Physicists have a reputation for being a bunch of stickybeaks—they will jump into unrelated fields and tell everyone that they are doing it wrong. This reputation is so well deserved that there is even a relevant XKCD. Sometimes, though, it all works out—usually because the physicists stick to their area of expertise, which just happens to be relevant to the problem.

In this case, we are talking about economics. It just so happens that the economy falls into the category of a complex system, which various physicists spend a lot of time playing with.

The paper in question seems to bring together a number of slowly developing concepts in economics. Taken together, and adding a touch of dynamical modeling, their merger leads to better forecasts for gross domestic product (GDP)—and I expect that other economic indicators can be attacked by a similar procedure.

Complexity is complex

Now, before you go “well, duh, of course the economy is complex,” the word complex has a specific meaning in this case. Complex systems are not necessarily all that complex: for instance, certain water wheels are complex.

Perhaps it is easier to think about it like this. Imagine that you are on mountainous terrain. Your movement through the terrain depends on your current direction of motion, the slope of the terrain, and your current position. If I could look down on this from above, I could measure these and predict your route through the terrain.

If everything was linear and not complex, then if I am inaccurate in my measurement, it won’t matter too much. My predictions will never be exactly correct, but they'll be close enough that I will find you. In a complex system, a small initial error will amplify, and pretty soon, I will be looking for you on a hilltop while you are trudging through a stream two valleys over. There are a whole bunch of techniques that have been developed to allow us to extract some modicum of predictability from these sorts of systems.

Applying physics to economics

The economy is a bit different from many physical models, though: there is no complete model of an economy. There isn’t even a good approximate model. Indeed, simple models that provide insight do not offer predictions. Instead, predictive models are statistical in nature. These make use of historical economic data to predict future economic data—essentially, the model looks for correlations between historical and recent data. These correlations are then used to take current economic data to predict future economic data. The model is then constructed from our understanding of how the measured data relates to economic activity.

The problem with this approach is that, if you don't have sufficient data, predictions quickly become inaccurate. To resolve this problem, we collect more information. That information allows new processes to be included in the model with the hope that this will yield increased accuracy over longer time intervals. And this certainly works: current models are better than older models.

To improve on predictive models about the economy, researchers took a counterintuitive approach. They reduced the number of parameters in their model to just two: economic fitness and gross domestic product, the idea being that if the economic fitness and GDP are measured at a given time, then the change in GDP can be predicted.

So what is the economic fitness? It is, in short, a measure of the complexity of a country’s exports. The idea is that exports represent the products from a country that are competitive with like products from the rest of the world. The larger the variety of exported products, the fitter an economy is. One advantage of it as a measure is that exports and imports are very carefully measured, because companies rely on that data to survive. And that data is collected and reported in a relatively standardized way. The researchers basically created a matrix that allows the variety of exports to be summed.

This number is then iteratively normalized with data from all other countries to come up with a self-consistent scale of economic fitness. Economic fitness drives changes in economic growth, which is accounted for in GDP.

Now, it is important to realize that no one really has a model (in the physical sense) of the link between economic fitness and GDP. But we do have statistical data that can be used to infer how the two are linked. We can estimate from the averages in the dataset how high the economic fitness of an economy has to be to support a given GDP and use that to determine if the GDP will increase or decrease.

The speed of the increase or decrease is estimated using a kind of force-response model. In other words, if the GDP is far away from that expected from the current economic fitness, there is a strong hidden economic drive to change the GDP. Hence, we can expect rapid economic growth (or contraction).

Predicting the past

This case is exemplified by China in 1995. China at that time had a low GDP but high economic fitness. As predicted by the model, China experienced 20 years of steep economic growth, with its GDP increasing remarkably. In a standard economic analysis, this seems extraordinary. But, the researchers argue that this is actually expected behavior: much like a stretched spring being released to jump back to its position.

The model also allows economic momentum to play a role. The speed at which economic fitness is changing also influences the change in GDP. The researchers found that using the trajectory of economic fitness to predict GDP leads to even more accurate results.

The researchers tested their model on historical data from 169 countries over three different five-year windows. They compared their GDP predictions with those produced by the international monetary fund (IMF) model and with the actual GDP data.

They found that their model was better than the IMF model, especially when they also took into account the trajectory of the economic fitness. Furthermore, a close analysis of how the IMF model and their dynamical model predictions differed showed that the sources of inaccuracy were different. That meant that combining the two models led to predictions that were even more accurate.

Another important factor is that there is a kind of self-similar behavior in trajectories. Even though the total size of the economy might be different, countries with similar ratios (I’m simplifying here) of economic fitness to GDP experienced similar trajectories. And a final point: the model also shows where predictability fails. Countries with a very low economic fitness are incredibly difficult to predict. This is true of both the IMF model and their model, but it highlights that the poorer you are, the more subject you are to the random buffeting of economic noise.

I would put a pithy little conclusion here, but I am not an economist, nor am I into economic forecasting. The model looks interesting, but I have no idea if it will be used or not. I don’t even know if GDP is the right thing to measure. But at least there is another tool available.

Nature Physics, 2018, DOI: 10.1038/s41567-018-0204-y