# 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.

# The Glacial Speed of Institutional Change

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

I just finished reading “The Long Process of Development” by Jerry Hough and Robin Grier. The quick response is that you should read this book. If that’s enough, then go get it. All the rest of this post is just some of my reactions to the book.

The basic idea of HG is to trace out how long it took England and Spain (and by extension, their colonies Mexico and the U.S.) to evolve the elements of “good institutions” that we think promote economic growth. Clearly the process went faster in some of these places than others, but the point is that it took centuries regardless of who we are talking about.

HG look at the development of an effective state in England through history. For them, England gets a minimally effective state with Henry VII in 1485. His victory in the War of the Roses (and in particular his ruthless elimination of others with claims to the throne) gave him a government that had at least some control over the entire area of England and Wales. So is that when England has good institutions? No, not really. From that point, it is another two hundred and four years until the Glorious Revolution and what we might call the beginnings of constitutional monarchy. All good? Not quite. It is another one hundred and forty three years before the Reform Act of 1832 generates the barest seeds of what might be called inclusive institutions. Even if you think that England in 1832 had “good institutions” for economic development, that was three hundred and forty-seven years after England got a functioning central government. If we lower our sights and say that the Glorious Revolution had given England the “good institutions” necessary for economic development, then that was still two hundred years after England got a functioning central government.

The second major example used by HG is Spain. By 1504, Isabella had acquired a kingdom that essentially looks like modern Spain in geographic reach. She was the monarch of Castile, the Moors had been forced out of Granada, and she had brought Aragon into the kingdom by marrying Ferdinand. HG then document that despite this geographic reach, the government of Spain was not an effective central government in the way that Henry VII or VIII had over England. Even Philip II’s reign in the late 1500’s did not consolidate government in a way that seems consistent with his numerous foreign military activities. HG argue that Spain was about 200 years behind England, and only reached an effective central government around 1700. It would be arguably another 280 years after that before Spain got what we would call “good institutions”.

Regardless of the exact historical case study, HG’s point is that developing modern institutions the support sustained economic growth takes centuries, even in one case – England – where all the breaks kept going their way.

What is the point of this regarding development and growth? HG suggest that a large number of developing countries have a central government with the capabilities roughly equal to those of Henry VII. Many of them began as separately defined states only in the 1960’s, and in the subsequent fifty years have perhaps gained the ability to extend their powers of taxation and coercion to all corners of their geographic area. In places like Afghanistan, they cannot even do that.

Asking, expecting, or advising these countries to adopt “good institutions” is to ask them to skip between two and five centuries of institutional evolution in one leap. Developing countries evolving their own stable institutional structures that support economic growth is going to be long, ugly, and likely violent – just like it was in every single currently rich country. HG’s work says that institutions are not just another technology. While you can play catch-up relatively easily with technology (e.g. adopting mobile phones without landline networks), you cannot do the same with institutions.

Further, institutional development is always going to involve some coercion. Some group is going to have to be dragged kicking and screaming into the new institutional arrangement. HG clearly reject the idea that new social contracts will spontaneously get re-negotiated as circumstances change, as in the old North and Weingast interpretation of the Glorious Revolution in England. In contrast they accept the more Mancur Olson-ian view, that social contracts are whatever the dude with the gun says they are. The only way to accelerate the development process is to accelerate the concentration of coercive power with one group/party/coalition. From that perspective, the problem with the U.S. attempts at state building in Afghanistan and Iraq was not that they intervened, but that this intervention was half-assed and ended before the job was done. If you are going to intervene, pick a winner and then make sure they win. Trying to equalize power across different factions is precisely the wrong thing you should do to encourage institutional development. That is me spinning the argument out to a logical extreme, but it makes the point.

A last mild critique of HG is that it has a fault similar to most other work on institutions. It does not define what a “good institutions” are. We know that England and the U.S. have them now, and that Spain seems to have them at least since after Franco. We know that England had “good” institutions in or around the 1800’s, and Spain apparently didn’t. And we know that England and Spain had “bad” institutions before the 1500’s. So it must be that institutional evolution takes somewhere between three and five centuries? But what precisely is it that England and Spain have today that they didn’t in 1500? What is a good institution?

HG are more clear than many on this point. They consciously limit themselves to examining whether a central government has effective control of taxation and violence within its borders. But of course, what does effective control mean? What does taxation mean – what’s the difference between a tribute, a donation, expropriation, and a tax? Does control of violence simply mean that all the people coercing others wear the same uniform?

This critique doesn’t eliminate the value of reading the book. The general point about the long time lags in the evolution of institutions (good or bad) is excellent. It is hard to fight time compression when reading history, and HG make clear that the institutions literature needs to get far more serious about that fight.