Fig 1.
Non-stationary sdynamics of economic systems in the fitness-income plane.
a: we report in the fitness-income plane the position of the countries in 1995. The red line indicates the expected level of income, given the level of fitness of a country, and it is the result of the minimization of the Euclidean distance of the countries from the line weighted by the country GDP. b: evolution in the fitness-income plane from 1995 to 2010. We observe a strongly heterogeneous dynamics of the countries in this plane. In order to point out emergent trends in this dynamics, we perform a coarse graining of the trajectories, as shown in panel c. A laminar-like regime is observed. With respect to the evolution of the countries with intermediate/large fitness, this regime is characterized by a regular flow and an income lower than what expected from the average red line (top left corner).
Fig 2.
The four regimes of the heterogeneous dynamics of economic complexity.
a) A finer coarse graining of the dynamics highlights two regimes for the dynamics of the evolution of countries in the fitness-income plane. There exists a laminar region in which fitness is the driving force of the growth and the only relevant economic variable in order to characterize the dynamics of countries. We argue that the evolution of countries in this region is highly predictable. There is also a second regime, which appears to be chaotic and characterized by a low level of predictability. In the laminar regime we also find two different kinds of evolution patterns for the emergent countries and developed ones respectively. In this heterogenous scenario for the economic dynamics of countries, regressions are no more the appropriate tool to develop a predictive scheme, which instead must face issues which are very close to the problems of predictability for dynamical systems (i.e. atmosphere, climate, wind, ocean dynamics, and weather forecast, etc). b) we report a continuous interpolation of the coarse grained dynamics to better illustrate the two regimes of predictability,
Fig 3.
The selective predictability scheme.
The scheme is based on the method of analogues [26, 27] which is a strategy to predict the future from the knowledge of the past. We track the evolution of the countries in a given box and we record where these countries have evolved in the following 10 years. By carrying out systematically this procedure for each box, we build the empirical distribution of the 10-years evolution of countries. We report the empirical 10-years distributions (ED) for two boxes: the former from the chaotic-like regime and the latter from the laminar-like one, as defined in Fig. 2. A visual inspection reveals that the EDs from the chaotic-like regime tend to have a larger dispersion than the ones from the laminar one, which are instead very concentrated in few boxes. To quantify this effect we introduce a measure of concentration for the EDs: , where
and N(i) are respectively the number of occupied boxes by the ED associated to the box i and the number of points giving rise to ED. This measure, see S1 Information for further considerations, confirms the existence of two regimes characterized by two very different levels of predictability: a laminar regime (green boxes) for which the flow is regular and tends to be concentrated in few boxes and a chaotic regime characterized by very dispersed distributions of the country evolution. We argue that in the first regime the fitness is the key ingredient to develop a forecasting scheme for the evolution of the economic systems.
Fig 4.
Back testing of the 5-years Selective Predictability Scheme.
a), we train the EDs on the time interval 1995–2005. We test the rate of success of the forecast of the position of a country in 2010, according to the ED associated to the departure box of the country in 2005. We compute how many times we are able to guess correctly the box in which the country will be after 5 years. Although the very limited statistics of this back testing procedure, the results confirm the fact that, not only the forecasted area in which we expect to find the country is smaller in the laminar regime, as demonstrated by Fig. 3, but even the dynamics appears to be more predictable because of a general higher rate of success of the selective predictability scheme in the laminar region. b), we report the histogram for the relative error of the forecast of 2010’s GDP per capita. Differently from the fitness histogram (not reported), the distribution is not peaked around 0. We believe this systematic under evaluation of growth is due to a training set shorter than the typical length of an economic cycle.