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.
Highlights
In the last decade a new approach to macroeconomics has been developed to better understand the growth of countries [1,2]
It is worth noting that the values of fitness Fc and quality Q p = Pp−1 of the original map defined by Equations (1) and (2) cannot be obtained in this new metric when the parameter δ tends to zero
We might think that the normalization procedure necessary in the old metric in order to fix the arbitrary constant would get rid of the common factor δ−1 and deliver the same values of the new metric
Summary
In the last decade a new approach to macroeconomics has been developed to better understand the growth of countries [1,2]. The mathematical properties of the algorithm involved in the evaluation of the metrics, as well as the economic meaning of the metrics and possible applications, have been discussed in previous papers [3,4,5]. These two new metrics have been successfully used to develop state-of-the-art forecasting approaches for economic growth [6,7,8]
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