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.

Has the Long-run Growth Rate Changed?

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

My actual job bothered to intrude on my life over the last week, so I’ve got a bit of material stored up for the blog. Today, I’m going to hit on a definitional issue that creates lots of problems in talking about growth. I see it all the time in my undergraduate course, and it is my fault for not being clearer.

If I ask you “Has the long-run growth rate of the U.S. declined?”, the answer depends crucially on what I mean by “long-run growth rate”. I think of there as being two distinct definitions.

• The measured growth rate of GDP over a long period of time: The measured long-run growth rate of GDP from 1985 to 2015 is ${(\ln{Y}_{2015} - \ln{Y}_{1985})/30}$. Note that here the measurement does not have to take place using only past data. We could calculate the expected measured growth rate of GDP from 2015 to 2035 as ${(\ln{Y}_{2035} - \ln{Y}_{2015})/20}$. Measured growth rate depends on the actual path (or expected actual path) of GDP.
• The underlying trend growth of potential GDP: This is the sum of the trend growth rate of potential output per worker (we typically call this ${g}$) and the trend growth rate of the number of workers (which we’ll call ${n}$).

The two ways of thinking about long-run growth inform each other. If I want to calculate the measured growth rate of GDP from 2015 to 2035, then I need some way to guess what GDP in 2035 will be, and this probably depends on my estimate of the underlying trend growth rate.

On the other hand, while there are theoretical avenues to deciding on the underlying trend growth rate (through ${g}$, ${n}$, or both), we often look back at the measured growth rate over long periods of time to help us figure trend growth (particularly for ${g}$).

Despite that, telling me that one of the definitions of the long-run growth rate has fallen does not necessarily inform me about the other. Let’s take the work of Robert Gordon as an example. It is about the underlying trend growth rate. Gordon argues that ${n}$ is going to fall in the next few decades as the US economy ages and hence the growth in number of workers will slow. He also argues that ${g}$ will fall due to us running out of useful things to innovate on. (I find the argument regarding ${n}$ strong and the argument regarding ${g}$ completely unpersuasive. But read the paper, your mileage may vary.)

Now, is Gordon right? Data on the measured long-run growth rate of GDP does not tell me. It is entirely possible that relatively slow measured growth from around 2000 to 2015 reflects some kind of extended cyclical downturn but that ${g}$ and ${n}$ remain just where they were in the 1990s. I’ve talked about this before, but statistically speaking it will be decades before we can even hope to fail to reject Gordon’s hypothesis using measured long-run growth rates.

This brings me back to some current research that I posted about recently. Juan Antolin-Diaz, Thomas Drechsel, and Ivan Petrella have a recent paper that finds “a significant decline in long-run output growth in the United States”. [My interpretation of their results was not quite right in that post. The authors e-mailed with me and cleared things up. Let’s see if I can get things straight here.] Their paper is about the measured growth rate of long-run GDP. They don’t do anything as crude as I suggested above, but after controlling for the common factors in other economic data series with GDP (etc.. etc..) they find that the long-run measured growth rate of GDP has declined over time from 2000 to 2014. Around 2011 they find that the long-run measured growth rate is so low that they can reject that this is just a statistical anomaly driven by business cycle effects.

What does this mean? It means that growth has been particularly low so far in the 21st century. So, yes, the “long-run measured growth rate of GDP has declined” in the U.S., according to the available evidence.

The fact that Antolin-Diaz, Drechsel, and Petrella find a lower measured growth rate similar to the CBO’s projected growth rate of GDP over the next decade does not tell us that ${g}$ or ${n}$ (or both) are lower. It tells us that it is possible to reverse engineer the CBO’s assumptions about ${g}$ and ${n}$ using existing data.

But this does not necessarily mean that the underlying trend growth rate of GDP has actually changed. If you want to establish that ${g}$ or ${n}$ changed, then there is no retrospective GDP data that can prove your point. Fundamentally, predictions about ${g}$ and ${n}$ are guesses. Perhaps educated guesses, but guesses.

Significant Changes in GDP Growth

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

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

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

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

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

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

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

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

Is the U.S. Really Below Potential GDP?

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

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

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

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

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

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

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

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

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

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

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

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

You’ve Got Potential

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

A couple things I read this week, along with a frustrating parking-lot conversation with someone who asked me about the economy, got me thinking about how we talk about GDP. I think we can and should be a little more clear in economics about what we mean by “Potential GDP”. Obviously this term comes up a lot in discussions about the current state of most economies, as a lot of the policy discussion depends on how far (if at all) GDP is “below potential”.

There is a difference between “potential GDP” and what I guess we could call “potential potential GDP”. It may be easiest to start with an analogy to get these terms straight. Think of your health. Your regular level of health is your “potential health” – how you feel and how capable you are when you are not explicitly sick. Getting the flu would be like a recession, as you are clearly “below potential health”.

“Potential potential health” is different from your “potential health”. “Potential potential health” is your health if you starting working out regularly, stopped eating so many Christmas cookies, skipped that second beer, took the stairs, actually got up from your desk once in a while, did the stretches your therapist suggested, meditated daily, ate more vegetables and less bacon, etc. etc. “Potential potential health” is the best health you could possibly achieve given your genetics. “Potential health” is your non-sick state of health.

In terms of GDP, what do we have?

• Potential GDP: This is our non-recessionary level of GDP. We spend most of our time in this state, but it is not the best we can do. It is simply the typical level of GDP we have been achieving lately.
• Potential Potential GDP: This is the best possible level of GDP we could get given our current level of technology (which I would equate with your genetics). It is the GDP we could have if we eliminated market inefficiencies like information issues, and collusion, and regulatory capture, and rent-seeking, and externalities, etc. etc. Take all the Harberger triangles you can find and eliminate them, so to speak.

Why do I think we should distinguish these concepts? Because “potential GDP” gets confused very often with “potential potential GDP”. It is literally impossible to get GDP higher than “potential potential GDP”, and thus it is impossible to sustain a GDP higher than “potential potential GDP” for any period of time. “Potential potential GDP” is the budget constraint for the economy. We cannot possibly produce more than this.

But that is not true about “potential GDP”. It is *not* the short-run, medium-run, or long-run budget constraint for the economy. It is not something structurally fixed. But people treat it as such. They presume that any aberrations away from “potential GDP” must be offset over the long-run by equal and opposite aberrations. Booms (GDP above “potential GDP”) *must* be met by slumps (GDP below “potential GDP”). Similarly, slumps must eventually erase themselves. None of that is true, as “potential GDP” is not the budget constraint for the economy.

This matters for how one thinks about business cycles. We cannot uniquely decompose actual GDP into “potential GDP” and deviations from potential – in other words, into trend and cycle. Doing so presumes that the cyclical components “cancel out” over time. Econometrically, the methods used to separate trend and cycle *require* that the cycles cancel out around the trends. Roger Farmer’s recent post makes this point more clearly than I just did. As he says, by accepting the trend/cycle decomposition of GDP – i.e. by assuming that “potential GDP” is the budget constraint – business cycle economists have implicitly limited themselves to a small class of explanations for fluctuations.

Once you stop thinking of “potential GDP” as being necessarily a supply-side phenomenon, then failures of aggregate demand, or “animal spirits”, or self-fulfilling expectations can move around “potential GDP” as well. This is Farmer’s point about the economy having essentially an infinity of equilibrium GDP levels. We can get stuck at a new, lower level of GDP. There is nothing that necessitates that the economy move “back to potential”, as “potential GDP” is a fluid concept. There is also nothing necessary about recessions as some kind of economic retribution for booms. Stop. “Potential GDP” doesn’t work that way. If we can coordinate on a higher level of GDP, then great. We win – more cookies and Diet Coke for me. That isn’t some kind of cheat. It’s not “living beyond our means”. It’s just us finding a way to shift a little closer to the *real* limit, “potential potential GDP”.

The Limited Effect of Reforms on Growth

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I said in my last post that transitional growth is slow, and therefore changing potential GDP – as many of the recent Cato Growth proposals would do – could not add much to the growth rate of GDP in the near term.

There were several questions that came up in the comments, so let me try to be more clear about distinguishing between influences of trend growth and short-run shocks. Output in period ${t+1}$ is

$\displaystyle y_{t+1} = (1+g)y_t + (1+g)\lambda (y^{\ast}_t - y_t) \ \ \ \ \ (1)$

where the first term on the right is the normal trend growth rate, and the second term is the additional transitional growth that occurs because the economy is not at potential GDP, ${y^{\ast}_t}$.

We need to distinguish between changes in potential GDP and changes in current GDP. Let’s take the above equation, plug in ${\lambda=0.02}$, and then use it to iterate forward from period 0 (today) until some arbitrary period ${t}$. You get

$\displaystyle y_t = (1+g)^t \left[(1-0.98^t)y^{\ast}_0 + 0.98^t y_0 \right]. \ \ \ \ \ (2)$

In period ${t}$, GDP will have grown by a factor of ${(1+g)^t}$ due to trend growth in GDP. The term in the brackets shows the cumulative effect of having ${y_0 \neq y^{\ast}_0}$ in the initial period. The 0.98 terms are just ${1-.02}$, and capture the changing role of this transitional growth over time. Note that as ${t}$ goes up, ${0.98^t}$ goes to zero and the effect of initial GDP ${y_0}$ falls to nothing. As ${t}$ gets big, the economy reaches potential GDP.

Now let’s assume that period 0 is 2014. Potential GDP is 17 trillion and actual GDP is 16 trillion, and the trend growth rate is 2%. Let’s consider two alternative policies to enact today that take effect in 2015.

• Policy A: a short run spending surge sufficient to make GDP in 2015 equal to potential GDP. Policy A immediately eliminates the gap between actual and potential GDP, but has no other long term effect.
• Policy B: raises potential GDP by 1 trillion dollars, but adds no immediate spending to GDP. The effect on potential GDP is permanent.

For Policy A, GDP in 2015 (period 1) is

$\displaystyle y_1 = (1.02)^1\left[(1-0.98)\times 17 + 0.98 \times 17 \right] = 17.34. \ \ \ \ \ (3)$

The growth rate of GDP from 2014 to 2015 is ${(17.34 - 16)/16 = 0.084}$ or about 8.4%. That’s a massive GDP growth rate for a developed economy like the US. But it is a one-time shock to the growth rate. From 2015 to 2016, and from 2016-2017, and every year thereafter, the growth rate will be exactly 2% because the economy is precisely back on trend. Policy A gives a one-year gigantic boost to the growth rate.

What about Policy B? GDP in 2015 here is

$\displaystyle y_1 = (1.02)^1\left[(1-0.98)\times 18 + 0.98 \times 16 \right] = 16.36. \ \ \ \ \ (4)$

This is nearly 1 trillion less than Policy A. The growth rate of GDP from 2014 to 2015 is ${(16.36 - 16)/16 = 0.023}$. As the prior post noted, reforms that raise potential GDP don’t have big effects on growth rates. But while the effect on growth is small, it is persistent. From 2015-2016, the growth rate of GDP will be roughly…0.023. It’s actually minutely smaller than from 2014-2015, but rounding makes them look the same. It will take a few years before the growth rate declines appreciably. Fifty years from now the growth rate will still be almost 0.021. Changing potential GDP, like with Policy B, is like turning an oil tanker with a tug boat. It doesn’t go fast, but it goes on for a long time.

So is Policy B worse than Policy A? It depends entirely on your time preferences. In 2015 GDP under Policy A is nearly 1 trillion dollars higher than with policy B. But 100 years from now, GDP will be nearly 1 trillion dollars higher with Policy B. We can actually figure out how soon it will be before Policy B passes Policy A. Set

$\displaystyle (1.02)^t \left[(1-0.98^t)17 + 0.98^t 17 \right] = (1.02)^t \left[(1-0.98^t)18 + 0.98^t 16 \right] \ \ \ \ \ (5)$

and solve for ${t}$. This turns out to be roughly 34 years from now, in 2048. It takes a long, long, time for changes in potential GDP to really pay off. If you want to increase the level of GDP in the near term, and hence raise near-term growth rates by implication, then you have to, you know, boost GDP. GDP is a measure of current spending, so raising GDP means raising current spending. There isn’t a trick to get around this.

Now, could I be underselling Policy B as a near-term boost to growth rates and GDP? Let’s consider a few possibilities:

• I’m underestimating the size of ${\lambda}$. As I mentioned last time, there is lots of empirical evidence that this is pretty small. But okay, let’s make ${\lambda = 0.05}$, more than double my 0.02 value. Now in 2015 policy B yields GDP of 16.4 trillion and a growth rate of 2.6%. Yes, it helps policy B, but doesn’t get it anywhere close to Policy A. It is still 14 years before GDP under Policy B is larger than under Policy A.
• I’m underestimating the boost to potential GDP that Policy B can deliver. So let’s ask, given ${\lambda = 0.05}$, how much would ${y^{\ast}_0}$ have to go up to match the 8.4% growth rate of Policy A? Potential GDP would have to jump to roughly 36 trillion, meaning it has to roughly **double** in size thanks to the policy. I think it is totally fair to say that this is implausible in a country like the US.
• But China was able to do it. Right, when China opened up, made reforms, etc.., it was able to raise its potential GDP by a large amount. You could probably plausibly argue that it raised potential GDP by a factor of something like 8-10. But the rapid growth in China over the last 30 years is not some victory lap for good state-led policy reforms, it’s a testament to just how screwed up Maoism was as an economic system. [Egad! An institutions explanation!]
• What if Policy B raised the trend growth rate, ${g}$? If it changed ${g}$ appreciably, then Policy B would be something really special. Let’s review for a moment a few of the changes that did not change the long-run growth rate in the US: the introduction of electricity, the income tax, the Great Depression, the New Deal, Medicare, higher tax rates, the Cold War, the oil crisis, lower tax rates, de-regulation, the IT revolution, and New Coke. There have been shifts in the level of potential GDP, such as the IT revolution shifting up potential GDP and inducing a period of relatively rapid transitional growth in the 1990’s. But it’s hard – if not impossible if you take Chad Jones‘ semi-endogenous growth idea seriously – to fundamentally alter ${g}$. It is dictated by changes in the scale of the global economy, not by policy effects within the US.

I’m all for policy reforms that raise potential GDP, and several of those proposed in the Cato forum would probably do that. We might want to undertake several of them at once to counteract the drags on potential GDP that Robert Gordon has outlined.

But we can’t be fooled into thinking that any of them would make a really appreciable difference to economic growth today. You can revolutionize education, or corporate taxation, or urban planning, or immigration all you want, but the gains those changes induce will take decades to manifest themselves.

The Slowdown in Reallocation in the U.S.

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One of the components of productivity growth is reallocation. From one perspective, we can think about the reallocation of homogenous factors (labor, capital) from low-productivity firms to high-productivity firms, which includes low-productivity firms going out of business, and new firms getting started. A different perspective is to look more closely at the shuffling of heterogenous workers between (relatively) homogenous firms, with the idea being that workers may be more productive in one particular environment than in another (i.e. we want people good at doctoring to be doctors, not lawyers). Regardless of how exactly we think about reallocation, the more rapidly that we can shuffle factors into more productive uses, the better for aggregate productivity, and the higher will be GDP. However, evidence suggests that both types of reallocation have slowed down recently.

Foster, Grim, and Haltiwanger have a recent NBER working paper on the “cleansing effect of recessions”. This is the idea that in recessions, businesses fail. But it’s the really crappy, low-productivity businesses that fail, so we come out of the recession with higher productivity. The authors document that in recessions prior to the Great Recession, downturns tend to be “cleansing”. Job destruction rates rise appreciably, but job creation rates remain about the same. Unemployment occurs because it takes some time for those people whose jobs were destroyed to find newly created jobs. But the reallocation implied by this churn enhances productivity – workers are leaving low productivity jobs (generally) and then getting high productivity jobs (generally).

But the Great Recession was different. In the GR, job destruction rose by a little, but much less than in prior recessions. Job creation in the GR fell demonstrably, much more than in prior recessions. So again, we have unemployment as the people who have jobs destroyed are not able to pick up newly created jobs. But because of the pattern to job creation and destruction, there is little of the positive reallocation going on. People are not losing low productivity jobs, becoming unemployed, and then getting high productivity jobs. People are staying in low productivity jobs, and new high productivity jobs are not being created. So the GR is not “cleansing”. It is, in some ways, “sullying”. The GR is pinning people into *low* productivity jobs.

This holds for firm-level reallocation well. In recessions prior to the GR, low productivity firms tended to exit, and high productivity firms tended to grow in size. So again, we had productivity-enhancing recessions. But again, the GR is different. In the GR, the rate of firm exit for low productivity firms did not go up, and the growth rate of high-productivity firms did not rise. The GR is not “cleansing” on this metric either.

Why is the GR so different? The authors don’t offer an explanation, as their paper is just about documenting these changes. Perhaps the key is that a financial crash has distinctly different effects than a normal recession. A lack of financing means that new firms cannot start, and job creation falls, leading to lower reallocation effects. A “normal” recession doesn’t involve as sharp a contraction in financing, so new firms can take advantage of others going out of business to get themselves going. Just an idea, I have no evidence to back that up.

[An aside: For the record, there is no reason that we need to have a recession for this kind of reallocation to occur. Why don’t these crappy, low-productivity firms go out of business when unemployment is low? Why doesn’t the market identify these crappy firms and compete them out of business? So don’t take Foster, Grim, and Haltiwanger’s work as some kind of evidence that we “need” recessions. What we “need” is an efficient way to reallocate factors to high productivity firms without having to make those factors idle (i.e. unemployed) for extended periods of time in between.]

In a related piece of work Davis and Haltiwanger have a new NBER working paper that discusses changes in workers reallocations over the last few decades. They look at the rate at which workers turn over between jobs, and find that in general this rate has declined since 1980 to today. Some of this may be structural, in the sense that as the age structure and education breakdown of the workforce changes, there will be changes in reallocation rates. In general, reallocation rates go down as people age. 19-24 year olds cycle between jobs way faster than 55-65 year olds. Reallocation rates are also higher among high-school graduates than among college graduates. So as the workforce has aged and gotten more educated from 1980 to today, we’d expect some decline in job reallocation rates.

But what Davis and Haltiwanger find is that even after you account for these forces, reallocation rates for workers are declining. No matter which sub-group you look at (e.g. 25-40 year old women with college degrees) you find that reallocation rates are falling over time. So workers are flipping between jobs *less* today than they did in the early 1980s. Which is probably somewhat surprising, as my guess is that most people feel like jobs are more fleeting in duration these days, due to declines in unionization, etc.. etc..

The worry that Davis and Haltiwanger raise is that lower rates of reallocation lower productivity growth, as mentioned at the beginning of this post. So what has caused this decline in reallocation rates across jobs (or across firms as the first paper described)? From a pure accounting perspective, Davis and Haltiwanger gives us several explanations. First, reallocation rates within the Retail sector have declined, and since Retail started out with one of the highest rates of reallocation, this drags down the average for the economy. Second, more workers tend to be with older firms, which have less turnover than young firms. Last, the above-mentioned shift towards an older workforce that tends to shift jobs less than younger workers.

Fine, but what is the underlying explanation? Davis and Haltiwanger offer several possibilities. One is increased occupational licensing. In the 1950s, only about 5 % of workers needed a government (state or federal) license to do their job. In 2008, that is now 29%. So it can be incredibly hard to reallocate to a new job or sector of work if you have to fulfill some kind of licensing requirement (which could involve up to 2000 hours of training along with fees). Second is a decreased ability of firms to fire-at-will. Starting in the 1980s there were a series of court decisions that made it harder for firms to just fire someone, which makes it both less likely for people to leave jobs, and less likely for firms to hire new people. Both act to lower reallocation between jobs. Third is employer-provided health insurance, which generates some kind of “job lock” where people are unwilling to move jobs because they don’t want to lose, or create a gap in, coverage.

Last is the information revolution which may have had perverse effects on reallocation. We might expect that IT allows more efficient reallocation as people can look for jobs more easily (e.g. Monster.com, LinkedIn) and firms can cast a wider net for applicants. But IT also allows firms to screen much more effectively, as they have access to credit reports, criminal records, and the like, that would have been prohibitive to acquire in the past.

So we appear to have, on two fronts, declining dynamic reallocation in the U.S. This certainly contributes to a slowdown in productivity growth, and may perhaps be a better explanation than “running out of ideas from the IT revolution” that Gordon and Fernald talk about. The big worry is that, if it is regulation-creep, as Davis and Haltiwanger suspect, we don’t know if or when the slowdown in reallocation would end.

In summary, reading John Haltiwanger papers can make you have a bad day.

Re-basing GDP and Estimating Growth Rates

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

Leandro Prado de la Escosura recently posted a voxeu column about splicing real GDP series after re-basing. Re-basing of real GDP means adopting a new set of reference prices to value output in each year. Think of what Nigeria did last year, when they re-based from 1990 prices to using 2010 prices, and all of the sudden measured real GDP was about twice as big.

de la Escosura’s point is that when we re-base and “retrocast” real GDP numbers to past years, we may obscure evidence of rapid economic growth. You should go read his post, and his associated paper, to understand his point in full. But let’s use the Nigerian 2013 re-basing to get the basic idea. Let’s say that in 1990 Nigeria produced 1000 units of food, and zero motorcycles. In 2010 Nigeria produced 1000 units of food again, but produced 200 motorcycles. So there clearly is real growth in output.

In 1990, the price of food was 1 naira per unit and motorcycles were 500 naira. 1990 real GDP in 1990 prices is 1000(1) + 0(500) = 1000. 2010 real GDP in 1990 prices is 1000(1) + 200(500) = 101,000. This is a dramatic growth rate of real GDP (10,100% actually).

After re-basing, what do we get? In 2010 the price of food was 2 naira per unit, and motorcycles were 100 naira each. So 1990 real GDP in 2010 prices is 1000(2) + 0(100) = 2000. 2010 real GDP in 2010 prices is 1000(2) + 200(100) = 22,000. Still a lot of growth, but only 1100%. The growth rate of real GDP between 1990 and 2010 went from over 10,000% to about 1100%, an order of magnitude drop. Growth looks much slower in Nigeria after re-basing.

Why? Because with dramatic economic growth came dramatic changes in relative prices. Motorcycles dropped severely in price, while food went up slightly. Combined, this makes food look more valuable compared to motorcycles by 2010. So valuing 1990 output in 2010 prices tends to make 1990 look pretty good, because in 1990 they had lots of food relative to motorcycles.

de la Escosura’s argument is that in 1990, for sure, the 1990 prices are the right way to value real GDP. Similarly, in 2010, for sure, the 2010 prices are the right way to value real GDP. So leave those years priced in their own prices. For the nineteen intervening years, 1991-2009 inclusive, compute their real GDP in both 1990 and 2010 prices. Then average those two estimates depending on how far from each year we are.

So for 1991, let real GDP be (1991 GDP at 1990 prices)(18/19) + (1991 GDP at 2010 prices)(1/19). For 1992, let real GDP be (1992 GDP at 1990 prices)(17/19) + (1992 GDP at 2010 prices)(2/19), and so forth. For de la Escosura, this better captures the growth in real GDP over time. For our example, 1990 real GDP in 1990 prices is 1000, and 2010 real GDP in 2010 prices is 22,000, and the growth rate is 2,200%. It essentially splits the difference of the two different benchmarks, preserving some of the rapid growth seen using the 1990 prices.

This isn’t necessarily a new concept. Johnson, Larson, Papageorgiou, and Subramanian discuss this issue in their paper on the Penn World Tables. Their suggestion for a chained PWT price index amounts to a similar suggestion.

The big point is that by re-basing you are necessarily screwing with the implied growth rate of real GDP because you are screwing with the value of real GDP in the first year (1990 in our example). If there has been a lot of economic growth and relative prices have changed, then almost certainly the first year will have a higher measured real GDP when we re-base. With a higher initial level of GDP, the growth rate will necessarily be smaller.

If your worry about computing growth rates, then this is an issue you have to worry about a lot, and something like de la Escosura’s method or the Johnson et al suggestion is what you should do. If you worry about comparing income levels across countries, then this critique is not crucial (although you have other things to worry about).

Innovation does not equal GDP Growth

I’m way behind on this (it came out August 8th), but Joel Mokyr posted an op-ed in the Wall Street Journal about being optimistic regarding growth. I liked this particular passage:

The responsibility of economic historians is to remind the world what things were like before 1800. Growth was imperceptibly slow, and the vast bulk of the population was so poor that a harvest failure would kill millions. Almost half the babies born died before reaching age 5, and those who made it to adulthood were often stunted, ill and illiterate.

I’d like to think that growth economists are also here to spread this message. It’s easy to be pessimistic about the near-term economic future when we are slogging our way slowly out of a terrible recession. But extrapolating from the current situation to say that long run sustained growth is over is taking it too far.

Mokyr (and us mere growth economists) are more optimistic about things. Why? [Because we’re tenured professors who can’t be fired. But that’s only part of it.] Because the ultimate source of economic growth over history has been technological innovation, and there is still an essentially infinite scope for this to continue. Mokyr lays out a long list of innovations that are coming down the pipeline: driverless cars, nanotechnologies, materials science, biofuels, etc. etc. We aren’t running out of ideas, and just because you or I can’t think of what they could possibly invent anymore doesn’t mean that other people aren’t busy inventing things.

But will these new innovations really provide a boost to GDP? Maybe not, but that’s a failure of GDP, not of innovation. Let’s give the mike to Mokyr:

Many new goods and services are expensive to design, but once they work, they can be copied at very low or zero cost. That means they tend to contribute little to measured output even if their impact on consumer welfare is very large. Economic assessment based on aggregates such as gross domestic product will become increasingly misleading, as innovation accelerates. Dealing with altogether new goods and services was not what these numbers were designed for, despite heroic efforts by Bureau of Labor Statistics statisticians.

We measure GDP because we can, and because it gives us a good indication of very short-run variations in economic activity. But it is only a measure of “currently produced goods and services”. That is, GDP measures the new products or services provided in a specific window of time (e.g. the 3rd quarter of 2014, or all of 2013). If all the effort in producing a new product comes in development, but it is then copied for free, this means that there is a one-time contribution to GDP in the year it was developed, and then nothing afterwards.

Things like refrigerators, Diet Coke, and cars contribute to GDP every period because we have to make new versions of them over and over again. But in one sense that is a bug, not a feature. Imagine if, having invented Diet Coke, you could make copies for free. That would lower GDP, as Coca-Cola would drop to essentially zero revenue from here forward. But it’s demonstrably better, right? Free Diet Coke? Where do I put in the IV line?

Diet Coke is a good example here. Let’s say that you could replicate the physical inputs of Diet Coke for free, but that Coca-Cola still owned the recipe, and you had to pay them to use it. This would still lower GDP, as Coca-Cola would no longer be earning anything from the physical production of Diet Coke, only from renting out the recipe each time you wanted a Diet Coke. This is still a win, even though GDP goes down. Lots of current innovations are like making Diet Coke for free, but owning the recipe. They are worthwhile despite the fact that they do not necessarily contribute much to GDP, and might even detract from it.