Complexity of Products: The Effect of Data Regularisation.

Orazio Angelini,Tiziana Di Matteo

doi:10.3390/e20110814

Abstract

Among several developments, the field of Economic Complexity (EC) has notably seen the introduction of two new techniques. One is the Bootstrapped Selective Predictability Scheme (SPSb), which can provide quantitative forecasts of the Gross Domestic Product of countries. The other, Hidden Markov Model (HMM) regularisation, denoises the datasets typically employed in the literature. We contribute to EC along three different directions. First, we prove the convergence of the SPSb algorithm to a well-known statistical learning technique known as Nadaraya-Watson Kernel regression. The latter has significantly lower time complexity, produces deterministic results, and it is interchangeable with SPSb for the purpose of making predictions. Second, we study the effects of HMM regularization on the Product Complexity and logPRODY metrics, for which a model of time evolution has been recently proposed. We find confirmation for the original interpretation of the logPRODY model as describing the change in the global market structure of products with new insights allowing a new interpretation of the Complexity measure, for which we propose a modification. Third, we explore new effects of regularisation on the data. We find that it reduces noise, and observe for the first time that it increases nestedness in the export network adjacency matrix.

Highlights

Complexity and Fitness measures were originally proposed [1] within the field of EconomicComplexity (EC) to capture respectively the level of sophistication of a given class of products found on the international export market and the advancement of the productive system of a country.These two measures are calculated from international trade data, and they stem from the hypothesis that the difference between countries’ competitiveness comes from their respective capabilities [2,3,4].Capabilities are non-exportable features of the productive system of a country that allow it to produce a certain class of products
We prove that the SPSb prediction method converges, for a large number of iterations, to a Nadaraya-Watson kernel regression (NWKR)
We focused on the analysis of Product Complexity, which had received little attention since [20]

Summary

Introduction

Complexity and Fitness measures were originally proposed [1] within the field of EconomicComplexity (EC) to capture respectively the level of sophistication of a given class of products found on the international export market and the advancement of the productive system of a country.These two measures are calculated from international trade data, and they stem from the hypothesis that the difference between countries’ competitiveness comes from their respective capabilities [2,3,4].Capabilities are non-exportable features of the productive system of a country that allow it to produce a certain class of products. Complexity (EC) to capture respectively the level of sophistication of a given class of products found on the international export market and the advancement of the productive system of a country. These two measures are calculated from international trade data, and they stem from the hypothesis that the difference between countries’ competitiveness comes from their respective capabilities [2,3,4]. The observation that a country c exports product p contains a strong signal It implies that c is competitive enough in the production of p for export to be convenient on the Entropy 2018, 20, 814; doi:10.3390/e20110814 www.mdpi.com/journal/entropy

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Results

Conclusion