You Can’t Reform Your Way to Rapid Growth

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

One of the big advantages of having written this blog for a while is that I can start recycling old material. I’m going to do that in response to the small back-and-forth that Noah Smith (also here) and John Cochrane had regarding Jeb! Bush’s suggestion/idea/hope to push the growth of GDP up to 4% per year. Cochrane asked “why not?”, and offered several proposals for structural reforms (e.g. reforming occupational licensing) that could contribute to growth. Smith was skeptical, mainly of the precise 4% value. Why 4? Why not 5? Why not 3 1/3?

Oddly enough, the discussion of Jeb!’s 4% target is also a good entry point to talking about Greece, and the possibility that the various structural reforms insisted on by the Germans will manage to materially change their situation. But we’ll get to that.

First, what are the possibilities of generating 4% GDP growth in the U.S.? I’m presuming that we’re talking about whether we can boost per capita growth up to 4% per year for some relatively short time frame, because history suggests that sustained 4% growth in GDP is incredibly unlikely. From Jeb!’s perspective, I’m guessing either 4 or 8 years is the right window to look at, but let’s say we’re trying to achieve this for just 5 years.

Here’s where I’ll dig back into the archives, where I talked about the boost to growth that you can get from various structural reforms. Literally copying and pasting from that post, there are two ways to boost GDP growth. Either

  • Actively raise current GDP through increased spending by some sector of the economy.
  • Raise potential GDP and let transitional growth speed up.

Let’s attack the second one first, as several of Cochrane’s proposals involve raising potential GDP through structural reforms, but involve no immediate spending changes.

We can do some quick calculations of the growth effects of structural reforms by using the following equation

\displaystyle  Growth = \frac{Y_{t+1}-Y_t}{Y_t} = (1+g)\left[\lambda \frac{Y^{\ast}_t}{Y_t} + (1-\lambda)\right] - 1. \ \ \ \ \ (1)

This says that growth in GDP has a standard component of {1+g}, where {g} is roughly 2.8% per year: 0.8% from population growth and 2% from long-run growth in per capita GDP. The term in the brackets is the adjustment to growth that we get from being below potential GDP, where {Y^{\ast}_t} is potential GDP, and {Y_t} is actual GDP per capita. The parameter {\lambda} governs how fast convergence from actual to potential occurs, and hence determines the growth kick we get from raising potential GDP. The empirical literature on this has consistently found that {\lambda} is about 0.02, which means relatively slow convergence.

In 2015 U.S. GDP is about 16 trillion, and let’s say that right now, potential GDP is roughly 17 trillion. If that is true, then we should have growth of about

\displaystyle  Growth = (1.028)\left[.02 \frac{17}{16} + .98\right] - 1 = 0.0293 \ \ \ \ \ (2)

meaning 2.93% growth.

Is it plausible to have structural reforms that will boost that 2.93% growth to 4% growth? Well, I don’t know precisely how much of boost to potential GDP we’d get from the structural reforms that Cochrane proposed and that Jeb! would apparently enact. But let’s say that it is a pretty substantial amount, like $3 trillion. This means that potential GDP in the US is now $20 trillion dollars, which is a 18% boost in potential GDP. I am granting here that these structural reforms have a massive effect on potential GDP. I am skeptical that they would actually have such a large effect.

Growth after these massive structural reforms will be

\displaystyle  Growth = (1.028)\left[.02 \frac{20}{16} + .98\right] - 1 = 0.0331 \ \ \ \ \ (3)

or 3.31% growth in GDP. That’s not 4%. That’s not really close to 4%. (In one of those wonderful unintentionally funny coincidences, though, it is almost exactly Noah’s off-the-cuff 3 1/3% growth rate.) Massive structural reforms will not push the economy to 4% growth. And after the first year of growth at 3.31%, growth will keep falling until it settles back towards 2.8% per year. So the reforms will never yield 4% growth.

But won’t the massive structural reforms lead to a wave of investment as people get all excited about the new direction that America is headed? Yes. And that is precisely what the equation captures. The convergence result here is measuring the additional growth we get as people invest more due to their perception that the return on those investments is higher due to the structural reforms. Empirically, the fact that {\lambda = 0.02} means that this tends to happen slowly over a few decades, rather than all at once.

You can just scrape 4% growth is you continue to assume that structural reforms to the U.S. economy can add $3 trillion to potential GDP and that the convergence parameter is in fact {\lambda = 0.05}, or more than twice as big as any reliable empirical estimate. Or you could keep {\lambda = 0.02}, and assume that structural reforms were capable of pushing potential GDP to $26 trillion, a 53% increase over potential GDP today. Both are huge stretches, and almost certainly wrong.

It is this same logic that is at play in Greece, by the way. Same convergence equation, same {\lambda}. What’s different? Greece’s trend growth in GDP is probably more like {g = 0.02}, given relatively slow (and probably negative) population growth. Greek GDP right now is about 180 billion euro. What are the possibilities of massive structural reforms, such as those demanded by Germany, generating rapid growth in Greece?

Let’s assume that the Greeks have completely taken the German structural reforms to heart. So much so that Greece simply adopts the entire German legal system, culture, and technology in one giant gulp. This doubles Greek potential GDP to 360 billion euro, which would imply that Greek GDP per capita would be roughly equal to that of Germany.

These sweeping structural reforms will generate growth of

\displaystyle  Growth = (1.02)\left[.02 \frac{360}{180} + .98\right] - 1 = 0.0404 \ \ \ \ \ (4)

or 4% growth in GDP in the first year after reforms. Thereafter, growth will continue to come in below 4% as Greece converges to its new Teutonic economic bliss point.

I know very little about the Greek crisis. I know very little about the terms of the deal that Greece signed. But my limited reading tells me that this is not the kind of growth that will be sufficient for them to crawl out of the hole they find themselves in.

Massive structural reforms are not capable of generating immediate short-run jumps in growth rates in the U.S., Greece, or any other relatively developed economy. They play out over long periods of time, and the empirics we have suggest that by long periods we mean decades and decades of slightly above average growth. Ask the Germans. They’ve been fiddling around with structural labor market reforms since the 1980’s, and when exactly were they able to keep up sustained GDP growth of 5 or 6%?

The U.S. and Greece are not China in 1980 or South Korea in 1960, where you could plausibly imagine that structural reforms could boost potential GDP by a factor of 5 or 6 and generate growth rates of 8-10%. We are nibbling around the edges, by comparison.

Structural reforms don’t generate massive short-term changes in growth rates because they are fiddling with marginal decisions, making people marginally more likely to invest, or change jobs, or get an education, or start a company. By permanently changing those marginal decisions, structural reforms act like glaciers, slowly carving the economy into a new shape over long periods of time. Think of occupational licensing reform. If you enacted that tomorrow, GDP would not move at all. But over the course of the next few years, as new people graduated high school or college, or lost jobs, some of them, on the margin, would now find it worthwhile to become a physical therapist, or a hairdresser, or an interior decorator. They’d presumably be more efficient in these positions than flipping burgers, so the economy would be more efficient and GDP would be higher. But this takes years.

If you want to radically boost GDP growth now, then someone has to spend money now. Take infrastructure spending. Let’s say that miraculously Congress passed a $1 trillion dollar plan to rebuild bridges, ports, roads, and airports around the U.S. Let’s say this is going to be spent $200 billion a year for 5 years starting in 2016.

Now what is growth in 2016? GDP was going to grow naturally at about 2.93%, so we’d have about 16.5 trillion in GDP just from that. Add in 200 billion in infrastructure spending and you get 16.7 trillion in GDP. Now, what is the actual growth rate from 2015 to 2016? (16.7-16)/16 = 0.0438, or about 4.4% growth. This doesn’t even allow for the possibility that there could be a multiplier greater than 1 on the infrastructure spending.

In addition, the beauty of infrastructure spending is that is doesn’t just push us closer to potential, it almost certainly raises potential GDP as well, and keeps the growth rate above average for longer. How much? I don’t know, but I’d personally guess that it raises potential by more than 1-for-1 with the actual spending. But let’s be conservative, and assume that it simply raises potential such that the economy always stays about 1 trillion behind potential GDP. So in 2016 potential is 17.7 and actual GDP is 16.6. What is growth from 2016 to 2017? Well, it grows by about 2.93% again due to being not quite at potential, and then add in another 200 billion in infrastructure spending. That gives us 17.4 trillion in actual GDP. So actual growth from 2016 to 2017 is (17.4 – 16.7)/16.7 = 0.0419, or about 4.2% growth.

So long as we keep up the $200 billion in infrastructure spending, we can get growth of about 4% per year. Jeb!, you’re welcome. Problem solved.

The difference with infrastructure spending is that it does not nibble around the edges or play with marginal decisions. It dumps a bunch of new spending into the economy. And that is the only way to juice the growth rate appreciably in the short run. Structural reforms will raise GDP, and in the long run may raise GDP by far more than immediate infrastructure spending. But that increase in GDP will take decades, and the change in growth will be barely noticeable. You want demonstrably faster growth right now? Then be prepared to spend lots of money right now.

In the Greek situation, the implication is that without some kind of boost to spending now, they are unlikely to ever grow fast enough to ever get out of this hole they are in. If the Germans and EU are serious about keeping Greece in the eurozone and refusing to write down the debt, then they should seriously consider investing heavily and immediately in Greece. Structural reforms, even if implemented with perfection, are highly unlikely to be sufficient. The Greeks don’t have time to wait for the glaciers of structural reform to scrub the economy clean. If the Greeks aren’t allowed to do any stimulus spending, then the EU should do the stimulus spending for them. It is probably the only way that everyone gets what they want.

Understanding Diffusion Models of Growth

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

There has been a recent bloom of research that studies the diffusion of ideas and economic growth. Alvarez, Buera, and Lucas (2013), Lucas (2009), Lucas and Moll (2014), and Perla and Tonetti (2014) are some of the most prominent examples. In each case, firms or individuals learn new techniques after meeting other firms or individuals with better ideas. The papers show the assumptions under which this type of diffusion or imitation process will lead to constant, sustained growth.

I’ve been trying to get my head around what these models teach me about the process of economic growth. I’m going to use Perla and Tonetti (PT) as a specific example in this post, but that’s only because I need an example, and it was the last one I read.

Here’s a quick verbal summary of the model of imitation in PT:

There are a bunch of risk-neutral firms, each with an individual level of productivity. The firm can produce using its own productivity level, or it can shut down for a period and search for better productivity to imitate. If it searches, it is randomly matched with another firm that is producing, and imitates that firms productivity level for free. Searching firms compare the expected value of productivity they get from imitating to the cost of shutting down, and only low-productivity firms search and imitate. Firm productivity is Pareto-distributed. The average level of productivity is rising over time because low-productivity firms imitate high-productivity terms. Because of the specific nature of the Pareto, the distribution remains Pareto even as the average rises.

The PT model delivers sustained growth through this search and match process, while maintaining a distribution of firm-level productivities. But that isn’t due to the economics of imitation, that is due to the specific mathematical structure assumed. To see this, compare the PT model to my newly created model of growth:

There are a bunch of risk-neutral villages, each with an individual level of Tecknologie. The village can consume what it produces, or it can sacrifice all of that production as a sacrifice to the glorious Hephaestus, God of craftsmen, in the hopes that he will bestow on them insight into a new type of Tecknologie. Hephaestus is fickle, like many of the Gods, and his ways are mysterious to mortals. Hence, if the village offers the sacrifice, the new Tecknologie that Hephaestus grants them is unknown, but is equal to the Tecknologie in one of the other villages around them. Villages compare the expected level of Tecknologie from Hephaestus to the cost of sacrifice, so only low-Tecknologie villages perform sacrifices. Village Tecknologie is Pareto-distributed. The average level of Tecknologie is rising over time because low-Tecknologie villages sacrifice and are blessed by Hephaestus. Because of the specific nature of the Pareto, the distribution remains Pareto even as the average rises.

These models are mathematically identical. With a sophisticated use of search-and-replace I could rewrite PT to be a paper on the growth implications of Hephaestus worship in ancient Greece.

The point is that we can call “draw productivity from a Pareto distribution matching currently producing units (DPFAPDMCPU)” anything we want. PT call it “imitation”. In my little story I call it “blessings from Hephaestus”. You could call it “R&D”, or you could call it an “externality” or “diffusion” if you wanted. DPFAPDMCPU is just an assumption about how innovations arrive.

This isn’t to say that DPFAPDMCPU is wrong, or even a bad assumption to make. Every growth model makes some kind of unsupported assumption about how productivity arrives. Solow assumed that productivity grew exponentially, which led to constant growth in steady state. Aghion and Howitt said new innovations arrive as a Poisson process, but the productivity bump you get is always the same. In expectation, or if you have lots of sectors, you get constant growth in steady state. In a standard Romer model, the productivity bump you get from innovation is proportional to the effort you put into R&D, and growth is constant in steady state.

PT isn’t really a model of imitation and growth. It is a model of DPFAPDMCPU and growth. And DPFAPDMCPU has a clever implication, which is that the distribution of firm (or village) productivities stays Pareto forever even though we have all this churning in the distribution going on. That’s something that other assumptions about how innovations arrive can’t capture.

And PT get this distinction. This paragraph is from their conclusion:

This paper contributes an analytically tractable mechanism for analyzing growth and the evolution of the productivity distribution, with both the evolution of the productivity distribution and the technology adoption decision jointly endogenously determined in equilibrium. Thus, we can analyze the effect the productivity distribution has on adoption incentives, the effect of adoption behavior in generating the productivity distribution, and the corresponding growth implications of this feedback loop. We develop a solution technique that obtains closed-form expressions for all equilibrium objects—including the growth factor—as a function of intrinsic parameters.

Here they’ve dropped any use of the word “imitation” and talk about a generic process of “technology adoption”, which could be anything from R&D to Hephaestus-worship. PT state they have figured out how to use DPFAPDMCPU as the mathematical structure to model the arrival of new technologies to adopt, all while still ending up with a constant growth rate.

The question now is why or when DPFAPDMCPU is a better choice than other structures. In what situations, or for what types of products, or in what markets, is it reasonable to think of DPFAPDMCPU as the way that innovations arrive?

“Imitation” or “diffusion” doesn’t seem to cut it as motivation. If we take imitation seriously, then the DPFAPDMCPU structure has several issues:

  • Searching firms are randomly matched with producing firms. Why random? If you’re searching for someone to imitate, then wouldn’t you search for someone with particularly high productivity? The firms are assumed to have perfect foreknowledge of the distribution of productivity, so how come they do not know which firms are the best to imitate?
  • Why is matching one-to-one? If you can imitate a firm, then why can’t all of us imitate one firm? Why can’t we all imitate the best firm?
  • Search costs resources, but imitation is free. That is, the searcher has to give up production to look for someone to imitate. But once they match, they can copy the productivity level for free. So productivity techniques are absolutely non-excludable. But knowing that imitation is happening, why wouldn’t high-productivity firms hold out and demand some kind of side-payment for being imitated?

In short, I’m struggling at this point to see the specific economic context for these models of diffusion/imitation that use DPFAPDMCPU or something similar. Am I missing some kind of obvious examples here? If I am, is there a reason to think that most of the innovation that occurs is due to non-excludable imitation?

Lots of models deliver a prediction of constant growth in steady state, so why are these that use the DPFAPDMCPU assumption a better description of why that happens? I think this literature would benefit from providing a clearer answer to that question.

Embedded Ideas and Economic Growth

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

In the last post I laid out three conditions that could when describing how economic growth worked, and said we had to pick two. In short, I argued that we should pick (1) constant returns to scale in rival inputs, and (2) non-rival ideas earn some part of output. This meant that (3), rival inputs earn their marginal product, had to be done away with.

One particular complaint about my characterization of the issue is that it did not address the concept of ideas “embedded” in people (or things). Something like “the ability to solve differential equations” is a skill that is embedded in some people, and not in others. Once you think about embedded ideas, the argument goes, then you have to consider those ideas “rivalrous”. The person who knows differential equations can’t be two places at once. The idea of solving these equations is just along for the ride in this persons head, so the idea is rivalrous as well. The strongest form of this argument would then say that it only makes sense to think of all ideas as embedded and rivalrous, and by dropping non-rival idea completely we can maintain the idea that all rival inputs earn their marginal product.

I think this is wrong. Yes, some non-rival ideas or skills are embedded in people or things. I don’t have any problem with that. But an embedded skill is still non-rival. Tomorrow someone new is going to learn to solve differential equations and that will have absolutely zero effect on my ability to solve them. I can copy the skill over and over and over, teaching the whole world to solve differential equations, and that will not diminish the ability in anyone else. That’s the definition of non-rivalry.

Saying a skill or idea is embedded in a person (or thing) is a statement about exclusion only. People who did not take the right math classes are excluded from solving differential equations. Those of us who know how to do it own an excludable skill. But it is still a non-rival skill.

Non-rival ideas or skills can even be uniquely embedded in a person or thing. Usain Bolt is uniquely capable of running 100 meters in 9.58 seconds. There has never been anyone in recorded history to run 100 meters this fast. Despite that, running a 9.58 is a non-rival skill. If this year Justin Gatlin runs a 9.58, that isn’t because he took away the skill from Bolt, which would mean the skill was rival. They could both run this fast; it is a non-rival skill.

Saying a skill is unique is a statement about exclusion, not rivalry. If no one ever again runs 100 meters as fast Usain Bolt did, that doesn’t mean running a 9.58 is a rival skill, it means that running a 9.58 is an exceptionally excludable skill. So excludable that it is impossible. But still non-rival.

Making non-rival skills hard to copy doesn’t change their non-rivalry. The fact that teaching everyone in the world how to solve differential equations would be very, very time-consuming doesn’t make this a rival idea. High costs of time or resources to create copies of skills make those skills highly excludable, but not rivalrous.

World class athletes are still probably the best example here. Roger Federer has a set of highly exclusive – and yet non-rival – skills. It is almost impossible to copy Federer’s skill set. I certainly could not, even if I had started training at age 4. But Djokovic and Nadal, after years and years of grueling training and practice, have copied enough of them that they can now beat Federer (sometimes). The skills of playing world class tennis are embedded and highly exclusive. But they are still non-rival.

So what does this have to do with growth theory? The non-rivalry of ideas or skills allows for continuous economic growth. But it is the excludability of those ideas or skills that provides incentives for individuals to create them or learn them.

Romer originally focused on non-rival ideas that were incredibly easy to copy, like software, books, or blueprints. Being easy to copy, these things are not easily excludable, and hence it would be hard to earn rents on them without some kind of protection. Things like patents or copyrights give these easy-to-copy ideas excludability. Those intellectual property rights provide the incentive for people to create new easy-to-copy ideas.

Boldrin and Levine focus on non-rival ideas that are incredibly hard to copy, like the embedded skills of solving differential equations or playing world class tennis. The sheer effort involved in copying makes these ideas highly excludable. The owners can earn rents even without explicit property rights over the idea or skill. Roger Federer doesn’t own a patent on world class tennis playing. It’s just nearly impossible to copy his skill.

In both situations, growth will arise because of the acquisition of new non-rival ideas or skills. In both situations, that acquisition occurs because the exclusivity of the idea or skill allows them to earn rents on it, and those rents are sufficient to offset the costs of inventing or acquiring it in the first place.

Where I think BL went wrong is in claiming that embedding skills or ideas in people or machines makes them rival. They used that term incorrectly. Embedding makes skills or ideas excludable, even though they are still non-rival. Once they claimed that some ideas were rival, they had to contort themselves into arguing that non-rival ideas don’t earn any rents ever to satisfy the “pick 2 of 3” conditions I laid out in the last post. If you want to accuse BL of “mathiness”, then it would be because they mis-matched the language (rivalry) with the math (excludability).

For his part, Romer has probably over-stated the importance of monopoly power over ideas. Yes, a patent gives you monopoly power over an idea. And without that patent, an easy-to-copy idea would most likely not be produced. But some ideas or skills are hard to copy, and the people who hold them do not necessarily need a monopoly over them in order to earn rents. Some ideas are hard enough to copy that you can earn rents even though you face some Cournot-style competition from the few others capable of copying you (i.e. Federer, Nadal, Djokovic). Romer doesn’t really need strict monopoly power, he just needs rents to accrue to idea owners.

The ultimate point is that the world can make sense with (a) non-rival ideas/skills, (b) that are embedded and highly excludable, (c) with Cournot-style competition among owners of the ideas/skills, and yet still satisfy Romer’s conditions that (d) we have constant returns to scale in rival inputs and (e) positive payments to non-rival ideas/skills. (b) and (c) are not incompatible with (d) and (e). But saying that non-rival ideas simply don’t exist doesn’t make any sense to me.

Last point. Given the last post, we know that such a world would require that rival inputs (raw labor, capital, land) earn less than their marginal product. The rents earned by owners of those embedded non-rival skills have to come from somewhere. How do I square that with the wages earned by someone with an embedded skill, like Federer, or someone who knows how to solve differential equations?

The important point here is to not confuse someone’s total reported “wages” with the return earned by their rival input. My total paycheck is some combination of a return to my rival input (i.e. time) and the return to my non-rival, embedded and excludable skills (i.e. teaching 1st-year grad macro). The fact that UH does not separately compensate me for these inputs doesn’t mean that my wage is being paid only for rival inputs. Some of my paycheck is rents I earn for providing a scarce, embedded, excludable but non-rival set of inputs. Some of my paycheck is compensation for my rival input, time. What the conditions I laid out last post say is that this compensation for rivalrous time is below the marginal product of my time.

What Assumptions Matter for Growth Theory?

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

The whole “mathiness” debate that Paul Romer started tumbled onwards this week while I spent four days in a car driving from Houston to Quechee, Vermont. I was able to keep up with several new entries (Harford, Rowe, Andolfatto, Romer) regarding the specifics of growth theory when it was my turn in the passenger seat. I also had running around in my head a series of e-mails I shared with Pietro Peretto, who helped clear up a lot of questions regarding this debate (The usual disclaimer applies – Pietro is not responsible for anything stupid I say here).

Somewhere along I-40 and I-81 I was able to get a little clarity in this whole “price-taking” versus “market power” part of the debate. I’ll circle back to the actual “mathiness” issue at the end of the post.

There are really two questions we are dealing with here. First, do inputs to production earn their marginal product? Second, do the owners of non-rival ideas have market power or not? We can answer the first without having to answer the second.

Just to refresh, a production function tells us that output is determined by some combination of non-rival inputs and rival inputs. Non-rival inputs are things like ideas that can be used by many firms or people at once without limiting the use by others. Think of blueprints. Rival inputs are things that can only be used by one person or firm at a time. Think of nails. The income earned by both rival and non-rival inputs has to add up to total output.

Okay, given all that setup, here are three statements that could be true.

  1. Output is constant returns to scale in rival inputs
  2. Non-rival inputs receive some portion of output
  3. Rival inputs receive output equal to their marginal product

Pick two.

Romer’s argument is that (1) and (2) are true. (1) he asserts through replication arguments, like my example of replicating Earth. (2) he takes as an empirical fact. Therefore, (3) cannot be true. If the owners of non-rival inputs are compensated in any way, then it is necessarily true that rival inputs earn less than their marginal product. Notice that I don’t need to say anything about how the non-rival inputs are compensated here. But if they earn anything, then from Romer’s assumptions the rival inputs cannot be earning their marginal product.

Different authors have made different choices than Romer. McGrattan and Prescott abandoned (1) in favor of (2) and (3). Boldrin and Levine dropped (2) and accepted (1) and (3). Romer’s issue with these papers is that (1) and (2) are clearly true, so writing down a model that abandons one of these assumptions gives you a model that makes no sense in describing growth.

If there is a sticking point with McGrattan and Prescott, Boldrin and Levine, or other papers, it is not “price-taking” by innovators. It is rather the unwillingness to abandon (3), that factors earn their marginal products. Holding onto this assumption means that they are forced to abandon either (1) or (2).

From Romer’s perspective, abandoning (1) makes no sense due to replication. How could it possibly be that a duplicate Earth produces less than the actual Earth? Abandoning (2) also does not make sense for Romer. We clearly have non-rival ideas in the world. Some of those non-rival ideas are remunerated in some way, whether there is market power or not. So (2) has to be true.

The “mathiness” comes from authors trying to elide the fact that they are abandoning (1) or (2). McGrattan and Prescott have this stuff about location, which is just to ensure that (1) is false. Lucas (2009), as Romer explained here, is abandoning (2), and asserts that this is something we know as a result of prior work. It’s not.

Regardless, once you’ve established the properties that you think are true, now you can talk about market power or the lack of it. Romer, taking (1) and (2) as given, asks how non-rival inputs could possibly be earning output. They are costless (or close to costless) to copy, so how is it possible for them to earn anything? Romer says that non-rival ideas must be excludable, to some extent, in order to earn the output we see them earning in reality.

A patent or copyright is one way of giving a non-rival idea some exclusivity. If that patent is strong, then it gives the owner a monopoly on the idea, and hence they can exert some market power over that idea. Market power, in this case, means that the owner can charge any price they want and still be in business. They may set a price that maximizes profits, or not. Whatever. They will not lose all their business if they raise the price.

But even if the exclusivity of the non-rival idea is not complete, and the owner doesn’t have absolute market power, this doesn’t mean the non-rival idea earns nothing. Let’s say that an idea is non-rival, but copying is somewhat difficult. Reverse engineering an iPhone, for example, is non-trivial. So perhaps no single firm owns an idea outright, but there are only limited firms that can use the idea. These firms engage in some kind of Cournot game, which means that they all earn profits, but any single firm cannot charge any price they want. If they charge slightly more, they will lose all their business to other firms. In this case the non-rival idea earns some output (i.e. the profits to those firms), but no firm has full market power.

The lack of full market power here is fully compatible with (1) and (2) being true, and (3) being false. The issue with Boldrin and Levine isn’t that they allow people to compete with the innovator immediately, it’s that they dismiss the whole idea of non-rival ideas and abandon (2). For what it’s worth, Boldrin and Levine are not guilty of mathiness, in my mind. They are really clear that they deny such a thing as a non-rival idea exists. I don’t agree with them, but they don’t try to hide this.

Aside #1: What does all this have to do with Euler’s Theorem? This theorem is the reason (1), (2), and (3) cannot all be true at once. This was implicitly what I was saying in my last post. The production function is {Y = F(R,N)}, where {R} are rival inputs and {N} are non-rival. If the function is constant returns then {\lambda Y = F(\lambda R,N)}. Take derivatives of both sides with respect to {\lambda}, and you get {Y = R F_R(\lambda R,N)}. Evaluate at {\lambda = 1} without losing anything, or {Y = R F_R(R,N)}, meaning that total output equals rival factors times their marginal products. This holds, no matter what we say about how factors are paid, for a function CRS in rival inputs.

If I then say that each rival input {R} gets paid a wage/return equal to its marginal product, this means that the payments to {R} are exactly equal total output, {Y}. So there is nothing left over to pay owners of non-rival inputs. The only way to pay non-rival inputs anything is to force the wage/return to be less than {F_R}. Or to dismiss the assumption that the function is CRS with respect to rival inputs in the first place.

Aside #2: Yes, I spent four days driving from Houston to Quechee. Rules for long car trips with kids. First, no food in the car. Second, when the car stops, everyone pees. Third, stop every 2-2.5 hours, without fail.

Market Power versus Price-taking in Economic Growth

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

I’m sure you’ve been breathlessly following along with the discussion on “mathiness” that Paul Romer kicked off (see here, here, here). Romer used several growth models to illustrate his point about “mathiness”, and his critique centered around the assumption of price-taking by firms and/or individuals in these papers. His argument was that these papers used “mathiness” as a kind of camouflage for their price-taking assumptions. Romer argues that the reasonable way to understand growth is to allow for market power by some firms and/or individuals over their ideas.

From what I can see, the heart of this is about replication. What Romer has asserted is that any aggregate production function must have constant returns to scale (i.e. be homogenous of degree one) in its rival inputs. The mental exercise here is the following. Imagine that tomorrow there was a perfect replica of the Earth floating next to this one. What would be the output of the alternative Earth? It would be exactly the same as output here, right? It would have to be. It is an exact replica.

What we did was replicate the rival inputs (land, capital, people, education, etc..) and held constant the ideas/plans/technologies. As the output of the alternative Earth is exactly equal to the output of the current Earth, the production function has constant returns to scale with respect to the rival inputs, the things we duplicated. We doubled Earth, and got double the output. It follows that if I doubled Earth’s rival inputs and doubled the ideas/plans/technologies, then I’d get more than double the output. In short, I’d have increasing returns to scale.

What does this imply about market structure? Write down a production function that depends both on rival inputs ({X}, standing in for all the stocks of capital and people and land) and non-rival inputs ({A}, standing in for ideas/plans/technologies),

\displaystyle  F(A,X). \ \ \ \ \ (1)

What the replication argument says is that this function has constant returns to scale in terms of {X}, or {\lambda F(A,X) = F(A,\lambda X)}. This in turn implies that the following must be true

\displaystyle  F(A,X) = \frac{\partial F(A,X)}{\partial X} X. \ \ \ \ \ (2)

The above says that total output can be calculated as the marginal product of rival inputs (the derivative) times the total amount of rival inputs, {X}. This is just Euler’s theorem for homogenous functions.

What we also know has to be true about this production function is that the total amount paid to all the factors of production – rival and non-rival – can only add up to total output. In other words, we’ve got

\displaystyle  F(A,X) = Profits + wX \ \ \ \ \ (3)

where {Profits} are whatever we pay (possibly zero) to the owners of the ideas/plans/technologies. {w} is the “wage” paid to a rival factor {X}. If we had lots of rival factors, then we’d have lots of these terms with things like wages, rents paid to owners of land, rents paid to owners of capital, etc.. etc..

Both the two expressions I’ve shown have to hold, and this is where we get to the problem. If we want to assume that there is price-taking, then all the rival factors would be paid their marginal product. If they were underpaid, then other firms could pay them more, and use all the inputs from the original firm. But if wages are equal to marginal products, then {w = \partial F(A,X)/\partial X}. And if this is true, then the only possible way for the second expression to hold is if {Profits = 0}. If rival factors of production are paid their marginal products, there is nothing left over to pay out as profits.

If you have {Profits>0}, then you must have that {w<\partial F(A,X)/\partial X}, or rival factors of production are paid less than their marginal product. And the only way for this to be the equilibrium outcome is if there is not price-taking. If other firms could pay more, they would, and would equate the wage and marginal product. So positive profits imply some kind of market power (possibly a patent, or a legal monopoly, or some kind of brand identity that cannot be mimicked) for firms.

Romer’s 1990 paper argues that this second situation is the only one that makes sense for explaining long-run growth. If {Profits} did equal zero, then no one would bother to undertake innovative activity. What would be the point? So firms that innovate must earn some profits to incent them to undertake the innovation. This doesn’t mean they are gouging people, by the way. The positive profits may simply be sufficient to offset a fixed cost of innovating. But once you accept that innovation takes place in large part as a deliberate economic activity, Romer’s argument is that this inevitably implies that firms have some market power and rival factors are not being paid their marginal products. You have to be careful here. Romer is not arguing that this is how the world should work. He’s arguing that this is how it does work.

This framework makes it easier to understand what is going on in papers that assume price-taking or perfect competition. Take the Solow model, which implicitly has price-taking by firms. In the Solow model, technology {A} just falls out of the sky, and no deliberate activity is necessary to make it grow. So {Profits=0}, because there is no one to remunerate for innovating. Hence we can have price-taking by firms.

Learning by doing, a la Ken Arrow, makes a similar assumption. Arrow doesn’t have {A} exactly fall out of the sky. {A} is strictly proportional to {X} in a learning-by-doing model, so it grows only as fast as {X} grows. But similar to Solow, no one has to take any deliberate effort to make this happen. It’s a pure externality of the production process, and no one even realizes that it is occurring, so no one earns any profits on it.

Note that this concept is pretty crazy in terms of the replication argument. Arrow’s learning by doing model implies that when the alternate Earth shows up, we more than double output because all those additional rival factors generate some kind of ….. well, it’s not clear exactly how this is supposed to work. Presumably you’d have some kind of gains from trade type argument? The two Earth’s could trade with each other, and so we could let Earth 1 produce Lego and Earth 2 produce Diet Coke. But remember, these Earth’s are identical, so relative prices are identical, and so there isn’t any incentive to trade in the first place.

What of more modern models of price-taking and growth? I mentioned the McGrattan/Prescott (2010) paper in the last post, and effectively they assume that {F(A,X)} is constant returns to scale over both {A} and {X}. Formally, {\lambda F(A,X) = F(\lambda A, \lambda X)}. This means that the production function is decreasing returns to scale with respect to rival inputs, and

\displaystyle  F(A,X) > \frac{\partial F(A,X)}{\partial X} X. \ \ \ \ \ (4)

Now, given this, we could easily have price-taking ({w = \partial F(A,X)/\partial X}) and still have {Profits > 0}.

But does this assumption make sense? Well, what happens when the alternate Earth shows up? In the MP setting, when the alternate Earth arrives total output across our two planets is less than double what we produce today. But alternate Earth is an exact replica of our planet. So how could it possibly produce less than us? Or maybe alternate Earth produces the same amount, but its arrival somehow made us less productive here on the original Earth?

MP aren’t exactly after a model of endogenous growth, but Boldrin and Levine (2008) explicitly write down a model that is meant to show that perfect competition is compatible with firms/people making deliberate innovation decisions. It’s taken me a few days to get my head around how their work fits (or does not fit) in with Romer’s. BL don’t write a model that uses a standard production function, so it’s difficult to map it into the terms I’ve used above.

In the end, though, a (the?) key point is that BL assume that ideas are in fact rival goods. A working paper version of this paper mentions the following in the abstract: “We argue that ideas have value only insofar as they are embodied in goods or people, …” By assuming that ideas have no productive value by themselves, the production function is essentially just {F(X)}, and is constant returns to scale in the {X} rival inputs. Hence price-taking is something that could happen. Innovation in BL means providing more inputs (i.e. better inputs) into the production function, raising {X}. BL assume that the profits accruing to ideas themselves are zero. BL is similar to a model like Lucas (1988), where all innovation is embodied in human capital.

In BL, the incentives to innovate (i.e. to accumulate a new kind of input) come because you own a rival good that is scarce. Innovators in BL are like landlords in a classic Ricardian model. They have a fixed factor of production, and they earn rents on it. If those rents outweigh the cost of coming up with the idea in the first place (producing the 1st copy), then people will innovate.

Does the BL version make sense? It depends on how you conceive of technological progress. Is it embodied (and hence rival) or not (and so it is non-rival)? If all technological progress is embodied, then it is possible that all firms or persons are price-takers. But if any deliberate technological progress is non-rival (disembodied), then there are at least some firms or people with market power. Note that this doesn’t mean that all markets are imperfect, but firms that own non-rival ideas and have some ability to exclude others from using them (e.g. a patent) will charge more than marginal cost.

The important difference here is the all vs. any, I think. Everyone could be price-takers if all technology is embodied (and hence rival). That is a strong condition. It means there is literally no such thing as a non-rival idea. One way to think about this is kind of the opposite of the replication argument. What if tomorrow everyone who knew Linux was wiped off the face of the Earth? Would Linux be gone? Would we have to wait for some new pseudo-Torvalds to arrive and re-write it? I don’t think so. Someone could figure it out by reading manuals left behind. Would they learn it quickly? Maybe not. But the idea of Linux is clearly non-rival. And so long as there are any non-rival ideas that are useful, then if you want there to be economic incentives to produce them, there has to be some market power that allows firms to capture those rents.

By the way, BL use their model to argue that intellectual monopolies (like patents, copyright, etc..) may be counter-productive in fostering innovation. That can be true even if you have non-rival ideas. The fact that profits exist for non-rival ideas don’t require that intellectual monopolies be made eternal and absolute. Within any Romer-style model there is some sweet spot of IP protection that fosters innovation without incurring too much deadweight loss due to the monopolies provided. We certainly could be well past that sweet spot in reality, and be over-protecting IP with patents that are too strong and/or too long. But if you eliminated all IP protection, then the Romer-style setting would tell you that we would effectively shut down innovation in non-rival ideas, as they could not otherwise be compensated.

The Connection of Urbanization with Growth

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Paul Romer has a nice post up about how urbanization “passes the Pritchett test” for development. Pritchett’s test is that urbanization (in this case) is related both in the cross-section and the time-series to living standards, and positive shocks to urbanization are associated with higher living standards. So Romer argues that we should be studying urbanization as a route towards higher living standards in developing countries. This jives to some degree with his charter city concept, which proposes establishing new cities with functioning institutions in developing areas. There isn’t really anything to argue with about the rough correlations in the data. Urbanization is, and has been, associated with higher living standards for a long time.

But there are some subtleties in those relationships that mean simply urging everyone to flood into cities is not necessarily wise. Everything I’m going to talk about now is based on joint work of mine with Remi Jedwab, who studies urbanization in developing countries very deeply.

The first caveat I’ll point out is that the absolute pace of urbanization matters a lot. Moving an extra 10,000 people into a city in a year may improve productivity in that city and overall in the country. Moving 1,000,000 people into the same city in a year will probably generate such awful congestion costs that productivity in that city falls and country-level productivity may be lower. Remi and I lay out a simple model of this in a working paper that we have out (and which is being furiously revised right now). We show that if the absolute growth of city population is too large, then city wages will actually get pushed down due to the overwhelming congestion effects, even if there is some exogenous technological progress. That part isn’t incredibly shocking. What we then do is show that if population growth is endogenous, and rises as wages get lower, then too-rapid city population growth pushes a city into what we call a poor mega-city equilibrium. The city gets stuck with low wages and high population growth, and cannot overcome the congestion costs of that growth. We explain the arrival of poor mega-cities like Dhaka, Lagos, and Karachi as a kind of perverse result of the mortality transition after World War II, as it raised the absolute growth of cities beyond a critical threshold. Cities like these grow by 400,000 or 500,000 residents per year, while historically cities like New York or London only grew – at their peak – by maybe 200,000 per year. Urbanization that happens too rapidly can have counter-productive results.

The second caveat is that what drives urbanization matters. Remi and I, along with Doug Gollin, have a paper on urbanization and natural resources. If you look across countries, as Romer does, then there is a clear relationship of GDP per capita and urbanization rates. However, urbanization rates are not necessarily correlated with industry or tradable service production.
Urbanization and Industrialization

The figure above shows the lack of a firm relationship, and this shows up if you use just manufacturing, just manufacturing and finance, or some other reasonable definition of what constitutes tradable goods and services. There are lots of countries in the world that have high urbanization rates, but are not industrialized, and they tend to be resource exporters. And this isn’t just places like Dubai. Angola – a major oil exporter – has an urbanization rate equal to China’s. We document that natural resource exports are a significant driver of urbanization. We even have a neat little diff-in-diff type specification that looks at discoveries of resources and shows that urbanization rates jump in the decade after the discovery. Perhaps more important, though, we show that cities in places that urbanize because of natural resource booms have very different urban workforces than typical “industrial” urbanizers. Cities in places like Angola have a big percentage of their urban workforce in personal services and small-scale retail trade, and few people in industry or high-value services. This contrasts with China, where their urban workforce has a huge percentage of people in sectors that produce tradable goods or services (i.e. finance). The point is that urbanization is not homogenous. What drives urbanization matters, in that it determines what sectors people in those urban areas end up working in.

The last caveat kind of takes off from the second. Urbanization has been related to higher living standards over much of history, but that doesn’t mean it always will be. Remi and I did a survey paper on the relationship of urbanization and GDP per capita over time. Yes, they are positively related in every year we look at, going back to 1500. But that doesn’t mean that urbanization rates have increased primarily because countries have gotten richer.

Urbanization and GDP per Capita Over Time

What we see in the data is that urbanization rates have shifted higher at every level of GDP per capita over time. A country with GDP per capita of $1,000 had an urbanization rate of about 10-15% in 1500, but by 2010 a country with the same GDP per capita would be between 35-50%. Most urbanization over history has occurred not because of countries getting richer, but simply because urbanization has gone up everywhere. One implication is that the positive relationship of urbanization and living standards can only go down in the future. Rich countries are maxed at at urbanization rates of 100%. So if poorer countries continue to urbanize, then the relationship of GDP per capita and urbanization has to fall.

The over-arching point is that the positive relationship between urbanization and living standards we see in existing data is an equilibrium relationship, not necessarily a causal one. There are plausibly negative impacts of too-rapid urbanization on living standards. And Romer is careful in his post not to make any kind of strong causal claim. He thinks we should be studying urbanization more carefully to try and understand what exactly it is that generates the positive relationships. I’d strongly agree with that. I’d like to think that Remi and Doug and I have given some clues towards an answer, perhaps just by pointing out things that are not responsible for the positive relationship.

There is More to Life than Manufacturing

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One of my continuing questions about research in economic growth is why it insists on remaining so focused on manufacturing to the exclusion of the other 70-95% of economic activity in most economies.

I’ll pick on two particular papers here, mainly because they are widely known. The first is Chad Syverson’s “What Determines Productivity?“, a survey piece that reviews the literature on firm-level productivity measurement. The main theme of the survey is that productivity varies widely across firms. Which firms? Syverson cites his own work showing that within disaggregated manufacturing industries, productivity varies by a factor or roughly 2-to-1 between the 90th and 10th percentiles. The rest of the survey contains citation after citation of papers studying manufacturing sector productivity differences.

Hsieh and Klenow, in their paper looking at the aggregate impacts of these kinds of productivity gaps, look at manufacturing plants in India, China, and the U.S. They find that the productivity differences, if eliminated, would raise manufacturing productivity by 40-50% in China and India. What goes unsaid in Hsieh and Klenow is that a 40-50% increase in productivity in manufacturing would be something like a 10% increase in aggregate GDP in India, and a 15% increase in China. Both still impressive numbers, but much smaller than the headline result because the manufacturing sector is *not* the dominant source of value-added for any country.

Why do we persist in focusing on this particular subset of industries, sectors, and firms? I think one of the main reasons is that our data collection is skewed towards manufacturing, and we end up with a “lamppost” problem. We look for our lost keys underneath the lamppost because that’s where the light is, even though the keys are out in the dark somewhere.

Our system of classifying economic activity is part of the problem. It was designed to track manufacturing originally, and then other sectors were sort of stapled on as an afterthought. To see what I mean, consider the main means of classifying value-added by sector (ISIC codes) and the main means of classifying occupations (ISCO codes).

ISIC stands for International Standard Industrial Classification. It was designed to distinguish one goods-producing industry from another, not to provide any nuance with respect to services. The original ISIC system had 10 industries, and 2 of them were manufacturing. Those 2 manufacturing industries were divided into 20 total sub-industries. *All* of the other economic activity in the economy was assigned a total of 25 sub-categories. So we’ve got “manufacture of wood and cork, except for furniture” and “manufacture of rubber products” under manufacturing in general. But we’ve got “wholesale and retail trade” as a sub-category under commerce.

From ISIC’s perspective, separately tracking the manufacture of wood of cork products (but not furniture, that’s different) was important, but it was sufficient to just lump all wholesale and retail activity in the economy together. Even in 1960, all manufacturing value-added in the U.S. was only slightly larger than all wholesale and retail trade value-added. But the former is subdivided into 20 sub-categories, while the latter is simply a sub-category of its own. Our methods of categorizing value-added are a relic of an economy now 60-70 years old, and even back then this was un-related to the relative importance of different sectors.

And no, ISIC has not kept up with the times. Yes, the current ISIC revision 4 now breaks out wholesale and retail trade into its own sub-categories (2-digit) and sub-sub-categories (3-digit). Wholesale and retail trade now has 20 3-digit categories. Retail sale of automotive fuel, for example. Manufacturing has 71 3-digit categories. Manufacture of irradiation, electromedical, and electrotherapeutic equipment, for example.

In the current ISIC version, “Education” is a top-level sector, similar to “Manufacturing”. But while manufacturing still has 24 sub-sectors at the 2-digit level, and 71 at the 3-digit, education has 1 sub-sector at the 2-digit level, and 5 at the 3-digit level. “Human health and social work” is a top-level sector, and it has 3 2-digit sub-sectors, and 9 3-digit sub-sectors. We have “hospital activities” and “medical and dental practice activities” as 2 of the 9, so you can at least separate out your optometrist appointment from your emergency appendectomy.

Think of how ridiculous this is. We are careful to distinguish that your dining room table was produced by a different sub-sector than the one the produced the wooden salad bowl you use on that table. But we do not bother to distinguish my last tooth cleaning from my grandma’s last orthopedic appointment.

The calcification of our view of the sources of economic activity continues if we look at occupation codes. These are from ISCO, and the last revision to the codes was in 2008. ISCO uses a similar multi-digit system as ISIC. The one-digit code of 2 means “Professionals”, and below that is the two-digit code of 25, for “Information and communications technology professionals”. That two-digit code has the following lower-level breakdown:

  • 251 Software and applications developers and analysts
    • 2511 Systems analysts
    • 2512 Software developers
    • 2513 Web and multimedia developers
    • 2514 Applications programmers
    • 2519 Software and applications developers and analysts not elsewhere classified
  • 252 Database and network professionals
    • 2521 Database designers and administrators
    • 2522 Systems administrators
    • 2523 Computer network professionals
    • 2529 Database and network professionals not elsewhere classified

These are incredibly high level designations in the tech world. Imagine that you are building a new web site for your retail business, and you need someone to do user interface. Do you ask for someone who does “web and multimedia development”, or someone who does “software development”? No. Those are far too general. You’d post an ad for someone who does UI/UX design, with a knowledge of html, css, and perhaps javascript. You might also require them to know Photoshop. And this person is completely different than the person you’d hire to build your iPhone app, who needs to know Xcode at a minimum, and is different from the guy who builds the Android app.

On the other hand, we have the one-digit code of 7 that means “Craft and related trade workers”. Below that is code 71, for “Building and related trades workers, excluding electricians”. That category is broken down further as follows:

  • 711 Building frame and related trades workers
    • 7111 House builders
    • 7112 Bricklayers and related workers
    • 7113 Stonemasons, stone cutters, splitters and carvers
    • 7114 Concrete placers, concrete finishers and related workers
    • 7115 Carpenters and joiners
    • 7119 Building frame and related trades workers not elsewhere classified
  • 712 Building finishers and related trades workers
    • 7121 Roofers
    • 7122 Floor layers and tile setters
    • 7123 Plasterers
    • 7124 Insulation workers
    • 7125 Glaziers
    • 7126 Plumbers and pipe fitters
    • 7127 Air conditioning and refrigeration mechanics
  • 713 Painters, building structure cleaners and related trades workers
    • 7131 Painters and related workers
    • 7132 Spray painters and varnishers
    • 7133 Building structure cleaners

The separate occupations involved in building a house are pretty clearly delineated here: framers, plumbers, painters, etc.. Heck, ISCO makes sure to distinguish “spray painters” from regular old “painters”, and those are all different from people who clean building structures (I’m guessing these people have power washers?).

While all the individual occupations of building are house are broken down, all the individual occupations of building a successful web-site are lumped into one, maybe two occupations? “Software developers” is not the same level of disaggregation as “plumbers”, despite ISCO having them both coded to a 4-digit level.

If you go back to the ISIC codes, you can get an idea of how our conception of economic activity atrophied somewhere around 1960. What follows are some current descriptions of 3-digit sectors from ISIC.

This is for the “Manufacture of Furniture”:

This division includes the manufacture of furniture and related products of any material except stone, concrete and ceramic. The processes used in the manufacture of furniture are standard methods of forming materials and assembling components, including cutting, moulding and laminating. The design of the article, for both aesthetic and functional qualities, is an important aspect of the production process.

Some of the processes used in furniture manufacturing are similar to processes that are used in other segments of manufacturing. For example, cutting and assembly occurs in the production of wood trusses that are classified in division 16 (Manufacture of wood and wood products). However, the multiple processes distinguish wood furniture manufacturing from wood product manufacturing. Similarly, metal furniture manufacturing uses techniques that are also employed in the manufacturing of roll-formed products classified in division 25 (Manufacture of fabricated metal products). The molding process for plastics furniture is similar to the molding of other plastics products. However, the manufacture of plastics furniture tends to be a specialized activity.

Note the detailed differences accounted for in the definition of furniture manufacture. ISIC is careful to distinguish that wood furniture is distinct from just processing wood, because of some aesthetic element. And yes, the techniques for metal and plastic furniture are similar to other 3-digit industries, but there is something particular about furniture that sets it apart from these.

Now here’s the description of the “Computer Programming, Consultancy, and Related Activities” code:

This division includes the following activities of providing expertise in the field of information technologies: writing, modifying, testing and supporting software; planning and designing computer systems that integrate computer hardware, software and communication technologies; on-site management and operation of clients’ computer systems and/or data processing facilities; and other professional and technical computer-related activities.

On the other hand, anyone who does anything even remotely connected with IT gets lumped into one gigantic category. Write code in Ruby on Rails for web sites? Convert legacy systems at a major corporation from COBOL over to C? Do tech support for a bank? Manage a server farm? Create mobile apps in Xcode? All that shit’s basically the same, right? Computer stuff.

This concentrated focus on manufacturing is problematic because it means we cannot undertake detailed studies similar to Syverson’s or Hsieh and Klenow’s about the sectors that are actually growing rapidly. Is there a lot of productivity dispersion in software? How about in retail, or home health care? These industries actually account for large and growing shares of economic activity, so productivity losses in them are relatively important compared to manufacturing.

The classification system also helps sustain the myth that this sector is somehow inherently more valuable than other types of economic activity. It plays into this idea that a country is failing if its manufacturing sector is declining as a share of GDP. But that decline in manufacturing is simply evidence that we have gotten very, very adept at it, and that there is an upper limit on the marginal utility of having more manufactured goods. All that effort that goes into tracking individual types of manufacturing activity would be far better spent tracking more service-sector sub-categories and occupations, because those are actually going to expand in size in the future.

And yes, I just wrote 2000 words about ISIC and ISCO codes. What has happened to me?

Growth Effects, Level Effects, and Transitional Growth

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This post is about a metaphor for explaining growth dynamics to people. It might be useful if you are either trying to learn growth theory, or teach growth theory. I think the metaphor works nicely for explaining what we mean when we talk about level and growth differences by putting into a context that students can understand. Comments are welcome, I’d like to know if it is something I should try out with a live class next year.

Imagine that every country is a car, and those cars are traveling along a two-lane highway. The farther you go along the highway, the richer you are. Instead of mile markers you have GDP per capita markers, $1,000 per person, $2,000 per person, etc. etc. Your growth rate is your speed, as it measures how fast you go from one GDP p.c. marker to the next. Doing 70 MPH? You’re growing really fast. Doing 30 MPH? You’re growing slowly. But your speed does not tell me where you are along the highway. The car going 70 MPH could be way behind the car going 30 MPH, or it could be way ahead, or it could be in the process of passing the 30 MPH car. So we need another piece of information, which is your location. In terms of growth theory, I would call your location along the highway your level. A country could be much poorer than another (way behind on the highway), much richer (way ahead), or equally rich (at the same spot on the highway). Now the level, or location along the highway, is constantly changing. So it is more accurate to think of level as “how far behind the leading car are you?”

Using this metaphor, how do we think about explaining differences in observed GDP per capita across time or across countries?

First, a “level difference” is the distance between two cars traveling along the highway at the same speed. If they are both going 55 MPH, then this distance will remain constant over time, even though both of them will continue to drive forever on the highway. Level differences are about your position on the highway relative to other cars or trucks. Level differences in GDP per capita are about one country’s position relative to another, but holding the growth rate constant.

Second, a “growth difference” is a difference in the speed of the two cars. If one is going 70 MPH and the other 55 MPH, then even if the faster car starts out behind (poorer), it will pass the slower car, and then continue to expand its lead along the highway. The faster car will always end up richer, and the gap will grow over time. Growth differences would generate massive divergence in GDP per capita, just as persistent speed differences would generate massive divergence in your location along the highway relative to a slower car.

Finally, “transitional growth” is like a car accelerating temporarily to pass a truck doing 55 MPH in the right lane. Transitional growth changes your level difference with respect to the truck. You were behind, and now you are ahead. The only way to make that happen is 70 MPH temporarily. Your measured growth rate (the speed at which the GDP pc markers fly by) is higher than 55 MPH for a minute or two, but after you pass the truck you go back to 55 MPH (there is another truck in the way). But you do not have a permanent growth difference with the truck you just passed. You fundamentally are both doing 55 MPH. Transitional growth just means you jumped ahead of the truck. Transitional growth and level differences go hand in hand. Transitional growth is how you change level differences, just like temporary acceleration to 70 MPH changes your position with respect to the truck.

When we look at the advanced economies of the world (US, Japan, W. Europe, etc..), they seem have small level differences, and little to no growth differences. They are all driving at 55 MPH, roughly. The US is ahead of Japan, Germany, and France by a few car lengths, but nothing too major. Maybe Singapore is a little ahead of the US. But they all are driving at 55 MPH.

Why doesn’t the US just accelerate, and get faster economic growth? Here we need to imagine that there is a sheriff driving along in the right lane at exactly 55 MPH. Passing the sheriff is a bad idea – he’ll arrest you if you try. The sheriff dictates the long-run growth rate at the frontier of economic growth. Whatever happens, you cannot pass the sheriff. Now, within the growth literature there is some debate on whether the sheriff himself can speed up. Chad Jones’ semi-endogenous growth theory comes to the conclusion that the sheriff could perhaps temporarily accelerate, allowing all the countries stacked up behind him to accelerate temporarily as well. But the sheriff cannot really change the fundamental speed limit of 55 MPH. Others will argue that yes, the proper set of incentives or policies could permanently allow the sheriff to speed up to 56 or 57 MPH or more. Regardless of the exact nature of the sheriff, he represents some kind of limit to how fast you can move along the highway once you are the front.

How about countries like China, which seems to have been driving at 90 MPH for a few decades? We think of this as transitional growth, not a growth difference. In other words, China will eventually slow back down to 55 MPH like all the leading countries. China was able to grow so fast because it started out miles behind the leaders on the highway. Once it accelerated up to 90 MPH, it was able to keep that speed for a long time as it zipped down the left lane past a bunch of countries. But as it approaches the sheriff, its speed will slow down, and we are already seeing a little evidence that this is happening. Where exactly it ends up relative to the US or Europe is not clear. It could end up a mile behind, a few car lengths behind, a few car lengths ahead. But its rapid growth is probably transitional growth, not a fundamental growth difference. If China really did have a faster fundamental growth rate – if it could drive 65 MPH forever – then it would pass the sheriff. We’ve never seen anyone pass the sheriff yet, so I’m inclined to think you can’t do it. But maybe China knows a guy, or has diplomatic plates or something.

When we talk about particularly poor countries – Somalia, for example – then we perhaps are looking at both growth and level differences. In level terms, they are far, far behind the leaders, miles back. And their speed appears to be even slower than the leaders, maybe only 25 MPH. So not only are these countries poor, but they are falling further and further back from the leaders. Their economic growth is not sufficient for them to catch up to the leaders.

Do You Have to Choose Growth or Development? Part Deux

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

In my last post I talked about Lant Pritchett’s recent article which questioned the focus of the World Bank on only the extreme poor. He wondered whether the Bank was the right partner for developing countries hoping to grow to middle- or high-income living standards. I agreed with Pritchett that poverty alleviation efforts are not capable of generating what we might consider transformative growth, meaning significant convergence towards rich countries.

I got a lot of very thoughtful responses to that post (and one or two unhinged ones). One response came from Emre Ozaltin, who had written an earlier reply to Pritchett. Emre pointed out on Twitter some research showing that health improvements had accounted for 11% of growth in a set of developing countries, suggesting that this means poverty alleviation efforts do lead to growth.

Twitter just isn’t sufficient to make a coherent reply, so here we go. Even if health interventions really were responsible for 11% of growth in developing countries, that is not the same thing as saying that health interventions can create fundamental economic development.

Comparative Growth
Consider the figure, which shows the time path of GDP per capita in the U.S., South Korea, and Tanzania from 1950 to 2010. In 1960, South Korea and Tanzania are roughly equivalent in living standards. They are both far poorer than the U.S., by a factor of about 10 to 1. In the subsequent decades, though, South Korea and Tanzania have entirely different experiences. South Korea has transformative growth, and the U.S. is ahead of South Korea now by a factor of 1.5 to 1. In contrast, Tanzania doesn’t experience much overall growth at all, and the U.S. is ahead by a factor of 42 to 1.

When I talk about and study economic development, I mean the study of what caused South Korea to make that dramatic leap to rich-country status. What will promote that transformation in poor countries? There is no evidence that health or education interventions could be the answer to that question.

When Emre is talking about health generating growth, he is talking about the contribution of health to that mild growth seen in the last twenty years or so in Tanzania. Yes, there was growth. Yes, health interventions were (maybe) responsible for 11% of that growth. But that growth has not been sufficient to do anything to transform Tanzania into the next South Korea.

It doesn’t mean that these efforts were a waste, or should be stopped. There is no binary choice between poverty alleviation and promoting transformative growth. I believe firmly that from a humanitarian perspective, we should act to alleviate the conditions of poverty in these countries as much as possible. At the same time, we should also be doing what we can to promote the transformation of these economies, so that they take off in the way South Korea did.

I think Pritchett is worried that the Bank is ignoring transformative growth in favor of focusing only on poverty alleviation. And I agree with him in general that one should not abandon promoting transformative growth. But I don’t know that we should worry specifically if the World Bank changes its focus.

From the World Bank perspective, if they do want to focus on poverty alleviation, mazel tov. But do not claim that this is because it is a more robust way to generate fundamental economic development, or because you have somehow “seen the light”. You are making a distinct choice to focus on the humanitarian aspect of development, and ignore the promotion of transformative growth.

Do You Have to Choose Growth or Development?

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

A number of posts/comments have been floating around the last few days that deal with the goals or the World Bank. Lant Pritchett published a piece that asks whether rich countries are in fact good partners for poor countries looking to develop. Pritchett is worried that rich-country development agencies (including the World Bank) have altered their focus from promoting overall economic development, and “defined development down” to be only about alleviating the conditions for the extremely poor – those earning less than $1 per day.

Pritchett suggests that the reason for this is a “post-materialist” attitude within rich countries. More crudely, you could say that this is another example of rich countries attempting to impose their goals/values/hopes onto developing countries. We in rich countries in general – and most likely highly paid development agency workers specifically – have the luxury of saying that material economic growth is not that important. Pritchett argues that this is to ignore the goals/values/hopes of actual people in those developing countries, who very much would like some material economic growth, please.

I’m very much on Pritchett’s side on this, with a caveat I’ll get to later in the post. I wrote a post back when I started this blog on defining development economics. I contrasted “development economics” with the “economics of poverty”. Development economics, to me, is the study of what allows countries to shift from poor, agricultural, rural economies to rich, industrial, urban economies. It is “development economics” in a classic sense, but today you’d probably call it “growth economics” or “macroeconomic development”.

The economics of poverty is about the constraints facing poor people in un-developed economies, how they cope with those constraints organically, and what kind of interventions will alleviate these constraints. The problem is that what I call the economics of poverty is what everyone else calls “development economics” – field studies and surveys in poor countries, running randomized control trials of interventions, and the like.

Pritchett is arguing, in my mind, for the World Bank to return to thinking about growth economics, or about development in the classic sense. Looking for projects like ports, roads, energy generation, and the like. Scale-intensive activities that need someone to coordinate the investment, and investments that will not take place organically because they are essentially public goods. Things that might allow or push economies into sustained growth.

Pritchett’s article generated a response in defense of the World Bank’s focus on poverty alleviation. The main example I know of is here, by Emre Ozaltin. He argues that Pritchett has a “growth fetish”, and that we have evidence that this does not lead to development. That’s debatable, but Ozaltin is correct that this is not an either/or decision. One does not have forgo poverty alleviation to focus on growth, or vice versa.

But Ozaltin also overstates the case for focusing on poverty alleviation. He says, “The sum of the activities in which we are engaged are not incidental to the challenge of development. They are development. For example targeting, investing in health and education, and doing so in multisectoral and coordinated ways, are all critical to growth.”

No, they are not. We have no convincing evidence that improving on those dimensions leads to growth. Yes, we have hundreds of well-designed studies showing how specific interventions improve health or education outcomes, but that does not mean they lead to economic growth. Acting to alleviate poverty is a noble, useful, moral activity. But you do not get sustained growth as a freebie on top of it. What Pritchett is arguing (I think. I’m putting words in his mouth here.) is that the Bank has presumed that their poverty alleviation efforts will generate growth as a byproduct. They haven’t, and most likely won’t. Growth is a distinct dimension of development different from poverty alleviation.

Now, here is my caveat to supporting Pritchett’s position. Who cares if it is specifically the World Bank that provides that infrastructure investment supporting economic growth? If the aims and goals of the World Bank have changed to poverty alleviation, fine. Let that be their focus, and the business of promoting growth can be left in the hands of other entities.

This has essentially already happened, and it isn’t clear why one should try to stop it. Tim Taylor had a nice post on the World Bank. In it, he links to research showing that the World Bank is rapidly running out of countries that qualify for its help. Further, official development assistance (ODA) is being dwarfed by foreign direct investment, remittances, and sovereign bonds as a source of investment funds for developing countries. Development banks such as the Inter-American Development Bank, the African Development Bank, the Asian Development Bank, and the new bank proposed by China are all in the business of lending for large infrastructure projects. Let them.

I think Pritchett is wasting his time here, trying to turn the World Bank to a new (actually, old) heading. The Bank is a gargantuan organization, and has reached the point where self-perpetuation is as important as the actual mission. This isn’t to trash the World Bank, it’s no worse than any other large organization on this front. But if the nature of the interventions that the Bank wants to undertake has changed, so be it. Argue instead for increased funding to the existing development banks. Argue for the US to drop its opposition to the Chinese-led development bank. It may be useful or best to separate the poverty alleviation and growth-promotion, anyway. But you need both. Poverty alleviation alone is not a robust path to long-run sustained economic development.