# 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.

## 10 thoughts on “Growth Effects, Level Effects, and Transitional Growth”

1. That’s a great analogy, and I’m totally using it (via link to this post) in my intermediate macro unit on growth theory this fall! And I’ve seen the “don’t pass the sherriff” effect in person. Literally, the minute a car passed him, he pulled it over. Doubly cool!

2. So, who is the sheriff?

The earlier crises of productivity growth were resolved by violence and political advocacy. In England, if I remember correctly, the king stepped in to slap down the aristocracy by threatening to pack the House of Lords. In the US, there was a violent labor movement, and it took the impetus of World Wars I & II to get the necessary political changes.

• You and “am” both asked this. The sheriff is, in terms of growth theory, some kind of constraint on how fast you can innovate at the frontier. We take this as some kind of cosmic given, where the ability to innovate is limited by researchers duplicating efforts and the difficulty of advancing on current knowledge. The sheriff is not maliciously driving at 55, and nor is he free to just accelerate if we pick the right policies.

That being said, the reason we think the sheriff is the limit is simply because, empirically, we’ve never seen anyone pass the sheriff. Maybe he doesn’t care, and there are policies that cars could pursue that would let them accelerate permanently past the sheriff. But to date we haven’t seen it happen.

3. I must say, this is an excellent metaphor, especially as it comes full circle at the end.

It’s also interesting to think perhaps that earlier on in the highway, you could have reckless drivers and perhaps dangerous sounds, making it difficult for well intentioned cars to get there faster.

4. Yes but the Inequality grows .. why ??
Yes true !! … its normal .. but this is becouse in weak countries we do not shocks some well identified factors very important in these economies . This must be strictly coordinated with a more powerful international economic legislation and governance . These are the steps to follow :
a) we need to give spending and /or saving power to lower middle and lower up class through houshold basic cost reductions (taxes, energy, health, education etc.)
b) break the monopoly in the market for energy, insurance, banking and trade unions from one side and cut waste, inefficiency and corruption in government, Public Administration and political parties from the other side .

To go back to competitive development we dont need incentives in various sectors of industry .. we need to make in these lowe economies Public Administratione and Business work in a transparent, efficient , meritocratic and competitive way through a strict respect of law . The money for incentives should be used to lower taxes.
To give substance to these measures individual countries are no longer able to act alone as the financial variables are all interconnected in the world. As we said before it is useless a program of investment if simultaneously across countries (no exceptions) are not taken concerted maneuvers with international organizations (UN, World Bank, IMF, etc … )to REGULATE international finance and STOP Tax evasion, CLOSE Tax Havens ( all tax Havens .. ) and ensuring TRASPARENCY and MERITOCRACY.
We need to work on this two-pronged strategy otherwise the EU and others governments attempts will only attempts and weak countries will slip more and more below

5. Nice Article!