the CBO numbers and combined them with population figures and projections to get actual and projected GDP per capita for the U.S. Note, I’m using the CBO projections for actual GDP, not their potential GDP numbers. I want to look at the expected GDP numbers.

Second, I wanted to consider how this projected GDP per capita compared to long-run trends, rather than using inflation or unemployment to assess whether GDP per capita is “at potential”. I am looking instead whether GDP per capita has deviated from its long-run path. To do this I merged the GDP per capita projections from the CBO with the Maddison dataset on GDP per capita from 1970 to 2008. (The CBO goes back far enough that the two series overlap and I can adjust the actual levels of GDP per capita to match).

I took the trend in GDP per capita from 1990 to 2007, and extrapolated that out from 2008 to 2024. Then I plotted the actual and CBO-projected GDP per capita data against that trend. Here is what you get:

It’s clear here that in 2007 GDP per capita drops below the 1990-2007 trend line. Moreover, the CBO expects that GDP per capita will stay below that trend line out until 2024. It looks like a distinct “level shift” in the parlance of growth economics. GDP per capita is something like 13% below the 1990-2007 trend.

If you look at the post-war trend in GDP per capita from 1947 to 2007, you get something similar. The gap in 2024, 18% below trend, is actually worse than the gap using the post-1990 era.

But if you extend your view back even further, and incorporate the whole period of 1870-2007 to form the trend line, things look different. Now, if you plot the projected GDP per capita against the trend, it looks as if the U.S. is spot on.

GDP per capita is almost exactly where you’d expect it given the historical trend. The CBO expects GDP per capita to be a little low in 2024, about 2% behind the full trend line. Using the 1870-2007 trend, there doesn’t appear to be anything particularly unusual about the projected path of GDP per capita. The U.S. seems to be moving along the same balanced growth path it always has.

What really looks like the anomaly in U.S. data is the extended period from about 1990 to 2010 that we spent above trend. You could think of this as capturing John Fernald’s argument (or see here) that the IT boom of the 1990’s was a one-time level shift up in GDP. We got a big boost from that, but now the economy is settling back to the long-run growth path.

[You should not – NOT – use this as an argument that the financial crash and subsequent recession were necessary, useful, or welfare-improving. It is quite possible for the economy to have managed a graceful slide back to the long-run trend line after 2007 rather than experiencing it all in one dramatic plunge. The long-run trend is like gravity. Yes, it will win in the end, but that does not mean that I have to leap to the ground after cleaning out my gutters. I have a ladder.]

I really thought when I started playing with this data that I’d be writing a post about how the Great Recession had fundamentally shifted GDP per capita below the long-run trend, and that this represented a really fundamental shock given how stable the long-run trend had been until now. But the current path of GDP per capita doesn’t appear to be that surprising in historical perspective.

The big caveat here is that the CBO could be entirely wrong about future GDP per capita growth. If they have been overly optimistic, then we could certainly find ourselves falling below even the very long-run trend. Then again, they could have been pessimistic, and we might find ourselves above trend for all I know. But even with all the uncertainty, the expectation is that the U.S. economy will find itself right where you would have predicted it would be.

# 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.