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.