A new and stable estimation method of country economic fitness and product complexity

TL;DR

This paper introduces a new, stable, parameter-free metric for estimating country fitness and product complexity using a non-linear map, improving convergence and providing analytical insights into country-product relationships.

Contribution

It proposes a novel non-linear, non-homogeneous map for calculating fitness and complexity, with analytical solutions and a new efficiency indicator, enhancing stability and interpretability.

Findings

The new metric nearly reproduces existing results but is more stable.

Provides an approximate analytical solution for binarized matrices.

Introduces a country net-efficiency indicator for investment in capabilities.

Abstract

We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new metric is parameter free. This new map almost reproduces the results of the original homogeneous metrics already defined in literature and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm involved.